🤖 AI Summary
This work addresses nonlinear large-deformation elastodynamic systems. We propose the first structure-preserving discrete modeling and numerical method grounded in the port-Hamiltonian (pH) framework. Leveraging variational principles, we derive index-1 differential-algebraic equations and perform index reduction to construct a complete pH state-space model—featuring displacement, velocity, and **nonlinear strain as an independent state variable (novel in pH modeling)**—rigorously preserving passivity, losslessness, and angular momentum conservation. We further design a structure-preserving midpoint-type discrete-gradient time-integration scheme. Numerical experiments demonstrate exact long-term conservation of energy and angular momentum, significantly enhancing physical fidelity and numerical robustness. The method establishes a provably structure-stable paradigm for high-fidelity dynamic simulation of hyperelastic bodies.
📝 Abstract
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.
