The main direction of research is computational mechanics and optimal control of dynamical systems. Efficient technologies for structural mechanics and optimal control simulations are developed, facing contemporary life science and engineering questions. The problems under investigation consider flexible multibody dynamics, coupled problems, biomechanics, and robot dynamics as well as the optimization and optimal control of their dynamics including non-smooth or mixed-integer variants and multiobjective optimization. Furthermore, (human) motion is captured and investigated in our motion analysis laboratory and the measured data in analyzed directly and in simulations.
Research projects
Biomechanics (natural or impaired human movements and athletic’s high performance, human hand grasping)
Biological and artificial muscles models
Phase-field models for fracture
Multiscale and multirate systems with dynamics on various times
Current projects
Symplectic discretizations for optimal control problems in mechanics
(Third Party Funds Single)
Term: since 15. February 2023 Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
The focus of the work program is on the best possible integration of empathokinaesthetic sensor data in biomechanical models. Concretely, degenerative motion impairments of the hand are recorded by EmpkinS and reference sensors and the date is integrated optimally into the mathematical formulation of the optimal control problem, depending on the data type, measurement frequency and uncertainty, etc. Through movement tracking as well as via the prediction of movement, objective biomarkers are identified for healthy or impaired movement function.
We extend the rigorous identification of Griffith models from atomistic systems governed by Lennard-Jones interactions [FrSc15a] to general lattice systems including long-range and multi-body interactions. Here, we will apply techniques from the paper [BaBrCi20] and complement their analysis by showing the Cauchy-Born rule in the setting of small displacements. Applying the Gamma-convergence approach to composite materials, we also aim at studying the influence of different mesoscopic on the macroscopic fracture properties. This connects our perspective to projects P8 and P11. Our main goal is then to establish existence of an atomistic continuous–time evolution and relate it rigorously to continuum quasi-static evolutions [FrLa03, FrSo18] by means of evolutionary Gamma-convergence for rate-independent systems. Here, a key issue consists in verifying stability of unilateral minimisers along the irreversible fracture process.
The fracture of a brittle solid is crucially determined by material heterogeneities directly at the crack front where the stress field diverges and the usual homogenization strategies are no longer applicable. While this problem has attracted significant interest, currently no consistent theory that relates local changes in properties to the local fracture behavior and macroscopic failure criteria exists. In contrast to the long-range elastic interactions, the direct interaction of the crack front with heterogeneities cannot be described by continuum methods but requires an atomistic treatment.
The aim of this project is to study the influence of various types of heterogeneities on the energy dissipation mechanisms in different classes of materials.
In the simulation of continuum mechanical problems of materials with heterogeneities caused e.g. by a grained structure on a smaller scale compared to the overall dimension of the system, or by the propagation of discontinuities like cracks, the spatial meshes for finite element simulations are typically consisting of coarse elements to save computational costs in regions where less deformation is expected, as well as finely discretised areas to be able to resolve discontinuities and small scale phenomena in an accurate way. For transient problems, spatial mesh adaption has been the topic of intensive research and many strategies are available, which refine or coarsen the spatial mesh according to different criteria. However, the standard is to use the same time step for all degrees of freedom and adaptive time step controls are usually applied to the complete system.
The aim of this project is to investigate the kinetics of heterogeneous, e.g. cracked material, in several steps by developing suitable combinations of spatial and temporal mesh adaption strategies.
The RTG aims to improve understanding of fracture in brittle heterogeneous materials by developing simulation methods able to capture the multiscale nature of failure. With i) its rooting in different scientific disciplines, ii) its focus on the influence of heterogeneities on fracture at different length and time scales as well as iii) its integration of highly specialised approaches into a “holistic” concept, the RTG addresses a truly challenging cross-sectional topic in mechanics of materials. Although various simulation approaches describing fracture exist for particular types of materials and specific time and length scales, an integrated and overarching approach that is able to capture fracture processes in different – and in particular heterogeneous – materials at various length and time resolutions is still lacking. Thus, we propose an RTG consisting of interdisciplinary experts from mechanics, materials science, mathematics, chemistry, and physics that will develop the necessary methodology to investigate the mechanisms underlying brittle fracture and how they are influenced by heterogeneities in various materials. The insights obtained together with the methodological framework will allow tailoring and optimising materials against fracture. The RTG will cover a representative spectrum of brittle materials and their composites, together with granular and porous materials. We will study these at length and time scales relevant to science and engineering, ranging from sub-atomic via atomic and molecular over mesoscale to macroscopic dimensions. Our modelling approaches and simulation tools are based on concepts from quantum mechanics, molecular mechanics, mesoscopic approaches, and continuum mechanics. These will be integrated into an overall framework which will represent an important step towards a virtual laboratory eventually complementing and minimising extensive and expensive experimental testing of materials and components. Within the RTG, young researchers under the supervision of experienced PAs will perform cutting-edge research on challenging scientific aspects of fracture. The RTG will foster synergies in research and advanced education and is intended to become a key element in FAU‘s interdisciplinary research areas “New Materials and Processes” and “Modelling–Simulation–Optimisation”.
