Aufsätze in Konferenzbänden

Zusammenfassung

Seit ihrer Etablierung als theoretische Querschnittsdisziplin ist die Statik ein steter Treiber methodischer Innovation und digitaler Transformation. Ihr Gegenstand hat sich dabei vom Berechnen auf das Modellieren verschoben. Die Statik der Zukunft erschließt als kreative Disziplin bisher nicht gekannte Freiheiten und öffnet die engere Welt des Bauwesens für neue, interdisziplinäre Möglichkeiten. Anhand von vier Hypothesen zum Wesen der Statik wirft dieser Beitrag einen persönlichen Blick der Autoren auf Möglichkeiten und Herausforderungen in Forschung, Lehre und Praxis, die sich für deren Zukunft ergeben.

Zusammenfassung

Structural engineers often want to have a redundant structure where the loss of a member would not lead to structural collapse. For a truss, adding a bar beyond that required for static determinacy renders the structure redundant, but what is the spatial distribution of the static indeterminacy within the individual elements of a framework? Can an additional bar be redundant with several existing bars? Are there truss topologies and geometries that enhance redundancy? The assessment of structures based on such load-independent quantitative measures can be useful in early design stages to achieve an integrative planning process for designers and engineers. The degree of static indeterminacy and in particular its spatial distribution, quantified with the redundancy matrix can be used for assessing structural integrity of a framework. Focusing on structural properties independent of the individual member stiffness, such as geometry and topology, graph theory offers yet another tool to assess structural performance. This paper explores the integration of the Maxwell-Calladine count with the redundancy matrix from theoretical structural mechanics and with contributions of graph theory to explore a deeper understanding of structural redundancy.

Zusammenfassung

Zur Analyse von Tragwerken ist es in frühen Entwurfsphasen häufig ausreichend, Schnitt- und Verschiebungsgrößen, sowie Spannungen im Rahmen der linearen Elastizitätstheorie zu bestimmen. Eine weitere fundamentale Eigenschaft von Tragwerken ist der Grad der statischen Unbestimmtheit und deren Verteilung innerhalb des Tragwerks. Die Redundanzmatrix liefert diese Information und stellt damit ein lastfallunabhängiges Maß zur Beurteilung von Tragwerken hinsichtlich Robustheit, Assemblierbarkeit und Adaptierbarkeit zur Verfügung.

Zusammenfassung

Mit strukturmechanischer Einsicht und der Formulierung von Aktuierungszielen lassen sich Grundsätze für den Entwurf guter adaptiver Tragwerke sowie deren Auslegung ableiten. Dabei kann zwischen einer Adaption zur Reduktion der Verformungen und einer Adaption zur Manipulation der Kräfte im Tragwerk unterschieden werden. Durch den Einsatz von Aktoren zur Kraftmanipulation ist es möglich, die maximale Querschnittsausnutzung in der Struktur bei verschiedenen Belastungen zu reduzieren. Der jeweils optimale Aktuierungszustand ist derjenige, der die maximale Ausnutzung im Tragwerk minimiert. Mithilfe baustatischer Überlegungen kann diese Optimierungsaufgabe durch ein lineares Optimierungsproblem beschrieben und das globale Minimum mit dem Simplex-Algorithmus gefunden werden.

Zusammenfassung

Hierarchische Balken-, Platten- und Schalenformulierungen basieren auf einer geschickten Reparametrisierung der kinematischen Gleichungen, die sich für neuartige, glatte Diskretisierungsverfahren als vorteilhaft erweist. Im vorliegenden Beitrag werden die intrinsischen Eigenschaften des hierarchischen Konzepts anhand statischer und dynamischer Analysen von Flächentragwerken aufgezeigt und diskutiert.

Zusammenfassung

Adaptive structures are equipped with hydraulic actuators for compensating external loads and damping vibrations, enabling lightweight construction and an extended operational lifetime. In the context of structural health monitoring, these actuators also provide the means for active diagnostic approaches, which can improve the diagnostic performance over conventional passive methods. This paper investigates a model-based active diagnosis method for structural faults resulting in a local loss of stiffness. Parametric uncertainties, which are often substantial in civil engineering and pose a major challenge in model-based structural health monitoring, are handled in a probabilistic framework. An upper bound on the probability of a diagnostic error is used as objective of the input optimization, with an alternative objective additionally taking the actuation energy into account. In a simulation study, the proposed method achieves notable improvements in the diagnosis performance and reduces either the required time by up to 75% or the actuation energy by up to 60%.

Zusammenfassung

The mixed displacement (MD) method was initially developed to mitigate geometrical locking effects in beams, plates, and shells with the intention of having intrinsically locking-free characteristics while using equal-order interpolation for all degrees of freedom. In other words, it is an unlocking scheme that works independent of the element shape, polynomial order, and discretization scheme. It includes additional degrees of freedom that adhere to a carefully designed differential relation that can be interpreted as a kinematic law, incorporated in a mixed sense. Certain constraints are to be enforced on these additional degrees of freedom to obtain a well-posed system of equations. In this work, the MD method is extended for problems in solid mechanics. We present the underlying variational formulation, followed by its application to 2D solid elements. Additionally, we showcase an idea to enforce the additional constraints in a general sense. Various numerical examples, within the framework of the finite element method and isogeometric analysis, are outlined to demonstrate the performance of the MD method in the geometrically linear and geometrically nonlinear cases.

Zusammenfassung

In structural optimization processes, a common goal is to limit deflectionsor stresses through topological changes, shape adaption or cross-sectional adjust-ments. Beyond these well-established performance indicators, alternative measuresfor the assessment of structures based on the redundancy matrix can be used in thedesign and optimization process. This contribution shows the extension of the redun-dancy calculation to three-dimensional beam structures in detail. Using the conceptof redundancy for the design of structures, one goal is to homogeneously distributeredundancy within a structure in order to make an overall collapse due to failure ofindividual elements less likely. Furthermore, the sensitivity towards imperfections isquantified by the redundancy matrix, offering the opportunity to design connectionsof substructures, such that no constraint forces are introduced during the assemblyprocess. Those two concepts are showcased exemplarily within this contribution. Themethod is embedded into a computational co-design framework, which allows forquick, interactive feedback on design changes to strengthen the interplay between thedesign and engineering process.

Zusammenfassung

Actuators can be used to control the dynamic behavior of vibrating structures. The placement of the actuators in the system has a significant impact on how well adaptive structures perform. The actuator placement for damping particular modes can be assessed using the fraction of modal strain energy. Recent research in structural engineering has demonstrated that the redundancy concept is a useful tool for assessing actuator placement for quasi-static structural behavior because it provides information about the distribution of the degree of statical indeterminacy in the structure. In order to combine fundamental measures from control theory and structural engineering, the similarities between the frequency response function and the redundancy matrix are pointed out. It is shown that, by using the redundancy concept and the fraction of modal strain energy as assessment criteria for actuator placement, adaptive structures can be optimally designed to withstand both static and dynamic loadings.

Zusammenfassung

Structural failure in civil engineering can have catastrophic consequences such as property damage, economic losses and even loss of life. Therefore, early detection and identification are crucial. In addition to that, new technologies like adaptive structures demand for high safety as a prerequisite to gain acceptance. This contributio investigates the feasibility of using the redundancy matrix as a tool for detecting and identifying structural failure in adaptive structures via residual generation. Results provide prerequisites for detectability and suggest methodologies for the detection of structural failure by means of the redundancy matrix.

Zusammenfassung

Sheet metal forming simulations are crucial in various industries, such as automotive, aerospace, and construction. These simulations are commonly carried out using Reissner-Mindlin shell elements, which involve certain simplifying assumptions about zero normal stress in shell normal direction and cross-sectional fibers remaining straight during deformation 1. Because of this, the material model needs to be modified and no three-dimensional material model can be used. However, in critical forming situations such as bending with small radii relative to the sheet thickness, these assumptions do not hold, resulting in inaccurate simulation results. To address this issue, a higher-order 3D-shell element that incorporates a full three-dimensional constitutive model and that can account for cross-sectional warping and higher-order strain distributions has been developed 2. First findings on the benefits of using higher-order 3D-shell elements for accurately modeling sheet metal forming processes were presented in 3. The objective of this study is to expand upon this work by assessing the accuracy of simulations utilizing the higher-order 3D-shell element for critical sheet metal forming processes. Results of simulations with the higher-order 3D-shell elements are compared to experimental data and results obtained from simulations with solid elements and Reissner-Mindlin shell elements. It is demonstrated that simulations with higher-order 3D-shell elements provide more accurate predictions in sheet metal forming processes than the standard modeling approach, including but not limited to stress. Furthermore, we aim to support the efficient utilization of the higher-order 3D-shell element by identifying situations in which the additional deformation modes of this element are beneficial, and in which application of a standard shell element suffices. To achieve this, we analyze the influence of its higher-order deformation modes on the strain for parameter alterations in benchmark problems. To aid the modeling decision, mesh studies are conducted to quantify the influence of the element size on the results quality. Lastly, a comparison of numerical efficiency of different element formulations is given, showing the high efficiency of higher-order 3D-shell elements compared to solid elements. This contribution is part one of a two-part series that aims to present recent improvements of sheet metal forming simulations through a combination of higher-order 3D-shell elements and anisotropic 3D yield models. Part I focuses on the assessment of higher-order 3D-shell elements, while Part II investigates the effect of anisotropic 3D yield models with respect to the in-plane and out-of-plane behavior on sheet metal forming simulations. Together, these contributions aim to provide a comprehensive overview of the latest advances obtained in a joint research project at the Fraunhofer IWM in Freiburg and the Institute for Structural Mechanics at the University of Stuttgart.

Zusammenfassung

Floor and ceiling slabs are commonly used in construction and therefore provide a great potential to save material. In this paper, an adaptive ribbed ceiling is presented. The focus is on the design of the active prestressing. In addition, different design strategies of adaptive structures are compared with respect to their mass saving potential and the necessary actuation effort.

