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Schilling, Maximilian

Maximilian Schilling

M. Sc.

Scientific Staff
Institute for Structural Mechanics

Contact

+49 711 685 69236
Email

Pfaffenwaldring 7
70569 Stuttgart
Germany
Room: 1.123

Vita

1996: Born in Pforzheim
2014: Abitur at the Reuchlin Gymnasium, Pforzheim
2014–2017: Bachelor student of Aerospace Engineering at the University of Stuttgart
2017: Bachelor thesis at Daimler AG, Sindelfingen
2017–2018: Internship at Dr. Ing. h.c. F. Porsche AG, Weissach
2018–2021: Master student of Aerospace Engineering at the University of Stuttgart
2018–2019: Working student at Daimler AG, Sindelfingen
2019: Semester abroad at the University of Virginia (UVa), USA
2020–2021: Master thesis at MTU Aero Engines AG, Munich
Since 2021: Scientific staff at the Institute for Structural Mechanics, University of Stuttgart

Research

Publications

Articles in journals

Willmann, T., Schilling, M., & Bischoff, M. (2025). Data-Based Estimation of Critical Time Steps for Explicit Time Integration. International Journal for Numerical Methods in Engineering, 126, Article 4. https://doi.org/10.1002/nme.7666
- Abstract
Abstract
Finding the critical time step for conditionally stable time integration methods has been a decades-long problem. The apparently obvious option of directly computing it from a generalized eigenvalue analysis, identifying the largest eigenfrequency of the discrete system, is usually impractical because of its numerical expense and because a stiffness matrix is often unavailable in the context of explicit analysis. There exist two popular approaches to efficiently estimate the critical time step: A characteristic element length can be estimated based on heuristic formulas. The resulting estimate, however, cannot be guaranteed to be conservative. Another approach is to reformulate and simplify the underlying eigenvalue problem on the element level and to use certain inequalities to derive an upper bound for the largest eigenvalue. This is conservative but may show poor performance by significantly under-predicting the actual critical time step. Moreover, the necessary simplifications are usually specific to the investigated element formulation. Many works that develop time step estimators demonstrate their performance only for particular element configurations, making it difficult to compare the estimators. In this paper, data-driven approaches for time step estimation for 2d-elements that address several of the aforementioned problems are proposed. First, the set of all possible quadrilateral element geometries and its discrete representation are described. A detailed comparison of nine existing time step estimators based on more than ten million element configurations is presented. Additionally, the concept of an optimal safety factor function is introduced. This concept allows us to generate the optimal and conservative version of an existing estimator and thus solves two problems at the same time: It can be used to make non-conservative estimators conservative and to improve the performance of estimators that are conservative by construction. Finally, we formulate time step estimation as a function approximation problem. It allows us to derive customizable time step estimators solely based on data. Through two examples, we demonstrate that this data-driven approach yields time step estimators that outperform state-of-the-art estimators in terms of accuracy while also being efficient to evaluate.

Articles in proceedings

Schilling, M., Usta, T., Willmann, T., von Scheven, M., & Bischoff, M. (2025). Investigating the Potential of Higher-Order 3D-Shell Finite Elements in Stress Analysis of Laminated Structures. Advances in Automotive Production Technology - Digital Product Development and Manufacturing: Stuttgart Conference on Automotive Production (SCAP2024), 20-22 November 2024. https://doi.org/10.1007/978-3-031-88831-1_1
Schilling, M., Willmann, T., Wessel, A., Butz, A., & Bischoff, M. (2023). Higher-Order 3D-Shell Elements and Anisotropic 3D Yield Functions for Improved Sheet Metal Forming Simulations: Part I. 14th European LS-DYNA Conference 2023, Baden-Baden, Germany.
- Abstract
Abstract
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.

