Renate Sachse

Abstract

Fast snapping in the carnivorous Venus flytrap (Dionaea muscipula) involves trap lobe bending and abrupt curvature inversion (snap-buckling), but how do these traps reopen? Here, the trap reopening mechanics in two different D. muscipula clones, producing normal-sized (N traps, max. ≈3 cm in length) and large traps (L traps, max. ≈4.5 cm in length) are investigated. Time-lapse experiments reveal that both N and L traps can reopen by smooth and continuous outward lobe bending, but only L traps can undergo smooth bending followed by a much faster snap-through of the lobes. Additionally, L traps can reopen asynchronously, with one of the lobes moving before the other. This study challenges the current consensus on trap reopening, which describes it as a slow, smooth process driven by hydraulics and cell growth and/or expansion. Based on the results gained via three-dimensional digital image correlation (3D-DIC), morphological and mechanical investigations, the differences in trap reopening are proposed to stem from a combination of size and slenderness of individual traps. This study elucidates trap reopening processes in the (in)famous Dionaea snap traps – unique shape-shifting structures of great interest for plant biomechanics, functional morphology, and applications in biomimetics, i.e., soft robotics.

Abstract

The opening and closing of pine cones is based on the hygroscopic behavior of the individual seed scales around the cone axis, which bend passively in response to changes in environmental humidity. Although prior studies suggest a bilayer architecture consisting of lower actuating (swellable) sclereid and upper restrictive (non- or lesser swellable) sclerenchymatous fiber tissue layers to be the structural basis of this behavior, the exact mechanism of how humidity changes are translated into global movement are still unclear. Here, the mechanical and hydraulic properties of each structural component of the scale are investigated to get a holistic picture of their functional interplay. Measurements of the wetting behavior, water uptake, and mechanical measurements are used to analyze the influence of hydration on the different tissues of the cone scales. Furthermore, their dimensional changes during actuation are measured by comparative micro-computed tomography (µ-CT) investigations of dry and wet scales, which are corroborated and extended by 3D-digital image correlation-based displacement and strain analyses, biomechanical testing of actuation force, and finite element simulations. Altogether, a model allowing a detailed mechanistic understanding of pine cone actuation is developed, which is a prime concept generator for the development of biomimetic hygromorphic systems.

Abstract

(1) Significance of geometry for bio-inspired hygroscopically actuated bilayer structures is well studied and can be used to fine-tune curvatures in many existent material systems. We developed a material design space to find new material combinations that takes into account unequal effective widths of the layers, as commonly used in fused filament fabrication, and deflections under self-weight. (2) For this purpose, we adapted Timoshenko’s model for the curvature of bilayer strips and used an established hygromorphic 4D-printed bilayer system to validate its ability to predict curvatures in various experiments. (3) The combination of curvature evaluation with simple, linear beam deflection calculations leads to an analytical solution space to study influences of Young’s moduli, swelling strains and densities on deflection under self-weight and curvature under hygroscopic swelling. It shows that the choice of the ratio of Young’s moduli can be crucial for achieving a solution that is stable against production errors. (4) Under the assumption of linear material behavior, the presented development of a material design space allows selection or design of a suited material combination for application-specific, bio-inspired bilayer systems with unequal layer widths.

Abstract

Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi‐static motions of structures between two prescribed geometrical configurations that are optimal with regard to a specified quality function while taking large deformations into account. It is based on a variational formulation and the solution by two finite element discretizations, the spatial discretization (the standard finite element mesh) and an additional discretization of the deformation path or trajectory. For the investigations, an exemplary objective function, the minimization of the internal energy, integrated along the deformation path, is used. The method for motion design presented herein uses the Newton‐Raphson method as a second‐order optimization algorithm and allows for analytical sensitivity analysis. The proposed method is verified and its properties are investigated by benchmark examples including rigid body motions, instability phenomena and determination of inextensible deformations of shells.

Abstract

The design of adaptive structures is one method to improve sustainability of buildings. Adaptive structures are able to adapt to different loading and environmental conditions or to changing requirements by either small or large shape changes. In the latter case, also the mechanics and properties of the deformation process play a role for the structure’s energy efficiency. The method of variational motion design, previously developed in the group of the authors, allows to identify deformation paths between two given geometrical configurations that are optimal with respect to a defined quality function. In a preliminary, academic setting this method assumes that every single degree of freedom is accessible to arbitrary external actuation forces that realize the optimized motion. These (nodal) forces can be recovered a posteriori. The present contribution deals with an extension of the method of motion design by the constraint that the motion is to be realized by a predefined set of actuation forces. These can be either external forces or prescribed length chances of discrete, internal actuator elements. As an additional constraint, static stability of each intermediate configuration during the motion is taken into account. It can be accomplished by enforcing a positive determinant of the stiffness matrix.

Abstract

The mechanical principles for fast snapping in the iconic Venus flytrap are not yet fully understood. In this study, we obtained time-resolved strain distributions via three-dimensional digital image correlation (DIC) for the outer and inner trap-lobe surfaces throughout the closing motion. In combination with finite element models, the various possible contributions of the trap tissue layers were investigated with respect to the trap’s movement behavior and the amount of strain required for snapping. Supported by in vivo experiments, we show that full trap turgescence is a mechanical–physiological prerequisite for successful (fast and geometrically correct) snapping, driven by differential tissue changes (swelling, shrinking, or no contribution). These are probably the result of the previous accumulation of internal hydrostatic pressure (prestress), which is released after trap triggering. Our research leads to an in-depth mechanical understanding of a complex plant movement incorporating various actuation principles.