Zusammenfassung

For most sheet metal forming simulations, shell elements that consider a reduced stress state, in particular, assuming a zero transverse normal stress sigma_33 and neglecting the shear stress components sigma_13 and sigma_23 in the yield function, are used. Moreover, certain kinematic assumptions, like cross-sectional material fibers being assumed to remain straight during deformation, are typically applied. However, for some applications, like bending with small radii and thick sheets, this approach is not a workable solution to obtain accurate and reliable results, since the prerequisites that justify the aforementioned kinematic assumptions are not met anymore. In this contribution, a 3d-shell element is presented that allows for cross-sectional warping. For the evaluation, numerical results of a metal stripe drawn through a draw bead are compared against experimental data. The results demonstrate that the 3d-shell element is able to represent warping of cross-sectional material fibers during deformation. In addition, further numerical tests conducted with this element are shown.

Zusammenfassung

Taking advantage of adaptivity in the field of civil engineering is an ongoing research topic. Integration of adaptive elements in the load-bearing structure is already well established in many other engineering fields. First investigations promise large material saving potentials also in the field of civil engineering, especially when it comes to high-rise buildings or wide spanned structures like roofs or bridges. In times of emission problems and shortage of materials, the potentials of adaptive civil structures open various new possibilities. In the design and optimization process of adaptive civil structures, we address the differences between classical approaches for passive systems and new practices considering adaptivity. By using a suitable actuator placement, it is possible to manipulate the displacements of the structure as well as the force distribution within the structure. Both material and energy savings can be accomplished with an integrated design of the adaptive structure taking into account the actuation, suitable combination of structural design and actuator placement. For demonstration of the differences in the design process and in the resulting optimized structure, we use a small case study on a truss structure, which is inspired by a high-rise building, and consider static loads.

Zusammenfassung

Die Antwort einer Struktur auf Aktuierung wird maßgeblich vom Grad der statischen Unbestimmtheit und deren Verteilung in der Struktur beeinflusst. Die Redundanzmatrix enthält diese Informationen über das Tragwerk. Aus ihr können daher Rückschlüsse für die Aktorplatzierung und für die Bewertung der Aktuierbarkeit von Strukturen gezogen werden. Die Untersuchung eines Beispieltragwerks veranschaulicht einerseits die Einsatzmöglichkeiten der Redundanzmatrix und andererseits das Masseneinsparungspotential, das mithilfe des Einsatzes aktiver Elemente in passiven Strukturen erschlossen werden kann.

Zusammenfassung

Curved folding, a method to create curved 3D structures from a flat sheet, can be used to produce material and manufacturing efficient, static or dynamic structures. However, the complex assembly and folding sequence of curved crease patterns is the bottleneck in their fabrication process. This paper presents Self-shaping Curved Folding: a material programming approach to create curved crease origami structures that self-assemble from flat into 3D folded state upon exposure to external stimuli. We propose a digital fabrication process via the 3D-printing of shape-changing materials, accompanied by a computational design workflow in which the geometry of a crease pattern is correlated with the printing toolpaths and the layup of stimuli-responsive and passive materials to achieve a target shape-change. We demonstrate our method by producing multiple prototypes and documenting their shape-change upon actuation. Lastly, we explore the functional and performance benefits of self-shaping curved folding under three application scenarios relevant to the field of industrial design and architecture.

Zusammenfassung

In this contribution, a novel local, node-based time step estimate for reciprocal mass matrices with improved sharpness is proposed. Reciprocal mass matrices are sparse matrices used in explicit dynamics that allow computation of the nodal acceleration from the total force vector. They aim for higher critical time steps or/and accuracy than the lumped mass matrix approximation. Since the eigenvalue inequality by Fried does not hold for reciprocal mass matrices, element-based estimates may be not conservative and are consequently inadequate. Therefore, nodal time step estimates are preferred for reciprocal mass matrices. A nodal time step estimate requires an eigenvalue bound using row or/and column information associated with the nodal degrees of freedom. Recently, an efficient estimate was proposed that uses Gershgorin’s circle theorem and a corresponding bound. This estimate is always conservative but it usually leaves a 10-30% gap to the true eigenvalue. This raises the question whether a sharper estimate may be constructed by using a different eigenvalue bound. A recent paper by Cottereau and Sevilla compares five eigenvalue bounds for a diagonal mass matrix with spectral finite elements and indicates that the Ostrowski’s bound is the sharpest bound for most of the considered cases. In this contribution, the latter estimate is further developed for the case of reciprocal mass matrices and an extra improvement via similarity transformation for elements with rotary degrees of freedom is discussed. Finally, the estimate is tested for a set of common finite elements in explicit dynamics.

Zusammenfassung

Beyond the shell model of Reissner and Mindlin, which is available in LS-DYNA® for example in shell ELFORM=2/16, there have been many developments in the field of 3d-shell models in recent years. 3d-shell models can be beneficial in sheet metal forming simulations because they allow for three-dimensional stress states. 3d-shell elements are available in LS-DYNA®, e.g. ELFORM=25. In the doctoral dissertation of Fleischer it has been found that under certain conditions this element formulation suffers from an artificial stiffening effect. Although this finding dates back to 2009, this phenomenon has remained unexplained so far. In this contribution, the authors explain the reason for this stiffening effect and show a possibility to remove it. Moreover, an outlook on the development of higher order shell models for sheet metal forming simulation is given.

Zusammenfassung

In this contribution, coupled, parameterized second order systems are considered where the coupled, parameterized system is derived from the assembly of several parameterized component models. Two approaches for the Parametric Model Order Reduction of such coupled systems are presented and compared in a reduced order shape optimization example. In the first approach, the coupled, parameterized system is derived by coupling the parameterized, full order component models. Then, Parametric Model Order Reduction is executed for the coupled system. In the second approach, the parameterized, component models are first reduced independently of their actual mounting situation. Afterwards, the parameterized, reduced order component models are coupled to derive the parameterized, reduced order system model. It is shown that the first approach yields smaller parameterized, reduced order system models. However, the second approach allows to reuse and to recombine the parameterized, reduced order component models arbitrarily. It therefore introduces more flexibility in the modeling process, enabling for example a toolbox based optimization with parameterized, reduced order models.

Zusammenfassung

In this contribution a class of formulations for beams, plates and shells is presented, which intrinsically avoids locking, independent of the utilized discretization scheme. The key idea is the reparametrization of the kinematic equations to avoid locking on theory level – prior to discretization. Thus, the resulting formulations are locking‐free for any equal‐order interpolation. As demonstrator, we present both mixed and primal concepts for Timoshenko beams in both weak and strong form, as well as their theoretical relationships. Besides a weak form Galerkin‐type solution using B‐Splines, we show the generality of the presented concepts by employing isogeometric collocation based on the corresponding Euler‐Lagrange equations of the boundary value problem. The quality of both stress resultants and displacements is investigated. Although the underlying concept addresses beams, plates and shells, the present contribution illustrates the methodology for the Timoshenko beam.

Zusammenfassung

Within the collaborative research center Biological Design and Integrative Structures (CRC TRR 141), a research team of biologists, architects and engineers from Freiburg, Tübingen and Stuttgart is working on the development of biomimetic and bioinspired structures for implementation in architecture and building construction. One of the projects in this research center deals with the kinematics of planar, curved and corrugated plant surfaces as concept generators for deployable systems in architecture. It is an example for methods of engineering science at the interface between biology and architecture. The contribution will provide an insight into the process of analyzing the waterwheel plant Aldrovanda vesiculosa, a carnivorous plant that catches its prey by a quick closing movement of a snap trap consisting of two lobes attached to a midrib. At a first glance, the mechanism resembles the one of the famous Venus flytrap; however, it appears to be quite different from a mechanical point of view. In fact, a key aspect in the research presented here is the development of mechanical models and performing corresponding finite element analyses of the plant with the aim to obtain a better understanding of the compliant mechanism of Aldrovanda vesiculosa and its actuation. The latter is related to a change in turgor pressure in a so-called motor zone, adjacent to the midrib, possibly combined with prestressing effects. Apart from this scientific contribution to technical biology or reverse biomimetics, the abstraction of the trapping movement and its implementation in a façade element (Flectofold) as an example of biomimetic architectural design are briefly described.

Zusammenfassung

This paper presents results of the investigation of two biological role models, the shield bug (Graphosoma italicum) and the carnivorous Waterwheel plant (Aldrovanda vesiculosa). The aim was to identify biological construction and movement principles as inspiration for technical, deployable systems. The subsequent processes of abstraction and simulation of the movement and the design principles are summarized, followed by results on the mechanical investigations on various combinations of fibers and matrices with regard to taking advantage of the anisotropy of fiber-reinforced plastics (FRPs). With the results gained, it was possible to implement defined flexible bending zones in stiff composite components using one composite material, and thereby to mimic the biological role models. First small-scale demonstrators for adaptive façade shading systems – Flectofold and Flexagon – are proving the functionality.

Zusammenfassung

Part I deals with material modelling of woven fabric membranes. Due to their structure of crossed yarns embedded in coating, woven fabric membranes are characterised by a highly nonlinear stress-strain behaviour. In order to determine an accurate structural response of membrane structures, a suitable description of the material behaviour is required. A linear elastic orthotropic model approach, which is current practice, only allows a relative coarse approximation of the material behaviour. The present work focuses on two different material approaches: A first approach becomes evident by focusing on the meso-scale. The inhomogeneous, however periodic structure of woven fabrics motivates for microstructural modelling. An established microstructural model is considered and enhanced with regard to the coating stiffness. Secondly, an anisotropic hyperelastic material model for woven fabric membranes is considered. By performing inverse processes of parameter identification, fits of the two different material models w.r.t. measured data from a common biaxial test are shown. The results of the inversely parametrised material models are compared and discussed.