Monographs and Collections

Wessel, A., Butz, A., Schilling, M., Willmann, T., & Bischoff, M. (2023). Verbesserte Blechumformsimulation durch 3D-Werkstoffmodelle und erweiterte Schalenformulierungen - Teil 2 (Vol. 607). Europäische Forschungsgesellschaft für Blechverarbeitung e.V., Hannover. https://www.efb.de/efb-forschungsbericht-nr-607.html
- Abstract
Abstract
Der Stand der Technik bei der Simulation von Blechumformprozessen ist die Verwendung von Schalenelementen, die auf dem Reissner-Mindlin-Modell beruhen und mit vereinfachten Materialmodellen verwendet werden. Dieser Modellierungsansatz basiert auf einigen vereinfachenden Annahmen. Für die Strukturmodellierung werden ein Ebenbleiben der Querschnittsfasern und vernachlässig-bare Normalspannungen in Blechdickenrichtung angenommen. Für die Materialmodellierung wird das richtungsabhängige Materialverhalten nur in der Blechebene abgebildet und damit werden anisotrope Effekte außerhalb der Blechebene vernachlässigt. Dieser Modellierungsansatz erreicht bei bestimmten Blechumformprozessen seine Grenzen, da einige der getroffenen Annahmen nicht mehr zutreffen. Dieses Forschungsvorhaben verfolgte die Weiterentwicklung eines alternativen Ansatzes zur Simulation von Blechumformprozessen und die Qualifizierung dieses Ansatzes für den industriellen Einsatz. Der Ansatz, der im Folgenden als „3D-Blechmodellierung" bezeichnet wird, nutzt 3D-Schalenelemente höherer Ordnung, die nicht den Einschränkungen des Reissner-Mindlin-Modells unterworfen sind, für die Simulation von Blechumformprozessen. Diese werden mit 3D-Materialmodellen verbunden, die einen vollständigen dreidimensionalen Dehnungs- und Spannungszustand berücksichtigen. Für diesen Ansatz wurden im Rahmen des Forschungsvorhabens die im Vorgängerprojekt entwickelten 3D-Schalenelemente höherer Ordnung bezüglich unterschiedlicher Aspekte verbessert. Außerdem wurde die Methode der »virtuellen Versuche« verbessert und für eine weitere Werkstoffklasse qualifiziert. Numerische Benchmarks, Vergleiche mit Versuchsergebnissen und Simulationen von Realbauteilen zeigen die erhöhte Ergebnisqualität der 3D-Blechmodellierung und die erfolgreiche Qualifizierung für den industriellen Einsatz.

Presentations

Presentations at Conferences

Maximilian Schilling, Malte von Scheven, Manfred Bischoff. Higher-Order 3D-Shell Elements in LS-DYNA – Enhancing Stress Prediction in Laminates. Ansys EMEA Transportation Summit and LS-DYNA User Conference 2025, Munich, Germany, October 28–29, 2025 [contribution].

Maximilian Schilling, Malte von Scheven, Manfred Bischoff. Enhanced Stress Prediction in Fiber-Reinforced Laminates Using Higher-Order 3D-Shell Finite Elements. 8th ECCOMAS Young Investigators Conference 2025 (YIC 2025), Pescara, Italy, September 17–19, 2025.

Maximilian Schilling, Lisa-Marie Reinken, Tobias Willmann, Manfred Bischoff. Datenbasierte Zeitschrittschätzung in der Dynamik. Baustatik-Baupraxis Forschungskolloquium 2025, Bad Boll, Germany, September 08–11, 2025 [contribution].

Tobias Willmann, Maximilian Schilling, Manfred Bischoff. Data-Based Estimation of Critical Time Steps for Explicit Time Integration. FE ohne Schnee 2025, Hirschegg, Austria, July 20 – 23, 2025.

Maximilian Schilling, Tolga Usta, Malte von Scheven, Manfred Bischoff. Investigating the potential of higher-order 3D-shell finite elements in stress analysis of laminated structures. Stuttgart Conference on Automotive Production (SCAP) 2024, Stuttgart, Germany, November 21 – 22, 2024.