Abstract

Smart and adaptive outer façade shading systems are of high interest in modern architecture. For long lasting and reliable systems, the abandonment of hinges which often fail due to mechanical wear during repetitive use is of particular importance. Drawing inspiration from the hinge-less motion of the underwater snap-trap of the carnivorous waterwheel plant (Aldrovanda vesiculosa), the compliant façade shading device Flectofold was developed. Based on computational simulations of the biological role-model’s elastic and reversible motion, the actuation principle of the plant can be identified. The enclosed geometric motion principle is abstracted into a simplified curved-line folding geometry with distinct flexible hinge-zones. The kinematic behaviour is translated into a quantitative kinetic model, using finite element simulation which allows the detailed analyses of the influence of geometric parameters such as curved-fold line radius and various pneumatically driven actuation principles on the motion behaviour, stress concentrations within the hinge-zones, and actuation forces. The information regarding geometric relations and material gradients gained from those computational models are then used to develop novel material combinations for glass fibre reinforced plastics which enabled the fabrication of physical prototypes of the compliant façade shading device Flectofold.

Abstract

The fast motion of the snap-traps of the terrestrial Venus flytrap (Dionaea muscipula) have been intensively studied, in contrast to the tenfold faster underwater snap-traps of its phylogenetic sister, the waterwheel plant (Aldrovanda vesiculosa). Based on biomechanical and functional–morphological analyses and on a reverse biomimetic approach via mechanical modelling and computer simulations, we identify a combination of hydraulic turgor change and the release of prestress stored in the trap as essential for actuation. Our study is the first to identify and analyse in detail the motion principle of Aldrovanda, which not only leads to a deepened understanding of fast plant movements in general, but also contributes to the question of how snap-traps may have evolved and also allows for the development of novel biomimetic compliant mechanisms.

Abstract

Two novel hierarchic finite element formulations for geometrically nonlinear shell analysis including the effects of transverse shear are presented. Both methods combine a fully nonlinear Kirchhoff-Love shell model with hierarchically added linearized transverse shear components. Thus, large rotations can be taken into account while circumventing the peculiar task of finding a corresponding parametrization of the rotation tensor. The two formulations differ in the way the transverse shear effects are included, either using hierarchic rotations or hierarchic displacements. The underlying assertion is that in most practical applications the transverse shear angles are small even for large deformations. This is confirmed by various numerical experiments. The hierarchic construction results in an additive strain decomposition into parts resulting from membrane and bending deformation and additional contributions from transverse shear. It requires at least C1-continuous shape functions, which can be easily established within the isogeometric context using spline based finite elements. As reported earlier, this concept is intrinsically free from transverse shear locking. In the nonlinear case it dramatically facilitates representation of large rotations in shell analysis.

Abstract

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.

Abstract

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.

Abstract

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.

Abstract

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.

Abstract

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.

Abstract

Plant movements can inspire deployable systems for architectural purposes which can be regarded as ideal solutions combining resilient bio-inspired functionality with elegant natural motion. Here, we first give a concise overview of various compliant mechanisms existing in technics and in plants. Then we describe two case studies from our current joint research project among biologists, architects, construction engineers and materials scientists where the aesthetic movements of such role models from the plant kingdom are analysed, abstracted and implemented in bioinspired technical structures for sustainable architecture. Both examples are based on fast snapping movements of traps of carnivorous plants. The Waterwheel plant (Aldrovanda vesiculosa) captures prey underwater and the Venus flytrap (Dionaea muscipula) snaps in the air. We present results on the motion principles gained by quantitative biomechanical and functional-morphological analyses as well as their simulation and abstraction by using e.g. Finite Element Methods. The Aldrovanda mechanism was successfully translated into a similarly aesthetic and functional technical structure, named Flectofold, which exists in a prototype state. The Flectofold can be used as a façade shading element for complex curved surfaces as existing in modern architecture.

Abstract

In this thesis, a novel approach to support the design of motions for adaptive structures is presented and gradually developed: the so-called method of motion design. It is based on the observation that, depending on the control of the actuation, the same deformation state of a structure can be reached through various motion processes. The method of motion design allows to calculate optimal deformation paths with defined properties between the initial geometry and a given deformed end geometry of a structure in a formalized way. In order to motivate the efficiency of a movement and to make it mathematically quantifiable, the so-called cost of deformation is introduced as an exemplary target value based on the strain energy. By integration over the deformation path, the motion process is considered in its entirety in this optimization problem. The method of motion design is developed based on a variational formulation using the cost of deformation as underlying functional and the displacement field as the unknown function. One of the decisive features in this work is the discretization of the motion path, i.e., the deformation process. Due to the special structure of the functional with the integration of the strain energy, analytical sensitivities can be calculated by using quantities that are generally available in finite element software. The presented basic method is particularly well suited for the identification and design of kinematic and energy-minimal motion mechanisms, which emphasizes the potential for application to deployable shape changing structures. The motion design method is extended by the use of constraints such that the actuation can be prescribed, e.g., by actuator elements, or the entire motion can be stabilized. Finally, possibilities for enhancement of the motion design method and combinations with other methods to increase the efficiency of adaptive structures are investigated. They include a combination with shape optimization of the initial geometry, an integration within an actuator placement algorithm and variations of the underlying objective function.