Zusammenfassung

The higher inter-element continuity of the Isogeometric Analysis (IGA) applying NURBS functions for geometry as well as mechanics opens up new possibilities in the analysis of thin-walled structures, i.e. beams, plates and shells. An important advantage is the straightforward implementation of classical theories, which require C1-continuity, e. g. Kirchhoff-Love shell formulations. Based on these "simplest" models shear deformable theories, introducing Timoshenko and Reissner-Mindlin kinematics, are formulated in a hierarchic manner. In contrast to using total rotations the present formulations introduce incremental transverse shear rotations as primary variables. This reparametrization of the kinematic equations can be established in several different fashions, which is addressed in this contribution. All parametrizations have in common, that they lead to shear deformable beam, plate and shell formulations being intrinsically free from transverse shear locking. This is a remarkable feature since the spectrum of different smooth discretization schemes in IGA and other fields of computational shell analysis is continuously growing and the proposed hierarchic shell formulations are locking-free, independent of the underlying discretization.

Zusammenfassung

The higher inter-element continuity of the Isogeometric Analysis (IGA) applying NURBS functions for geometry as well as mechanics opens up new possibilities in the analysis of thin-walled structures, i.e. beams, plates and shells. The contribution addresses the straightforward implementation of classical theories requiring C1-continuity, such as the Euler-Bernoulli beam and Kirchhoff-Love shell theory. Based on these “simplest” models shear deformable theories, introducing Timoshenko and Reissner-Mindlin kinematics, are formulated in a hierarchic manner. In contrast to the usual Finite Element concept using total rotations the present model picks up traditional formulations introducing incremental rotations as primary variables. Furthermore an alternative version is discussed with a split of the displacements into bending and transverse shear parts. Both hierarchic concepts can be easily extended to 3D–shell models. The key aspect of this alternative parameterization is the complete a-priori removal of the transverse shear locking and curvature thickness locking (in the case of 3D-shells).

Zusammenfassung

Um dynamische Finite-Elemente-Berechnungen mit expliziter Zeitintegration zu beschleunigen, ist es in der Praxis üblich, Massenskalierung anzuwenden. Damit soll die kritische Zeitschrittweite erhöht werden ohne maßgeblich an Genauigkeit in den entscheidenden niederfrequenten Moden zu verlieren. Bei der konventionellen Massenskalierung (CMS) wird künstliche Masse zu den Diagonaltermen der diagonalisierten Massenmatrix addiert und die Diagonalform der Massenmatrix bleibt erhalten. CMS wird gewöhnlich auf eine geringe Anzahl kleiner oder steifer Elemente angewandt, deren hohe Eigenfrequenzen die kritische Zeitschrittweite begrenzen. Dabei wird allerdings die Trägheit der Struktur erhöht, was zu unphysikalischen Effekten führen kann. Mit einer sogenannten selektiven Massenskalierung kann wenigstens die translatorische Trägheit (d.h. der Impuls bei gleichmäßiger Anfangsgeschwindigkeit) erhalten werden, allerdings auf Kosten von Nebendiagonaltermen in der Massenmatrix. Diese Methode lässt sich gleichmäßig auf die gesamte Struktur anwenden und hat geringere unphysikalische Nebeneffekte. Bislang werden skalierte Massenmatrizen rein algebraisch, z.B. steifigkeitsproportional konstruiert. Die Auswahl an Skalierungs-Templates ist beschränkt und ihnen liegt keine konsistente Formulierung zugrunde. In diesem Artikel werden variationelle Methoden zur selektiven Massenskalierung vorgestellt, die nicht nur mathematisch konsistent sind, sondern es auch erlauben, gezielt bestimmte Eigenschaften wie die Erhaltung der Trägheit, Reduktion der höchsten Frequenzen und Genauigkeit bei den niedrigen Frequenzen einzustellen. Die Leistungsfähigkeit der Methode wird an numerischen Beispielen mit Tetraeder- und Hexaeder-Elementen demonstriert.

Zusammenfassung

For practical application in engineering numerical simulations are required to be reliable and reproducible. Unfortunately crash simulations are highly complex and nonlinear and small changes in the initial state can produce big changes in the results. This is caused partially by physical instabilities and partially by numerical instabilities. Aim of the project is to identify the numerical sensitivities in crash simulations and suggest methods to reduce the scatter of the results.

Zusammenfassung

The present study discusses optimization strategies for maximizing the structural ductility of Fiber Reinforced Concrete (FRC) with long textile fibers. Due to material brittleness of both concrete and fibers in addition to complex interfacial behavior between above constituents the structural response of FRC is highly nonlinear. This material nonlinearity including the interface response has to be taken into account for an optimal fiber layout in the structural domain. In the present contribution three kinds of optimization strategies based on a damage formulation are described. The performance of the proposed method is demonstrated by a series of numerical examples; it is verified that the ductility can be substantially improved.

Zusammenfassung

In this paper a two-dimensional discrete element method with rigid, polygonal particles is used to model material failure of granular as well as quasi-brittle materials. Different models for soft contact as well as cohesion between the particles are presented. The capabilities of the method are demonstrated simulating simplistic granular model materials as well as complex concrete specimens with an artificial microstructure.

Zusammenfassung

A Lagrange multipliers formulation for dynamical frictionless thermo-elastic contact problem is considered. Thermal deformations and dependency of contact thermal resistance on contact pressure are assumed to be the only two coupling effects. Application of standard Newmark method to the problem may lead to spurious numerical oscillations of contact pressures and heat fluxes, inaccurate or divergent solutions. A modification of the Newmark method is proposed where contact contributions are integrated non-monolithically with backward Euler. Elimination of spurious numerical oscillations is shown in a numerical example.

Zusammenfassung

The present study addresses an optimization strategy for maximizing the structural ductility of Fiber Reinforced Concrete (FRC) with long textile fibers. Due to material brittleness of both concrete and fiber in addition to complex interfacial behavior between above constituents the structural response of FRC is highly nonlinear. Consideration of this material nonlinearity including interface is mandatory to deal with this kind of composite. In the present contribution three kinds of optimization strategies based on a damage formulation are described. The performance of the proposed method is demonstrated by a series of numerical examples; it is verified that the ductility can be substantially improved.

Zusammenfassung

The study addresses the material layout optimization for heterogeneous materials considering non-linear response. In particular two different materials are investigated, namely cellular materials like polymer or metal foams and Fiber Reinforced Composites. The contribution describes all necessary methodical details, such as non-linear material formulations, optimisation building blocks like optimality criteria and sensitivity analyses in the context of non-linear formulations and related algorithmic aspects. Several numerical examples underline the basic concept 1, 2, 3.

Zusammenfassung

The coupling of thin, light-weight structures to incompressible flows is a particular challenge within the broad field of computational fluid-structure interaction. The problem is governed by the sensitive and highly non-linear dynamics of slender structures such as shells and membranes in conjunction with the omnipotent incompressibility condition. The contribution presents a partitioned fluid-structure interaction algorithm based on a second order accurate structural solver employing solid shell elements and an Arbitrary Lagrangean Eulerian flow formulation. Stabilized finite elements are used on the fluid domain. Selected aspects of the individual constituents and their interaction are discussed; among them is the problem of conditioning for the shell model, the flow solver satisfying the geometric conservation law and the reliability of the fluid formulation in case of small time steps and distorted mesh. In view of the incompressibility condition the coupling of the two partitions is in particular addressed. It is well-known that sequential coupling approaches, often used for their computational efficiency, may fail in certain situations when the incompressible flow interacts with an extremely slender low mass structure. It could be shown by a rigorous analysis that this is due to the so-called artificial added mass effect. This is an inherent instability of such schemes that unfortunately cannot be removed by reducing the time steps size. As a remedy a strongly coupled partitioning algorithm is applied iteratively adjusting the interface conditions; here different dynamically adapted relaxation methods can be utilized to accelerate the convergence of the iteration. The use of a fully converged coarse grid solution of the coupled problem as a predictor to the iteration scheme can significantly accelerate its convergence and increase the efficiency of the whole coupling scheme. A selection of two- and three-dimensional numerical examples demonstrates the capabilities of the formulation.

Zusammenfassung

In many areas of mechanical engineering contact problems of thin-walled structures play a crucial role. Car crash tests and incremental sheet metal forming can be named as examples. But also in civil engineering, for instance when determining the moment-rotation characteristics of a bolted beam-column joint, contact occurs. Effective simulation of these and other contact problems, especially in three-dimensional non-linear implicit structural mechanic is still a challenging task. Modelling of those problems needs a robust method, which takes the thin-walled character and dynamic effects into account. We use a segment-to-segment approach for discretization of the contact and introduce Lagrange Multipliers, which physically represent the contact pressure. The geometric impenetrability condition is formulated in a weak, integral sense. Choosing dual shape functions for the interpolation of the Lagrange Multipliers, we obtain decoupled nodal constraint conditions. Combining this with an active set strategy, an elimination of the Lagrange multipliers is easily possible, so that the size of the resulting system of equations remains constant. Discretization in time is done with the implicit Generalized--$\alpha$ Method and the Generalized Energy-Momentum Method. Using the ”Velocity-Update” Method, the total energy is conserved for frictionless contact. Various examples show the performance of the presented strategies.

Zusammenfassung

This paper addresses the algorithmic and implementation issues associated with fluid structure interaction simulations, specially on vector architecture. Firstly, the fluid structure coupling algorithm is presented and then a newly developed parallel sparse linear solver is introduced and its performance discussed.

Zusammenfassung

Numerical simulation of large scale computational fluid dynamics (CFD) and fluid-structure interaction (FSI) problems is still today a very challenging task. The correct modeling of fluid flow, governed by the instationary incompressible Navier-Stokes equations, and the nonlinear structural behavior are challenges of their own. In addition coupling of both physical fields introduces further requirements on stability and efficiency of the involved algorithms. For this class of problems computing time is still a limiting factor for size and complexity of the problem. Especially for FSI simulations the necessary iterative coupling schemes dramatically increase the required computing time. Here, the use of advanced coupling strategies, reducing either the time needed for one iteration or the number of iterations, can considerably speed up the simulation. We will introduce a class of coupling schemes enhanced by a coarse grid solution to reduce calculation time and accelerate convergence. In addition, the single fields – especially the fluid – demand high efficiency of the solution algorithm. Here, assembly of the element matrices and in particular the iterative solver for the global system of linear equations are the most time consuming parts of the computational process. Very often these algorithms only use a small fraction of the available computer power in scientific codes. Therefore it is highly advisable to take a closer look at the efficiency of algorithms and improve them to make the best out of the available computer power. We will present approaches to significantly increase efficiency in the assembly and solution part of a finite element code. Here, the special features of vector super computers will be exploited.