Maximilian Schilling, Malte von Scheven, Manfred Bischoff. A comparative analysis of the improved stress prediction with higher-order 3D-shell finite elements for laminated structures. 17. LS-DYNA Forum, Leinfelden, Germany, October 16, 2024.

Maximilian Schilling, Tobias Willmann, Manfred Bischoff. Advancing data-integrated time step estimation to improve simulation performance. 16th World Congress on Computational Mechanics (WCCM), Vancouver, Canada, July 21 – 26, 2024.

Maximilian Schilling, Tobias Willmann, Alexander Wessel, Alexander Butz, Manfred Bischoff. Higher-Order 3D-Shell Elements and Anisotropic 3D Yield Functions for Improved Sheet Metal Forming Simulations: Part I. 14th European LS-DYNA Conference 2023, Baden-Baden, Germany, October 18–19, 2023, [contribution].

Maximilian Schilling, Tobias Willmann, Manfred Bischoff. Improving Efficiency of Higher-Order 3D-Shell Elements for 3D Sheet Metal Forming Simulations. FE ohne Schnee 2023, Hirschegg, Austria, July 30 – August 02, 2023.

Maximilian Schilling, Tobias Willmann, Manfred Bischoff. Higher Order 3D-Shell Elements in Sheet Metal Forming Simulations: A Case Study. 7th ECCOMAS Young Investigators Conference 2023 (YIC2023), Porto, Portugal, June 19–21, 2023.

Maximilian Schilling, Tobias Willmann, Alexander Wessel, Alexander Butz, Manfred Bischoff. Weiterentwicklung der verbesserten Blechumformsimulation durch 3D-Werkstoffmodelle und erweiterte Schalenformulierungen. EFB-Kolloquium Blechverarbeitung, Würzburg, Germany, May 8–9, 2023.

Maximilian Schilling, Tobias Willmann, Manfred Bischoff. 3D-Shell Elements for Improved Prediction Quality in Sheet Metal Forming Simulations. 16. LS-DYNA Forum, Bamberg, Germany, October 11–13, 2022, [book of abstracts].

Maximilian Schilling, Tobias Willmann, Manfred Bischoff. Mixed-Dimensional Coupling for Higher Order Shell Elements in Sheet Metal Forming Simulations. 9th GACM Colloquium on Computational Mechanics (GACM 2022), Essen, Germany, September 21–23, 2022.

Further Activities in the Scientific Community

External profiles

Committee Activities at the University of Stuttgart

2022–2025: Member of the Faculty Council of Faculty 2
since 2025: deputy member of the Faculty Council of Faculty 2

Organization of Conferences and Mini Symposia

2025: Mini Symposium Innovative Approaches and Open Challenges in the Simulation and Modelling of Composite Structures, ECCOMAS 8th Young Investigators Conference (YIC 2025), Pescara, Italy, September 17–19, 2025 (Main Organizer).

Teaching

Computerorientierte Methoden für Kontinua und Flächentragwerke (M.Sc.), winter terms 2021/2022, 2022/2023
Schalen (M.Sc.), summer terms 2022, 2023, 2024
Computational Methods for Shell Analysis (M.Sc.), summer term 2023
Computational Mechanics of Structures (M.Sc.), winter term 2025/2026