Koelewijn, A., Nitschke, M., & Leyendecker, S. (2023). “In the Wild" Movement Analysis of Arbitrary Motions. Paper presentation at 18th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering (CMBBE), Paris, France.
Leyendecker, S. (2023). Biomechanical modelling and simulation — Muskuloskeletal, cardiac and protein system. In Proceedings of the invited lecture, Rotary Club. Nuremberg, Sebald, DE.
Lohmayer, M., & Leyendecker, S. (2023). Exergetic Port-Hamiltonian Systems for Multibody Dynamics. In Proceedings of the conference, 4th workshop of the doctoral college "Port-Hamiltonian Systems: Modelling, Numerics, and Control”. Karlsruhe Institute of Technology, Karlsruhe, DE.
Stavole, M., Sato Martin de Almagro, R., Brüls, O., & Leyendecker, S. (2023). Augmented Lagrangian contact formulation of the 2D Euler elastica. In Proceedings of the conference, ICIAM 2023 -- 10th International Congress on Industrial and Applied Mathematics. Tokyo, JP.
Stavole, M., Sato Martin de Almagro, R., Capobianco, G., Brüls, O., & Leyendecker, S. (2023). 2D Euler elastica in constrained environments. In Proceedings of the conference, HFSS International Conference on Highly Flexible Slender Structures (THREAD annual meeting). Rijeka, HR.
Stavole, M., Sato Martin de Almagro, R., Dörlich, V., & Leyendecker, S. (2023). Homogenized stiffness coefficients of unloaded endoscope shafts. In Proceedings of the conference, HFSS International Conference on Highly Flexible Slender Structures (THREAD annual meeting). Rijeka, HR.
Capobianco, G., Huang, D., Sato Martin de Almagro, R., & Leyendecker, S. (2022). Introduction to Numerics (INUMS). Paper presentation at invited lecture, FRASCAL Mini Lecture, Erlangen, DE.
Heinrich, S., Phutane, U., Coppers, B., Liphardt, A.-M., & Leyendecker, S. (2022). Towards optimal control grasping simulations with the full hand. In Proceedings of the conference, 9th GACM Colloquium on Computational Mechanics - for Young Scientists from Academia and Industry. Essen, DE.
Lohmayer, M., & Leyendecker, S. (2022). EPHS: A Port-Hamiltonian Modelling Language. In Proceedings of the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022. Bayreuth, DE.
Lohmayer, M., & Leyendecker, S. (2022). EPHS: A Port-Hamiltonian Modelling Language. In Proceedings of the conference, MTNS 2022: 25th International Symposium on Mathematical Theory of Networks and Systems. Bayreuth.
Phansalkar, D., Weinberg, K., Ortiz, M., & Leyendecker, S. (2022). A spatially adaptive phase-field model for dynamic fracture. In Proceedings of the conference, ECCOMAS - 8th European Congress on Computational Methods in Applied Sciences and Engineering. Oslo, NO.
Phansalkar, D., Weinberg, K., Ortiz, M., & Leyendecker, S. (2021). Uniform and adaptive in phase-field models for brittle fractures. In Proceedings of the conference, 5th Research Training Group GRK 2423 FRASCAL. online.
Lohmayer, M., & Leyendecker, S. (2020). Exergetic Port-Hamiltonian Systems — a tutorial. In Proceedings of the Student Compact Course -- Variational Methods for Fluids and Solids. Berlin, DE.
Sato Martín de Almagro, R.T., & Leyendecker, S. (2020). Fundamentals of beam theory and flexible multibody dynamics. In Proceedings of the Network wide training — Joint Training on Numerical Modelling of Highly Flexible Structures THREAD. Erlangen (ZOOM), DE.
The main direction of research is computational mechanics and optimal control of dynamical systems. Efficient technologies for structural mechanics and optimal control simulations are developed, facing contemporary life science and engineering questions. The problems under investigation consider flexible multibody dynamics, coupled problems, biomechanics, and robot dynamics as well as the optimization and optimal control of their dynamics including non-smooth or mixed-integer variants and multiobjective optimization. Furthermore, (human) motion is captured and investigated in our motion analysis laboratory and the measured data in analyzed directly and in simulations.