Zusammenfassung

A numerical approach to simulate the coupled problem of slender structures and incompressible Newtonian flows is described. The formulation is based on a partitioned scheme while finite elements are employed on the single fields. The structural field is discretized in space by finite elements based on a seven-parameter shell formulation capable of dealing with the complex dynamics of very slender structures. An efficient solver for the structural system of equations exploiting an algebraic multigrid approach has been developed. A stabilized fluid element following an ALE formulation of the incompressible Navier-Stokes equations is used to model the flow on a time dependent domain. The geometric conservation law is built in into the formulation to obtain a stable scheme which is second order accurate in time. The accuracy and reliability of the approach with respect to critical parameters such as very small time steps, distorted meshes or steep gradients in particular within the flow field has been analyzed. The approach is able to also deal with free fluid surfaces. The inherent instability of weakly coupled approaches is analyzed which reveals the devastating influence of the so-called `artificial added mass' effect. The convergence of the strongly coupled approach depends on an appropriately chosen relaxation parameter. Ways to automatically adjust the proper amount of relaxation are given. Special emphasis is also put on the efficient implementation particularly of the fluid problem. Vectorization is employed to significantly speed up the time spent for calculating element matrices on vector machines.

Zusammenfassung

The artificial added mass effct inherent in sequentially staggered coupling schemes is investigated by means of a fluid-structure interaction problem. A discrete representation of a simpliflied added mass operator in terms of the participating coefficient matrices is given and `instability conditions' are evaluated for different temporal discretisation schemes. With respect to the time discretisation two different cases are distinguished. Discretisation schemes with stationary characteristics might allow for stable computations when good natured problems are considered. Such schemes yield a constant instability limit. Temporal discretisation schemes which exhibit recursive characteristics however yield an instability condition which is increasingly restrictive with every further step. Such schemes will therefore definitively fail in long time simulations irrespective of the problem parameters. It is also shown that for any sequentially staggered scheme and given spatial discretisation of a problem, a mass ratio between fluid and structural mass density exists at which the coupled system becomes unstable. Numerical observations confirm the theoretical results.

Zusammenfassung

The efficient modeling of 3D contact problems is still a challenge in non-linear implicit structural analysis. Most of the existing contact algorithms use penalty methods to satisfy the contact constraints, which necessitates a user defined penalty parameter. As it is well known, the choice of this additional parameter is somehow arbitrary, problem dependent and influences the accuracy of the analysis. We use a primal-dual active set strategy, based on dual Lagrange multipliers to handle the nonlinearity of the contact conditions. This allows us to enforce the contact constraints in a weak, integral sense without any additional parameter. Due to the biorthogonality condition of the basis functions, the Lagrange multipliers can be locally eliminated. We perform a static condensation to get a reduced system for the displacements. The Lagrange multipliers, representing the contact pressure, can be easily recovered from the displacements in a variationally consistent way. For our application to thin-walled structures we adapt a three-dimensional non-linear shell formulation, including the thickness stretch of the shell to contact problems. A reparametrization of the geometric description of the shell body gives us a surface oriented shell element, which allows to apply the contact conditions directly to nodes lying on the contact surface. The discretization in time is done with the implicit Generalized Energy-Momentum Method. To conserve the total energy within our contact framework, we follow an approach from Laursen and Love who introduce a discrete contact velocity to update the velocity field in a post processing step. Various examples show the good performance of the primal-dual active set strategy applied to the implicit dynamic analysis of thin-walled structures.

Zusammenfassung

The efficient modeling and analysis of 3D contact problems is still a difficult aspect in non-linear implicit structural dynamics. Most of the existing contact algorithms use some kind of penalty method to enforce the contact constraints. This procedure necessitates a user defined penalty parameter, the choice or which is somehow arbitrary, problem dependent and might influence the accuracy of the analysis. We use a primal-dual active set strategy, based on dual Lagrange multipliers to handle the non-linearity of the contact conditions. This allows us to enforce the contact constraints in a weak, integral sense without introducing any additional parameter. Due to the biorthogonality condition of the basis functions, the Lagrange multipliers, which represent the contact pressure, can be locally eliminated. A static condensation will lead to a reduced system of equations for the unknown displacements. The Lagrange multipliers can be easily recovered from the displacements in a variationally consistent way. It is well known, that the combination of a contact algorithm with a numerical time integration scheme will not yield an energy conserving procedure, unless some additional discrete constraints are satisfied. The most popular way to design an energy conserving contact algorithm is to enforce the so called algorithmic persistency condition. Various strategies to fulfill this additional constraint lead to a compromise of violating the geometric admissibility. In this work we will pick up an idea by Laursen and Love, who introduce a discrete contact velocity to update the velocity field in a post processing step. This procedure leads to an energy conserving scheme while still satisfying the geometric contact constraints. Using the Generalized Energy-Momentum Method for the time discretization, we generalize the velocity update method accordingly. For our application to thin-walled structures we adapt a 7-parameter non-linear shell formulation for the application of contact problems. A reparametrization of the geometric description of the shell body will lead to a surface oriented shell element. Various examples will be presented to show the performance of the proposed algorithms.

Zusammenfassung

The efficient modeling and analysis of 3D contact problems is still a chalenge in non-linear implicit structural dynamics. Many of the existing contact algorithms use some kind of penalty method to enforce the contact constraints, which necessitates a user defined parameter. Its choice is somehow arbitrary, problem dependent and might influence the accuracy of the analysis. In this work, a primal-dual active set strategy, based on dual Lagrange multipliers is used to handle the non-linearity of the contact conditions. This allows to enforce the contact constraints in a weak, integral sense without introducing any additional parameter. Due to the biorthogonality condition of the basis functions, the Lagrange multipliers, representing the contact pressure, can be locally eliminated. A static condensation leads to a reduced system of equations for the unknown displacements. The Lagrange multipliers, representing the contact pressure, can be easily recovered from the displacements in a variationally consistent way. For the spatial discretization of thin-walled structures, a 7-parameter non-linear shell formulation is adapted for the application of contact problems. A reparametrization of the geometric description of the shell body results in a surface oriented finite shell element, which allows to apply the contact conditions directly to nodes lying on the contact surface. The time discretization is done whith the Generalized Energy-Momentum Method. Generalizing an idea by Laursen and Love, who introduce a discrete contact velocity to update the velocity field in a post processing step, according to the contact algorithm will lead to an energy conserving scheme while still satisfying the geometric contact constraints. Various examples will illustrate the good performance of the propsed strategy applied to the implicit dynamic analysis of thin-walled structures.

Zusammenfassung

The efficient modeling and analysis of 3D contact problems is still a chalenge in non-linear implicit structural dynamics. Many of the existing contact algorithms use some kind of penalty method to enforce the contact constraints, which necessitates a user defined parameter. Its choice is somehow arbitrary, problem dependent and might influence the accuracy of the analysis. In this work, a primal-dual active set strategy, based on dual Lagrange multipliers is used to handle the non-linearity of the contact conditions. This allows to enforce the contact constraints in a weak, integral sense without introducing any additional parameter. Due to the biorthogonality condition of the basis functions, the Lagrange multipliers, representing the contact pressure, can be locally eliminated. A static condensation leads to a reduced system of equations for the unknown displacements. It is well known, that the combination of a contact algorithm with a numerical time integration scheme will not yield an energy conserving procedure, unless some additional discrete constraints are satisfied. The most popular way to design an energy conserving contact algorithm is to enforce the so-called algorithmic persistency condition. Various strategies to fulfill this additional constraint lead to a compromise of violating the geometric admissibility. Following an idea by Laursen and Love, who introduce a discrete contact velocity to update the velocity field in a post processing step, will lead to an energy conserving scheme while still satisfying the geometric contact constraints. Using the Generalized Energy-Momentum Method for the time discretization, the velocity update method is generalized accordingly. For the analysis of thin-walled structures a 7-parameter non-linear shell formulation is adapted for the application of contact problems.

Zusammenfassung

The present study addresses the preliminary steps for the optimization of fiber reinforced cementitious composites (FRC) with respect to brittle failure behavior of a single component. FRC is one of the advanced materials that consist of a concrete matrix and glass, carbon, or aramid fibers. This kind of reinforcement is corrosion free and highly durable when used in concrete, which makes it possible to produce very thin structural concrete elements. It is well known that the properties of such composites depend on the layout of the material at the microscopic level (e.g. fiber size, fiber coating, impregnation, and surface roughness among other material characteristics). The investigation of the sensitivity of the structural response of the composite material with respect to the microscopic material parameters is part of this work. To improve the structural behavior of FRC, the significant parameters of the material models for the interface and the fibers are introduced as design parameters and adjusted by a controlling optimization process. Two different objectives are investigated: strength and ductility of FRC. To perform the structural analysis, an isotropic gradient–enhanced damage model for concrete as well as fibers is used. Numerically integrated interface elements are applied for modeling the debonding between the fibers and the matrix. To obtain a reliable composite by applying structural optimization, the nonlinear failure behavior of matrix material, fiber, and interface models are considered within the optimization process 3. Gradient–based optimization algorithms are used to adjust these parameters to improve both strength and ductility of such composite structures.

Zusammenfassung

In this paper we address various efficiency aspects of finite element (FE) simulations on vector computers. Especially for the numerical simulation of large scale Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems efficiency and robustness of the algorithms are two key requirements. In the first part of this paper a straightforward concept is described to increase the performance of the integration of finite elements in arbitrary, unstructured meshes by allowing for vectorization. In addition the effect of different programming languages and different array management techniques on the performance will be investigated. Besides the element calculation, the solution of the linear system of equations takes a considerable part of computation time. Using the jagged diagonal format (JAD) for the sparse matrix, the average vector length can be increased. Block oriented computation schemes lead to considerably less indirect addressing and at the same time packaging more instructions. Thus, the overall performance of the iterative solver can be improved. The last part discusses the input and output facility of parallel scientific software. Next to efficiency the crucial requirements for the IO subsystem in a parallel setting are scalability, flexibility and long term reliability.

