Discrete nonlinear elastodynamics in a port‐Hamiltonian framework

Author:

Kinon Philipp L.1ORCID,Thoma Tobias2ORCID,Betsch Peter1ORCID,Kotyczka Paul2ORCID

Affiliation:

1. Institute of Mechanics Karlsruhe Institute of Technology (KIT) Karlsruhe Germany

2. TUM School of Engineering and Design Technical University of Munich (TUM) Garching Germany

Abstract

AbstractWe provide a fully nonlinear port‐Hamiltonian formulation for discrete elastodynamical systems as well as a structure‐preserving time discretization. The governing equations are obtained in a variational manner and represent index‐1 differential algebraic equations. Performing an index reduction, one obtains the port‐Hamiltonian state space model, which features the nonlinear strains as an independent state next to position and velocity. Moreover, hyperelastic material behavior is captured in terms of a nonlinear stored energy function. The model exhibits passivity and losslessness and has an underlying symmetry yielding the conservation of angular momentum. We perform temporal discretization using the midpoint discrete gradient, such that the beneficial properties are inherited by the developed time stepping scheme in a discrete sense. The numerical results obtained in a representative example are demonstrated to validate the findings.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Wiley

Subject

Electrical and Electronic Engineering,Atomic and Molecular Physics, and Optics

Reference17 articles.

1. Modeling and Control of Complex Physical Systems

2. A port-Hamiltonian approach to modeling the structural dynamics of complex systems

3. Port-Hamiltonian flexible multibody dynamics

4. Port-Hamiltonian FE models for filaments

5. Kinon P. L. Thoma T. Betsch P. &Kotyczka P.(2023).Port‐Hamiltonian formulation and structure‐preserving discretization of hyperelastic strings.arXiv:2304.10957 [math.DS]. doi:https://doi.org/10.48550/arXiv.2304.10957

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