Port-Hamiltonian FE models for filaments

Thoma, Tobias; Kotyczka, Paul

doi:10.1016/j.ifacol.2022.11.078

Cited by 3 publications

(1 citation statement)

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“…In the present work, we show a PH formulation for elastodynamics that can capture both geometric and material nonlinearities. While we restrict ourselves to finite-dimensional systems in this contribution, also infinitedimensional problems fit into this model class after a suitable mixed finite element discretization [4,5].…”

Section: Introductionmentioning

confidence: 99%

Discrete nonlinear elastodynamics in a port‐Hamiltonian framework

Kinon,

Thoma,

Betsch

et al. 2023

Proc Appl Math and Mech

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We 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.

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Section: Introductionmentioning

confidence: 99%