Zusammenfassung

For the numerical simulation of large scale CFD and fluid-structure interaction (FSI) problems efficiency and robustness of the algorithms are two key requirements. In this paper we would like to describe a very simple concept to increase significantly the performance of the element calculation of an arbitrary unstructured finite element mesh on vector computers. By grouping computationally similar elements together the length of the innermost loops and the vector length can be controlled. In addition the effect of different programming languages and different array management techniques will be investigated. A numerical CFD simulation will show the improvement in the overall time-to-solution on vector computers as well as on other architectures. Especially for FSI simulations also the robustness of the algorithm is very important. For the transient interaction of incompressible viscous flows and nonlinear flexible structures commonly used sequential staggered coupling schemes exhibit weak instabilities. As best remedy to this problem subiterations should be invoked to guarantee kinematic and dynamic continuity across the fluid-structure interface. To ensure the efficiency of these iterative substructuring schemes two robust and problem-independent acceleration methods are proposed.

Zusammenfassung

For the dynamic behavior of lightweight structures like thin shells and membranes exposed to fluid flow the interaction between the two fields is often essential. Computational fluid-structure interaction provides a tool to predict this interaction and complement or eventually replace expensive wind tunnel experiments. Partitioned analyses techniques enjoy great popularity for the numerical simulation of these interactions. This is due to their computational superiority over simultaneous, i.e. fully coupled monolithic approaches, as they allow the independent use of suitable discretization methods and modular analysis software.We use, for the fluid, GLS stabilized finite elements on a moving domain based on the incompressible instationary Navier-Stokes equations, where the formulation guarantees geometric conservation on the deforming domain. The structure is discretized by nonlinear, three-dimensional shell elements. Commonly used sequential staggered coupling schemes may exhibit instabilities due to the so-called artificial added mass effect. As best remedy to this problem subiterations should be invoked to guarantee kinematic and dynamic continuity across the fluid-structure interface. Since iterative coupling algorithms are computationally very costly, their convergence rate is very decisive for their usability. To ensure and accelerate the convergence of this iteration the updates of the interface position are relaxed. The time dependent, ’optimal’ relaxation parameter is determined automatically without any user-input via exploiting a gradient method or applying an Aitken iteration scheme.

Zusammenfassung

This paper presents a two-scale approach for the mechanical and numerical modeling of composites like textile Fiber Reinforced Concrete (FRC) and Fiber Reinforced Polymers (FRP) characterized by long range material failure. The objective of the present study is to develop an efficient solution method exploiting the physically existing multiscale character of the problem. The proposed method belongs to the superposition based methods with local enrichment of the large scale solution u by a small scale part u0. The question of appropriate locality constraints for u0 will be investigated. The second central point is the handling of highly localized failure zones or cracks (strong discontinuities) within the composite on the small scale level. Besides usual continuum material models like the gradient enhanced damage formulation the eXtended Finite Element Method (X-FEM) coupled to the level set method is used to model the material behavior of composites on the small scale.

Zusammenfassung

This contribution focusses on computational approaches for fluid structure interaction problems from several perspectives. Common driving force is the desire to handle even the large deformation case in a robust, efficient and straightforward way. In order to meet these requirements main subjects are on the one hand necessary improvements on coupling issues as well as on Arbitrary Lagrangian Eulerian (ALE) approaches. On the other hand we discuss pros and cons of available fixed grid approaches and start the development of new such approaches. Some numerical examples are provided along the paper.

Zusammenfassung

The present work deals with the comparison of three-dimensional (3d) finite element analysis of thin-walled structures to computations based on reduced, two-dimensional (2d) models which a priori satisfy the plane stress assumption. We apply a plasticity-based non-linear softening material model for concrete1 to simple four-node 2d plane stress elements and to a 7-parameter 3d shell formulation. Numerical results are compared to experimental data for an L-shaped panel.

Zusammenfassung

This paper addresses the mechanical and numerical modeling of materials with microstructure in the nonlinear range. One intended application is the simluation of fiber reinforced concrete (cement), a material which allows to design very thin structures. The properties of this composite depend on the one hand on the material layout, e.g. the properties of its components, the fiber length, content, coating and orientation (length scale µm) and on the other hand on the structural layout, e.g. ply thickness (length scale cm). This gives an idea of the physically intrinsic scales appearing: A ”microscale”, the scale of material heterogeneity and a ”macroscale” related to the structural dimensions. The post critical behaviour of such a composite is driven by the accumulation of the failure mechanisms on the microscale. This can be fiber or matrix cracking, debonding between the fibers in a filament, or between fiber and matrix. Those failure mechanisms, taking place on the microscale, are incorporated in the macroscopic formulation using the variational multiscale method (VMM), introduced under this name by Hughes et al. 9. A central point of the presented scheme for an efficient solution of the discrete problem is the locality assumption for the small scale part of the solution, leading to decoupled problems on the micro scale. One focus of the presentation is the description of the material behaviour of composites on the microscale whereby two potential and well-known approaches will be presented. For applications with smeared failure of the matrix material we use an isotropic gradient enhanced damage model. In addition, the numerical model comprises conventional interface elements which account for interfacial failure between the particular material components. The second approach constitutes the utilization of the extended finite-element method (X-FEM) 13 to model discrete failure of the matrix material as well as of the particular interfaces.

Zusammenfassung

For the numerical simulation of large scale CFD and fluid-structure interaction (FSI) problems efficiency and robustness of the algorithms are two key requirements. In this paper we would like to describe a very simple concept to increase significantly the performance of the element calculation of an arbitrary unstructured finite element mesh on vector computers. By grouping computationally similar elements together the length of the innermost loops and the vector length can be controlled. In addition the effect of different programming languages and different array management techniques will be investigated. A numerical CFD simulation will show the improvement in the overall time-to-solution on vector computers as well as on other architectures.

Zusammenfassung

A robust computational approach for transient dynamic impact processes will be presented. Main focus will be on an adaptive remeshing strategy and constitutive models for metals and geomaterials under impact loading. Practical relevant numerical examples will complete this contribution.

Zusammenfassung

Different discrete element models (DEM) for the simulation of cohesive geomaterials like concrete, ceramics or marl will be presented. Starting from a basic polygonal two-dimensional DEM model for non-cohesive granular materials, more complex models for cohesive materials are obtained by inclusion of beam or interface elements between corresponding particles. The last step in the series of increasing complexity is the realization of a microstructure-based simulation environment which utilizes the enhanced DEM models. A type of artificial microstructure can be included, if different properties of the cohesive components (beam or interface) are assigned with respect to their position, i.e. inside the matrix, inside the aggregate and between aggregate and matrix. With growing model complexity a wide variety of failure features of geomaterials can be represented. Furthermore, the inclusion of an artificial microstructure which regards for stiffer aggregates embedded in a less stiffer matrix enables a coherent quantification of the model. A validation of these discrete models with regard to qualitative and quantitative aspects enriches the plan of the paper. Thereby, extracts of the extensive simulation program are reported bit by bit in the context of each section in order to clarify the respective subject matter. The paper is organized as follows: The second section provides a brief outline of the theoretical background of a standard (non-cohesive) form of the DEM model supplemented by a discussion on the modeling of cohesion within particle models. Afterwards, in the third section, the extension to an interface enhanced DEM model along with some representative simulation results is sketched. The fourth section presents the formulation of a microstructure-based DEM environment which utilizes the interface enhanced model according to the third section. Again, simulation results are used to validate the proposed method. A summary in the fifth section concludes with the attained insights and an outlook on future perspectives.

Zusammenfassung

Different discrete element models (DEM) for the simulation of problems in the context of damage mechanics will be presented. The target materials to be simulated are cohesive and non-cohesive geomaterials like concrete- or sand-type materials. Starting from a basic polygonal two-dimensional DEM model for non-cohesive granular materials, more complex models for cohesive materials are obtained by inclusion of beam or interface elements between corresponding particles. The last step in the series of increasing complexity is the realization of a microstructure-based simulation environment which utilizes the enhanced DEM models. With growing model complexity a wide variety of failure features of geomaterials can be represented. Furthermore, adequate homogenization approaches are derived which supplement the definition of the discrete models. These homogenization approaches allow us to relate microscopic quantities, like contact forces or displacements, to corresponding macroscopic quantities, like stresses or strains. Representative numerical examples are used to validate the proposed DEM models along with the homogenization.

Zusammenfassung

In the present contribution three different model classes for the numerical simulation of geomaterials will be presented. These classes are related to different material scales and are discussed in the first part of the paper. At first, macroscopic models in the context of invariant-based damage and plasticity theories are introduced. Then, a microplane model applying a volumetric-deviatoric split will be discussed. This model describes the material behavior at the material point by formulating constitutive laws on different planes followed by a homogenization process. The last model class discussed concerns a discrete particle model consisting of convex polygons that are able to withstand a limited cohesion. This includes a contact description for the particles as well as a bond formulation between the particles. The related forces are inserted into the equations of motion which are solved numerically based on the discrete element methodology. Macroscopic continuum models are typically involved in the large scale computation of engineering structures; microplane models are used to efficiently model anisotropic material behavior in a natural way. Despite their extreme numerical costs discrete models like particle models become more and more mature for large scale computations. In the second part, interrelations between the models are investigated in terms of homogenization procedures that bridge effects from a lower to a higher scale. In a first approach the constitutive equations of the particle and the microplane model are inspected and reveal remarkable similarities. Afterwards, a homogenization procedure for the particle model is introduced defining representative particle assemblies that allow the determination of average quantities like stresses and strains on a higher scale. Finally, it will be shown how the present version of the microplane formulation enables the interpretation and identification of the microplane constitutive laws in terms of well-known macroscopic constitutive laws. The interrelations between the model classes are illustrated by several numerical examples.