Supervision of Theses

Master Theses

Vamshi Pottabathini. A Rib-Based Non-Gradient Optimization Method for Gearbox Housing Design (25/01). Master Thesis. Supervision: Maximilian Schilling und Dr. Nils Brödling (Robert Bosch GmbH). Institute for Structural Mechanics, University of Stuttgart. 2025.
- Abstract
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Rahul Ambudipudi Venkata. Topology Optimization Methods for Brake Caliper Design Focusing on Caliper Opening Behavior: A Comparative Study (25/13). Master Thesis. Supervision: Maximilian Schilling und Robert Bosch GmbH. Institute for Structural Mechanics, University of Stuttgart. 2025.
- Abstract
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Vadim Gallyamov. Thermomechanical simulation of laser welding in AutoForm Assembly (24/09). Master Thesis. Supervision: Maximilian Schilling und Matthias Sester, Rainer Pölling (AutoForm). Institute for Structural Mechanics, University of Stuttgart. 2024.
- Abstract
- Poster with results
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Uygar Kovanci. Investigation and Mitigation of Volumetric Locking for Higher-Order Tetrahedral Elements (23/15). Master Thesis. Supervision: Maximilian Schilling und Tarun Kumar Mitruka Vinod Kumar Mitruka. Institute for Structural Mechanics, University of Stuttgart. 2023.
- Abstract
- Poster with results
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Aline Hinz. Chancen und Grenzen der isogeometrischen Analyse in industriellen Anwendungen (23/22). Master Thesis. Supervision: Maximilian Schilling. Institute for Structural Mechanics, University of Stuttgart. 2023.
- Abstract
- Poster with results
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Lingxiao Chen. Untersuchung dünnwandiger Strukturen unter Innendruck (22/05). Master Thesis. Supervision: Maximilian Schilling. Institute for Structural Mechanics, University of Stuttgart. 2022.
- Abstract
- Poster with results
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Shraddha Singh. Investigation of Compliant Constant-Force Mechanisms (22/13). Master Thesis. Supervision: Maximilian Schilling. Institute for Structural Mechanics, University of Stuttgart. 2022.
- Abstract
- Poster with results
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Jiaquan Wang. Datenkompression für die Ergebnisse von Finite-Elemente-Simulationen (21/23). Master Thesis. Supervision: Tobias Willmann und Maximilian Schilling. Institute for Structural Mechanics, University of Stuttgart. 2021.
- Abstract
- Poster with results
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Bachelor Theses

Heidi Andelfinger. Entwicklung und Implementierung eines Programms zur Lösung von statisch bestimmten Schubfeldsystemen (24/11). Bachelor Thesis. Supervision: Henrik Jakob und Maximilian Schilling. Institute for Structural Mechanics, University of Stuttgart. 2024.
- Abstract
- Poster with results
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Baha Yavuz. Methoden zur Berechnung von Kuppelschalen mit veränderlicher Dicke am Beispiel des Pantheons (24/13). Bachelor Thesis. Supervision: Maximilian Schilling. Institute for Structural Mechanics, University of Stuttgart. 2024.
- Abstract
- Poster with results
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Fatma Ayla Günes. Statische Untersuchung der Kuppel der Hagia Sophia im Kontext ihrer Umbauten (23/03). Bachelor Thesis. Supervision: Maximilian Schilling. Institute for Structural Mechanics, University of Stuttgart. 2023.
- Abstract
- Poster with results
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Ilayda Balci. Schwingungsauslegung einer Bühnenkonstruktion (23/09). Bachelor Thesis. Supervision: Maximilian Schilling. Institute for Structural Mechanics, University of Stuttgart. 2023.
- Abstract
- Poster with results
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Maximilian Schilling

Contact

Vita

Research

Publications

Articles in journals

Abstract

Articles in proceedings

Abstract

Monographs and Collections

Abstract

Presentations

Presentations at Conferences

Further Activities in the Scientific Community

External profiles

Committee Activities at the University of Stuttgart

Organization of Conferences and Mini Symposia

Teaching

Supervision of Theses

Master Theses

Bachelor Theses

Audience

Formalities

Services

Organization

Maximilian Schilling

Contact

Vita

Research

Publications

Articles in journals

Abstract

Articles in proceedings

Abstract

Monographs and Collections

Abstract

Presentations

Presentations at Conferences

Further Activities in the Scientific Community

External profiles

Committee Activities at the University of Stuttgart

Organization of Conferences and Mini Symposia

Teaching

Supervision of Theses

Master Theses

Bachelor Theses

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Audience

Formalities

Services

Organization