Research projects
Current projects
Symplectic discretizations for optimal control problems in mechanics
(Third Party Funds Single)
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Simulation of optimal control problems via geometric methods
(Own Funds)
URL: https://www.ltd.tf.fau.de
Simulation and optimal control of flexible mechanical systems with frictional contact
(Own Funds)
Analysis of Degenerative Motion Impairments through Integration of Empathokinaesthetic Sensor Data in Biomechanical Human Models (C04)
(Third Party Funds Group – Sub project)
Term: 1. July 2021 - 30. June 2025
Funding source: DFG / Sonderforschungsbereich (SFB)
URL: https://www.empkins.de/
P14 – Passage from Atomistic-to-Continuum for Quasistatic and Dynamic Crack Growth
(Third Party Funds Group – Sub project)
Term: 1. April 2019 - 31. December 2027
Funding source: DFG / Graduiertenkolleg (GRK)
We extend the rigorous identification of Griffith models from atomistic systems governed by Lennard-Jones interactions [FrSc15a] to general lattice systems including long-range and multi-body interactions. Here, we will apply techniques from the paper [BaBrCi20] and complement their analysis by showing the Cauchy-Born rule in the setting of small displacements. Applying the Gamma-convergence approach to composite materials, we also aim at studying the influence of different mesoscopic on the macroscopic fracture properties. This connects our perspective to projects P8 and P11. Our main goal is then to establish existence of an atomistic continuous–time evolution and relate it rigorously to continuum quasi-static evolutions [FrLa03, FrSo18] by means of evolutionary Gamma-convergence for rate-independent systems. Here, a key issue consists in verifying stability of unilateral minimisers along the irreversible fracture process.
Teilprojekt P2 - Atomistics of Crack-Heterogeneity Interactions
(Third Party Funds Group – Sub project)
Term: 2. January 2019 - 31. December 2027
Funding source: DFG / Graduiertenkolleg (GRK)
URL: https://www.frascal.research.fau.eu/home/research/p-2-atomistics-of-crack-heterogeneity-interactions/
The fracture of a brittle solid is crucially determined by material heterogeneities directly at the crack front where the stress field diverges and the usual homogenization strategies are no longer applicable. While this problem has attracted significant interest, currently no consistent theory that relates local changes in properties to the local fracture behavior and macroscopic failure criteria exists. In contrast to the long-range elastic interactions, the direct interaction of the crack front with heterogeneities cannot be described by continuum methods but requires an atomistic treatment.
The aim of this project is to study the influence of various types of heterogeneities on the energy dissipation mechanisms in different classes of materials.
Teilprojekt P9 - Adaptive Dynamic Fracture Simulation
(Third Party Funds Group – Sub project)
Term: 2. January 2019 - 31. December 2027
Funding source: DFG / Graduiertenkolleg (GRK)
URL: https://www.frascal.research.fau.eu/home/research/p-9-adaptive-dynamic-fracture-simulation/
In the simulation of continuum mechanical problems of materials with heterogeneities caused e.g. by a grained structure on a smaller scale compared to the overall dimension of the system, or by the propagation of discontinuities like cracks, the spatial meshes for finite element simulations are typically consisting of coarse elements to save computational costs in regions where less deformation is expected, as well as finely discretised areas to be able to resolve discontinuities and small scale phenomena in an accurate way. For transient problems, spatial mesh adaption has been the topic of intensive research and many strategies are available, which refine or coarsen the spatial mesh according to different criteria. However, the standard is to use the same time step for all degrees of freedom and adaptive time step controls are usually applied to the complete system.
The aim of this project is to investigate the kinetics of heterogeneous, e.g. cracked material, in several steps by developing suitable combinations of spatial and temporal mesh adaption strategies.
Fracture across Scales: Integrating Mechanics, Materials Science, Mathematics, Chemistry, and Physics (FRASCAL)
(Third Party Funds Group – Overall project)
Funding source: DFG / Graduiertenkolleg (GRK)
URL: https://www.frascal.research.fau.eu/
The RTG aims to improve understanding of fracture in brittle heterogeneous materials by developing simulation methods able to capture the multiscale nature of failure. With i) its rooting in different scientific disciplines, ii) its focus on the influence of heterogeneities on fracture at different length and time scales as well as iii) its integration of highly specialised approaches into a “holistic” concept, the RTG addresses a truly challenging cross-sectional topic in mechanics of materials. Although various simulation approaches describing fracture exist for particular types of materials and specific time and length scales, an integrated and overarching approach that is able to capture fracture processes in different – and in particular heterogeneous – materials at various length and time resolutions is still lacking. Thus, we propose an RTG consisting of interdisciplinary experts from mechanics, materials science, mathematics, chemistry, and physics that will develop the necessary methodology to investigate the mechanisms underlying brittle fracture and how they are influenced by heterogeneities in various materials. The insights obtained together with the methodological framework will allow tailoring and optimising materials against fracture. The RTG will cover a representative spectrum of brittle materials and their composites, together with granular and porous materials. We will study these at length and time scales relevant to science and engineering, ranging from sub-atomic via atomic and molecular over mesoscale to macroscopic dimensions. Our modelling approaches and simulation tools are based on concepts from quantum mechanics, molecular mechanics, mesoscopic approaches, and continuum mechanics. These will be integrated into an overall framework which will represent an important step towards a virtual laboratory eventually complementing and minimising extensive and expensive experimental testing of materials and components. Within the RTG, young researchers under the supervision of experienced PAs will perform cutting-edge research on challenging scientific aspects of fracture. The RTG will foster synergies in research and advanced education and is intended to become a key element in FAU‘s interdisciplinary research areas “New Materials and Processes” and “Modelling–Simulation–Optimisation”.
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