Zusammenfassung

Dry powder, as a special case of extremely fine grade granular materials, is a collection of discrete solid grains up to 0.2 mm in size. As the space between the particles is filled with air, the density of the bulk solid is always less than the density of the discrete solid components. The shape of the particles and the formation of the packing are further properties characterizing powder-like materials. Their complex behavior is of high interest for civil, chemical, mechanical and materials engineers. Since many varying applications and processes exist in these different fields, the requirements for appropriate models are also manifold. The consolidation of a loose packing to a dense and compact mold or the comminution of brittle material under high pressure into pulverized media are only two examples. A meaningful kinematic and constitutive model is therefore crucial for every transient dynamic analysis. In this paper, a continuum model for the simulation of dry powder under quasi-static as well as dynamic loading will be presented. It is implemented in the context of multiplicative hyperelastic-based finite strain elasto-plasticity in a Lagrangean framework. In the description of the algorithm, it is focussed on a robust return mapping scheme which is formulated in principal stresses. A nonsmooth multisurface plasticity with tension cutoff, Drucker-Prager failure envelope and strain hardening cap provides the reproduction of the relevant phenomena: tensile failure, material flow under shearing and compaction under pressure. Corresponding material parameters are determined by geotechnical experiments like uniaxial and triaxial compression tests. The results of quasi-static and impact loading simulations are compared with experimental results. Computational issues related to the challenges of continuum treatment of powder-like materials will be addressed.

Zusammenfassung

In this paper, a continuum model for the simulation of dry powder under quasi-static as well as dynamic loading will be presented. It is implemented in the context of multiplicative hyperelastic-based finite strain elasto-plasticity in a Lagrangean framework. A nonsmooth multisurface plasticity with tension cutoff, Drucker-Prager failure envelope and strain hardening cap provides the reproduction of the relevant phenomena: tensile failure, material flow under shearing and compaction under pressure. Corresponding material parameters are determined by geotechnical experiments like uniaxial and triaxial compression tests. The results of quasi-static simulations are compared with experimental results.

Zusammenfassung

An appropriate treatment of instationary free surface flows is of great relevance to many problems in engineering and applied sciences. In this context the presence of structural interactions constitute an additional challenge on the one hand but on the other hand even further broadens the application area. In this study we present a partitioned implicit approach for the efficient and robust treatment of free surface flows within fluid structure interaction simulations.

Zusammenfassung

This paper describes a three-level finite element method for solving the instationary incompressible Navier-Stokes equations. Separating large resolved scales, small resolved scales and unresolved scales enables us to deal with each of these scale groups differently. Whereas the computation of the large scales is performed using a standard Galerkin method the small scales are resolved by approximate residual-free bubbles exploiting an elementwise submesh with respect to the original discretization. The unresolved scales are merely regarded in their dissipative effect onto the small scales. A dynamic modeling process for this making use of an elementwise sub-submesh slightly finer than the submesh is incorporated as level 3 of the method. Currently, applications of this method to the numerical simulation of turbulent flows are underway.

Zusammenfassung

The present work is concerned with the numerical simulation of nonlinear behaviour in advanced composite material structures using the Finite Element method. Thereby special attention is payed to nonlinear material behaviour and shell structures. Often Fibre Reinforced Polymers are utilised within shell-like and layered structures because of their superior stiffness to weight ratio and the possibility to design material and structural behaviour, respectively. Unfortunately the use of a layered laminate may introduce the important failure mode of delamination. In this study phenomenological material models known from literature are presented, which are capable of describing the overall structural response including local effects like delaminations. Based on the work of Hashagen, 1998 an anisotropic plasticity model combined with anisotropic hardening, which is capable to describe the overall nonlinear structural response, is first presented. In order to study the effect of the anisotropic hardening plasticity model structural examples are compared and assessed. Secondly the frequently observed and very dangerous type of failure delamination is considered in particular. For this the delamination process is described within a thin layer of finite thickness in the framework of three-dimensional finite shell-elements with layerwise Reissner-Mindlin kinematics Braun et al., 1994. The Hashin Hashin, 1980 delamination criterion is utilized in the framework of a softening plasticity formulation based on Sprenger, 2000. The softening behaviour is assumed to be linear with transition to an exponential function at high equivalent plastic strains. The approach is assessed through a comparison of experimental and numerical results of a DCB test. An elaboration on the overall approach can be found in Hörmann, 2002.

Zusammenfassung

Geomaterials belong to the most widely used materials in engineering. Materials like concrete, marl, cement or sand are typical examples. The failure modes of these materials range from brittle to ductile behavior and usually involve anisotropic biases through an overall stiffness degradation. This degradation results for example from a coalescence of microcracks or a typical failure mode localization. In the present contribution three different model classes for the numerical simulation of geomaterials will be presented. These classes are related to different material scales and are discussed in the first part of the paper. At first, macroscopic models in the context of invariant-based damage and plasticity theories are introduced. Then, a microplane model applying a volumetric-deviatoric split will be discussed. This model describes the material behavior at the material point by formulating constitutive laws on different planes followed by a homogenization process. The last model class discussed concerns a discrete particle model consisting of convex polygons that are able to withstand a limited cohesion. This includes a contact description for the particles as well as a bond formulation between the particles. The related forces are inserted into the equations of motion which are solved numerically based on the discrete element methodology. Macroscopic continuum models are typically involved in the large scale computation of engineering structures; microplane models are used to efficiently model anisotropic material behavior in a natural way. Despite their extreme numerical costs discrete models like particle models become more and more mature for large scale computations. In the second part, interrelations between the models are investigated in terms of homogenization procedures that bridge effects from a lower to a higher scale. In a first approach the constitutive equations of the particle and the microplane model are inspected and reveal remarkable similarities. Afterwards, a homogenization procedure for the particle model is introduced defining representative particle assemblies that allow the determination of average quantities like stresses and strains on a higher scale. Finally, it will be shown how the present version of the microplane formulation enables the interpretation and identification of the microplane constitutive laws in terms of well-known macroscopic constitutive laws. The interrelations between the model classes are illustrated by several numerical examples.

Zusammenfassung

This paper discusses partitioned analysis approaches for the transient interaction of incompressible viscous flows and nonlinear flexible structures with large deformations. It is shown that for this kind of coupled systems the commonly used sequential staggered coupling schemes exhibit weak instabilities and may eventually fail, mainly due to inconsistencies in the coupling boundary conditions. As best remedy to this problem subiterations should be invoked which ensure kinematic and dynamic continuity across the fluid-structure interface, thus ensuring stable and accurate numerical solutions even for long-time simulations. For the desirable acceleration of convergence of such iterative substructuring schemes two robust and problem-independent methods are proposed and their efficiency is demonstrated with selected numerical examples.

Zusammenfassung

Classical continuum mechanics formulations applying e.g. standard finite elements can consider only a small number of discontinuities and cannot encompass the entire fracturing process. However more enhanced continuum models, for example based on the gradient or the Cosserat theory, may provide the possibility to account for a granular microstructure in a straight forward way. On the other hand, the mechanical behaviour of granular materials can be well described on a smaller scale via discrete element models (DEM) if the motion of the individual grains is taken into account. The time evolution of such a model is followed solving the Newtonian equations of motion of the individual elements numerically. Our concern in this paper is the relation between the microscopic quantities, like the contact forces and displacements, and corresponding macroscopic quantities, like stresses and strains via corresponding homogenization techniques. In this contribution we will propose a new technique and validate it by two-dimensional DEM simulations with polygonal particles. The evaluation of different boundary value problems proves the efficiency of the homogenization technique. In this context the dynamical, kinematical and energetical quantities of a representary elementary volumes are determined. A non-symmetric macroscopic stress tensor, as well as the existence of couple stresses are obtained.

Zusammenfassung

In this work we present a Three-Level FEM for the numerical simulation of the incompressible Navier- Stokes equations. Based on the variational multiscale method and the residual-free bubble concept we pursued the technique of a Two-Level FEM in our previous work. Level 1 is therein attributed to the solution of the large-scale equation by a standard finite element space. On level 2 we seek an approximation of the elementwise residual-free bubbles with the help of a stabilized finite element method restricted to individual elements. This represents our small-scale solution. The Two-Level FEM aimed at the simulation of laminar flows. Now we want to turn our focus on the numerical simulation of turbulent flows by way of a large eddy simulation and in this work our first respective steps are described. With regard to this objective we extend our basic algorithm paying particular attention to the fulfillment of the continuity equation. Moreover, in lieu of the stabilization term we alternatively propose the inclusion of a subgrid viscosity term henceforth. This term should provide us with the required dissipative effect of the unresolved scales on the small-scale equation. The dynamic calculation of the subgrid viscosity constitutes the third level of our algorithm.

Zusammenfassung

Fiber Reinforced Polymers (FRP) are increasingly used in all kinds of engineering applications, e.g. retrofitting of structural members, structural parts of aircrafts or cars and already complete pedestrian and vehicle bridges. Due to the brittle nature of most FRP, which depends on the used materials for fibers and matrix, and in order to minimize the costs of these materials, it is of utmost interest to predict the load carrying capacities and failure modes correctly. It is widely accepted that three main failure modes of FRP exist: (i) fiber rupture, (ii) matrix micro cracking and (iii) debonding of the interface fiber/matrix. Combining several layers of equally or differently oriented FRP leads to a laminated structure eventually involving the additional and very important failure mode of delamination. In this contribution we will restrict ourselves to this failure mode, since it is predominant compared to the other ones. The delamination process between two adjacent FRP layers is geometrically described by a thin softening process zone, such that a continuum mechanics model is still applicable. Consequently the introduction of zero thickness interface elements is avoided, but the most likely delamination interface must be known in advance by means of a First Ply Failure (FPF) analysis. The present approach is prefered compared to a discrete geometrical description of the delamination since it omits remeshing of the delamination front, which has in general a complex geometry. Finite shell elements with layerwise Reissner-Mindlin kinematics are used, leading to the fact, that the number of degrees of freedom per node depends on the number of layers having its own kinematics.Three different material models are used to simulate the nonlinearity of the process zone. Firstly, the Hashin delamination criterion is utilized in the framework of a softening plasticity formulation based on the work of Sprenger and Wagner et al., respectively. The softening behaviour is assumed to be linear with transition to an exponential function at high equivalent plastic strains. Secondly, the Hashin criterion is transferred into strain space and applied in the context of an isotropic damage formulation. Linear or modified power law softening damage evolution is assumed. Thirdly, a damage formulation is derived which uses the definition of a specific damaged material tensor and leads to an energy release rate based failure criterion. All material models use the fracture energy Gc as controlling parameter for the softening regime Schellekens and de Borst.

