Generalized Maxwell viscoelasticity for geometrically exact strings: Nonlinear port-Hamiltonian formulation and structure-preserving discretization

被引：0

作者：

Kinon, P. L. ^{[1
]}

Thoma, T. ^{[2
]}

Betsch, P. ^{[1
]}

Kotyczka, P. ^{[2
]}

机构：

[1] Karlsruhe Inst Technol KIT, Inst Mech, Otto Ammann Pl 9, D-76131 Karlsruhe, Germany

[2] Tech Univ Munich TUM, TUM Sch Engn & Design, Boltzmannstr 15, D-85748 Garching, Germany

来源：

IFAC PAPERSONLINE | 2024年 / 58卷 / 06期

关键词：

Nonlinear port-Hamiltonian systems; generalized Maxwell model; structure-preserving discretization; mixed finite elements; discrete gradients;

D O I：

10.1016/j.ifacol.2024.08.264

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This contribution proposes a nonlinear and dissipative infinite-dimensional port-Hamiltonian (PH) model for the dynamics of geometrically exact strings. The mechanical model provides a description of large deformations including finite elastic and inelastic strains in a generalized Maxwell model. It is shown that the overall system results from a power-preserving interconnection of PH subsystems. By using a structure-preserving mixed finite element approach, a finite-dimensional PH model is derived. Eventually, midpoint discrete derivatives are employed to deduce an energy-consistent time-stepping method, which inherits discrete-time dissipativity for the irreversible system. An example simulation illustrates the numerical properties of the present approach. Copyright (C) 2024 The Authors.

引用

页码：101 / 106

页数：6