Zusammenfassung

In the present paper, an alternative microplane formulation based on a split which is motivated from a macroscopic viewpoint will be derived. Thereby, both, elastic and inelastic material behavior is taken into account in an unique way. The constitutive formulation is embedded in a thermodynamically consistent framework for microplane models. Consequently, the material behavior at a material point is characterized by constitutive laws formulated on the individual microplanes, allowing to describe anisotropic material behavior in a very natural and simple way. Special features of the new microplane formulation will be discussed in comparison to existing microplane models presented in the literature. It will be shown that this alternative approach remedies several deficiencies of former microplane formulations. One particular advantage of the present version is that the macroscopic response is directly reflected on the mesoscale.

Zusammenfassung

The present contribution focuses on the infuence of geometrical nonlinearities on the structural behavior in the design process. The notion of the stiffest structure loses its clear definition in case of nonlinear kinematics; here we will discuss this concept on the basis of three different objectives. Apparently topology optimization is often a generator of slender struts, which tend to buckle before the structure is completely loaded. To include the instability phenomena into the design process the critical load level will be determined directly; this condition will be included as an inequality constraint. Further on in order to reduce the imperfection sensitivity a geometrically modified structure including the imperfection shape is introduced in addition. The present optimization procedures are demonstrated by examples showing rather the principle effects of the enhancements than real practical design problems.

Zusammenfassung

Ultimate load analyses and nonlinear dynamics, parallel and efficient solution approaches, adaptivity and error estimation, multi-scale analyses, structural optimization and coupled problems simulation are some of present challenges in computational mechanics. The present talk addresses peculiarities of shell structures in such an advanced computational environment. Here their dominant feature plays a central role, namely their usually large slenderness, allowing them to be optimal on the one hand but possibly leading to an extreme parameter sensitivity on the other hand. This is reflected not only in their physical behavior but also involved in their numerical models and formulations. Despite the general character the present contribution will focus on a few selected areas where these shell specific features are dominant. For example these aspects will be demonstrated in the context of structural optimization, coupled problem simulation and ultimate load analyses. The paper abandons the attempt to present and discuss details of this wide area. Rather it is intended to exemplary select a few typical characteristics and provide an introduction into the topic following the typical objective of a plenary lecture. To this aim principal shell phenomena and modeling aspects are addressed; this comes along with several remarks about nowadays computational environment and some aspects of interdependency between mechanical response and computational model. Through this introduction one should be able to internalize the underlying idea behind this topic and to be sensitized for the peculiar features of these thin-walled curved structures. For more detailed discussions of the different aspects and fields the reader is also referred to further publications of our research group that are listed under http://www.uni-stuttgart.de/ibs/

Zusammenfassung

A two-dimensional model of heterogeneous cohesive frictional solids where the material structure is idealized by a discrete granular particle assembly is presented. The discrete model is composed of convex polygons which are linked together by simple beams accounting for cohesive effects. Varying its parameters the model naturally interpolates between a continuous solid state and a discontinuous dry granular state of the material. In order to illustrate the application range of our model various numerical simulations have been carried out. The emphasis lies on the studying of quasi-static loading scenarios of rectangular solids, like compression, tension, simple shear and recently carried out biaxial simulations. In the context of biaxial setups four different lateral pressures have been investigated and their effect on the macroscopic stress-strain response was studied as well as the evolving shear zones. A comparison with experimental observations provides a verification of the qualitative application of the model.

Zusammenfassung

From a physical point of view geomaterials, like concrete, ceramics or marl can be considered as cemented granulates forming a heterogeneous macroscopic solid. The failure mechanisms of this materials are characterized by complex failure modes under various loading situations and a highly anisotropic bias due to their inhomogeneous microstructure. The growth and coalescence of microcracks lead to the formation of macroscopic crack patterns and, finally, to a fragmentation into separate particle clusters, forming a solid--granulates mix. In this paper we present a two-dimensional model of heterogeneous cohesive frictional solids where the material structure is idealized by a discrete granular particle assembly. Our discrete model is composed of convex polygons which are linked together by simple beams accounting for cohesive effects. Varying its parameters the model naturally interpolates between a continuous solid state and a discontinuous dry granular state of the material. In order to demonstrate the wide applicability of the model simulations ranging from the quasi-static uniaxial loading and shearing of a solid to the dynamic fragmentation due to explosion, impact and collision of solids, will be presented. A comparison with experimental observations is carried out in order to verify the qualitative application of the model. To provide a geometrical description of the damage state, different characteristic quantities will be introduced and their relevance will be examined. In the context of a geometric description of the state of damage different failure identicators will be introduced and their relevance will be examined. In this context especially a defect correlation length will be introduced. This is done in order to calculate the width of an evolving localization zone as well as to determine the switch-over point where the failure within a specimen changes from a crack nucleation to a crack propagation mode. By a histogrammatic representation of the position of evolving cracks with regard to the effective shear zone (line) three different regions are observed and thus lead to a determination of the shear band width. It will generally be demonstrated that this simulation method allows us to monitor quantities which are hard to measure or are not measurable at all in experiments. Hence, this model provides a deeper understanding of the fracture and fragmentation processes well beyond the description of the final state.

Zusammenfassung

An adaptive approach, with remeshing as essential ingredient, towards robust and efficient simulation techniques for fast transient, highly non–linear processes including contact is discussed in this paper. The necessity for remeshing stems from two sources: the capability to deal with large deformations that might even require topological changes of the mesh and the desire for an error driven distribution of computational resources. The overall computational approach is sketched and two crucial aspects – the choice of suitable error indicators and the problem of surface recovery – are discussed in more detail. Numerical examples demonstrate the performance of the approach.

Zusammenfassung

The constitutive description of the mechanical behavior of granular systems is of great interest to the fields of geotechnics and various other related applications. By taking into account the discrete nature of the microstructure of a granular assembly, numerous different discrete models have been developed, Most of them are based on a finite number of discrete, semi-rigid spherical or polygon-shaped particles interacting by means of contact forces. The specification of an appropriate contact law is probably the most significant part of the discrete model. For example, the contact behavior can be formulated in a linear or nonlinear elastic fashion according to the classical Hertz model or include frictional effects along the line of Coulomb's friction law. In order to compare the results of the discrete element simulation with macroscopic measurements, different averaging techniques can be applied to derive homogenized quantities characterizing the overall behavior of the assembly. Thus, the definition of the macroscopic stress tensor has been studied intensively in the beginning of the 80s and can now be considered as well-established While discrete models take into account the individual behavior of each single particle, continuum-based approaches can only describe the material behavior in an average sense. Although, in most cases, the choice of the specific constitutive formulation is motivated by microstructural considerations, the material response is characterized exclusively in terms of stresses or strains and a set of internal variables, which represent microstructural effects in a phenomenological fashion. The microplane plasticity model is a classical representative of this class of continuum-based constitutive models. It is based on the early ideas of Mohr, who suggested to characterize the response of a material point by describing its behavior in various representative directions in space. Similar to the particle models, the choice of the constitutive assumption relating the corresponding stress and strain vector of each direction can be considered as the most important feature of the model. The overall response of the material point is obtained by integrating the resulting stress vectors over the entire solid angle. Although derived from two completely different fields, both models show significant similarities from a theoretical point of view. This contribution aims at highlighting the equivalences of the two different material formulations. Therefore, the basic ideas of the microplane model are summarized as well as a basic introduction to discrete particle modelling. Particular interest is dedicated to the fact, that the initially continuous microplane model has to be discretized for computational reasons while the initially discrete particle model must be 'continuumized' in order to relate its material parameters to macroscopic quantities. Finally, the two different approaches are compared and advantages and disadvantages of both formulations are discussed.

Zusammenfassung

Usually mechanical laws are applied for a prescribed design of a structure in order to determine its response. The external loads, boundary conditions, and also the geometry which is defined by the topology and the shape of the structure are given. However, the mechanical principles can also be used to determine the conceptual layout (topology) for a prescribed structural response. This inverse method is called ’Structural Optimization’. To obtain a reliable design, it is essential to base optimization as far as possible on realistic physical behaviour. In the present work, an elastoplastic material model with linear isotropic/kinematic hardening/ softening for small strains is used. The objective of the chosen design problem is the maximum structural ductility for a prescribed amount of mass in the design space and will be compared to results of a topology optimization analysis based on a pure elastic solution in a three–dimensional design space. Since the structural response is history–dependent, as it is in flow theory of plasticity, the sensitivities are also history–dependent. Two approaches for the calculation of sensitivities, the direct differentiation method and an efficient self–adjoint sensitivity analysis are tested with respect to their reliability. Numerical examples for the topology design of three–dimensional structures are presented.

Zusammenfassung

This paper discusses partitioned analysis approaches for the transient interaction of incompressible viscous flows and nonlinear flexible structures with large deformations. It is shown that for this kind of coupled systems the commonly used sequential staggered coupling schemes exhibit instabilities and eventually fail, mainly due to inconsistencies in the treatment of the coupling boundary conditions. As best remedy to this problem subiterations should be invoked which ensure kinematic and dynamic continuity across the fluid–structure interface, thus ensuring stable and accurate numerical solutions even for long-time simulations. For the effective convergence acceleration of such iterative substructuring schemes two robust and problem-independent methods are proposed and their efficiency is demonstrated with selected numerical examples.

Zusammenfassung

The numerical simulation of the interaction of fluids and solids not only has a wide range of applications in all different engineering disciplines and natural sciences it is still one of the present challenges in computational mechanics. This talk will first provide a short overview on different areas and approaches of Fluid–Structure Interaction (FSI). The main concern of the presentation will then be on special modeling, discretization and solution aspects of a transient and nonlinear FSI–approach for incompressible, viscous flows with thin–walled structures.

Zusammenfassung

A challenge for parallel iterative solvers in nonlinear shell analysis comes from the fact that shell analyses inherently tend to be ill conditioned problems. This challenge becomes especially pronounced when three-dimensional shell formulations - including thickness change - are used. A preconditioning idea for such models along with its advantageous influence on the performance of (parallel) iterative solvers is introduced and discussed in this paper.

Zusammenfassung

The failure mechanisms of heterogeneous geomaterials like concrete, ceramics or marl are characterized by complex failure modes under various loading situations and a highly anisotropic bias due to their inhomogeneous microstructure. The growth and coalescence of microcracks lead to the formation of macroscopic crack patterns resulting in an overall stiffness degradation and eventually in a structural failure. Behaving quasi-brittle under load, this materials are characterized by a localization of deformations in typically narrow zones. This class of materials show different physical and geometrical properties depending on the level of observation. Taking into account the point of view and the chosen scale the structural fluctuations play a more or less dominant role and thus determine the point for which a material can be regarded as homogeneous. This is accompanied by the fact, that with decreasing resolution length on a specific level the internal material structure is less identifiable up to the point when the material is considered as continuous. Basically a class of continuum models can be applied at each size scale, if the local quantities, e.g. damage, are smeared over a certain region. Emerging heterogeneities, anisotropies and discontinuities are then cast in the form of macroscopic continuum variables. From the point a localization phenomenon, like a crack, occurs due to a specific loading the material cannot be treated as continuous any longer. Due to their theoretical basis continuous simulation models cannot account for the discrete nature of material failure in a natural way. Therefore, discrete models like particle, lattice or molecular/granular dynamics models are used. Although prohibitive in large scale computations this class of models is able to predict and simulate the fracture behaviour of small scale applications of geomaterials. We will present different numerical mesolevel models within the framework of computational material mechanics allowing completely diverse insights into the material behaviour. In order to obtain an anisotropic damage evolution in a natural and conceptually simple way geomaterials are modelled as a discrete granular particle assembly composed of convex polygons that are linked together by simple beams accounting for cohesive effects. An internal length scale is incorporated intrinsically into the model by a statistically controlled particle generation process. Compression simulations with different boundary conditions are used to verify the qualitative application of the model. A transition from a continuous to a discontinuous state of the material results as a naturally output of the simulation. The continuous approach presented in the second part is based on the microplane concept allowing for directional dependent stiffness degradation at the material point level. Different concepts regarding the enhancement of the microplane formulation are outlined. Among these are versions for elasto-damage, elasto-plasticity and their combination on the one hand and a gradient enhancement on the other hand. Finally, a comparison of both, discrete and continuous models, namely the discrete element model and the continuous elastic microplane model, shows some remarkable similarties between both schemes. This allows a schematic comparison noting the corresponding inter-relations between both models.

Zusammenfassung

Thin shells are per definition optimized structures. If they are designed properly they can carry heavy loads over large spans with a minimum of construction material by activating an almost pure membrane stress state. In this context the shape of a shell plays a key role. The present paper deals with the comparison of two prominent numerical formfinding methods. The first procedure is related to the hanging model principle, traditionally used in physical experiments. Here this principle is simulated through numerical computation. As in the physical model the cutting pattern, the material used and the applied load case are important parameters. The second scheme is more general; it utilizes the structural optimization concept and allows a multitude of design criteria. In this concept the shape is described by a CAGD model and the structural analyses are supplemented by sensitivity computation and mathematical optimization. Both methods are compared for a typical free form shell over a quadrilateral plan.

Zusammenfassung

This paper discusses special aspects of a three-dimensional formulation for the modelling of shell structures. Such a formulation offers various merits compared to `classical' shell models. With respect to the realization of such a model one is on the other hand also confronted with a number of challenges. One challenge that is adressed in this paper is the ill conditioning of such three-dimensional shell models compared to `classical' models. Especially in the context of iterative solvers or in the case of explicit dynamical simulations this challenge might become in particular urgent. In this article an approach is presented and discussed that offers a remedy to this challenge. This approach is based on the use of a scaled director. It can be interpreted as a kind of `smart' preconditioning of three-dimensional shells based on an in-depth knowledge of the underlying physical model. It is able to effectively improve the condition number of the global stiffness matrix almost without additional numerical costs. The scope of it is to achieve an improved numerical behaviour of such models in nonlinear static and dynamic simulations. Details on the formulation as well as its impact on iterative solvers and explicit dynamical simulations will be given.

Zusammenfassung

This paper discusses the numerical simulation of the dynamic interaction of shells exhibiting large deformations and incompressible, viscous flows. Fluid structure interaction is herein viewed as a three–field coupled problem, consisting of the physical and/or computational fields — fluid, structure and moving mesh in the context of an Arbitrary Lagrangean Eulerian (ALE) formulation. Special focus is given to the three–dimensional shell formulation, the stabilized 3D finite element flow solver and on some coupling issues between these models. Selected numerical examples demonstrate the performance of the overall computational procedure.

Zusammenfassung

Stabilized finite element methods have been developed mainly in the context of Computational Fluid Dynamics and have shown to be able to add stability to previously unstable formulations in a consistent way. In this contribution a deformation dependent stabilization technique, conceptually based on the above mentioned developments in the CFD area, is developed for Solid Mechanics to cure the well known Enhanced Assumed Strain (EAS) method from artificial instabilities (hourglass modes) that have been observed in the range of large compressive strains. In investigating the defect of the original formulation the dominating role of the kinematic equation as cause for the instabilities is revealed. This observation serves as key ingredient for the design of the stabilizing term, introduced on the level of the variational equation. A proper design for the stabilization parameter is given based on a mechanical interpretation of the underlying defect as well as of the stabilizing action. This stabilizing action can be thought of an additional constraint, introduced into the reparametrized Hu–Washizu functional in a least square form, together with a deformation dependent stabilization parameter. Numerical examples show the capability of this approach to effectively eliminate spurious hourglass modes, which otherwise may appear in the presence of large compressive strains, while preserving the advantageous features of the EAS method, namely the reduction of the stiffness for an ‘in–plane bending’ mode, i.e. when plane stress elements are used in a bending situation.

Zusammenfassung

Two different numerical models within the framework of computational material mechanics will be presented allowing completely diverse insights into the material behaviour. In order to obtain an anisotropic damage evolution in a natural and conceptually simple way "concrete" is modelled as a discrete granular particle assembly composed by convex polygons that are linked together by simple beams accounting for cohesive effects. An internal length scale is incorporated intrinsically into the model by a statistically controlled particle generation process. The theoretical background of the model will be presented in an ample manner and its application to small samples pointing out basic features of either the elastic response of a modelled solid subjected to a fixed loading and the crack propagation up to complete failure and fragmentation will be shown. For the sake of a qualitative comparison of discrete and continuum mechanical models the theoretical background of a typical continuum-oriented formulation, namely the microplane model, is briefly outlined. This continuous approach is based on continuum damage mechanics in combination with the microplane concept, allowing for directional dependent stiffness degradation. In order to simulate nonlocal effects higher order gradients are included in the constitutive equations, thus introducing an internal length scale. This model is in its nature remarkably similar to particle models, as shown recently in a related publication of the institute. The discrete and the continuum model will be compared in a qualitative fashion by means of compressive and tensile simulations. Moreover, a comparison with experiments regarding the mesoscopic mechanisms as failure modes and the development of localization zones will be presented.

Zusammenfassung

Structural optimization based on linear material behavior and a linear kinematic relation is common practice in this�eld. In order to obtain a reliable design it is important to apply a more realistic physical behavior, i.e. to consider buckling, elastoplastic behavior and a nonlinear kinematic relation. In the present study an elastoplastic von Mises material model with linear isotropic/kinematic hardening/softening for small strains but large displacements under plane stress conditions is used. The objective of the design problem is to maximize the structural ductility for a given range of prescribed displacements. The mass is kept constant during the optimization process. The crucial point of the entire optimization procedure is to determine the derivatives with respect to the optimization variables, i.e. the sensitivity analysis. For path-dependent problems such as elastoplasticity the derivatives are also path-dependent and have to be determined after each incremental step. These sensitivities of the structural response, objective and constraints are obtained by a variational direct approach for shape as well as topology optimization problems. In order to speed up the topology optimization procedure a simpli�ed approach is applied to evaluate the sensitivity of the objective by a variational adjoint method. The optimization problems are solved by mathematical programming (MP) methods and optimality criteria (OC) methods, respectively. The numerical procedures determining the derivatives are veri�ed by test examples for 2-dim design problems under plane stress conditions.

Zusammenfassung

The development of new analysis approaches for the simulation of transient, nonlinear fluid structure interaction problems are the driving force behind this study. Fluid structure interaction is herein viewed as a three–field coupled problem, consisting of the physical and/or computational fields – fluid, structure and moving mesh. For the possibility of covering a wide range of examples and application areas, rather general models have to be used for the single fields of the coupled problem. The instationary, incompressible Navier–Stokes equations are employed herein together with a geometrically nonlinear elastodynamic model for the structure. The present computational approach is completely based on finite elements for the spatial discretization. The space time relation is adopted in a semi–discretization approach employing different direct time integration schemes. The main part of this contribution is concerned with different solution methods for coupled problems. From the computational point of view it is highly desirable to base developments of solvers for coupled problems on the philosophy of partitioned analysis. Both loose and strong partitioned coupling procedures are discussed. Algorithmic examplification is done on the one hand for fluid structure interaction problems and on the other hand for artificially partitioned problems in nonlinear structural dynamics. Numerical examples are given for both types of partitioned coupling procedures and problem types.