No Cover Image

Journal article 310 views 21 downloads

A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics

Marlon Franke Orcid Logo, Felix Zähringer, Moritz Hille, Rogelio Ortigosa, Peter Betsch Orcid Logo, Antonio Gil Orcid Logo

International Journal for Numerical Methods in Engineering, Volume: 124, Issue: 10, Pages: 2135 - 2170

Swansea University Author: Antonio Gil Orcid Logo

  • 62464.pdf

    PDF | Version of Record

    This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

    Download (3.78MB)

Check full text

DOI (Published version): 10.1002/nme.7209

Abstract

A novel mixed framework and energy-momentum consistent integration scheme in the field of coupled nonlinear thermo-electro-elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of poly-convex strain energy functions. For this elastodynamic...

Full description

Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2023
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa62464
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: A novel mixed framework and energy-momentum consistent integration scheme in the field of coupled nonlinear thermo-electro-elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of poly-convex strain energy functions. For this elastodynamic framework, the properties of the so-called tensor cross product are exploited to derive a mixed formulation via a Hu-Washizu type extension of the strain energy function. Afterwards, a general path to incorporate non-potential problems for mixed formulations is demonstrated. To this end, the strong form of the mixed framework is derived and supplemented with the energy balance as well as Maxwell’s equations neglecting magnetic and time dependent effects. By additionally choosing an appropriate energy function, this procedure leads to a fully coupled thermo-electro-elastodynamic formulation which benefits from the properties of the underlying mixed framework. In addition, the proposed mixed framework facilitates the design of a new energy-momentum consistent time integration scheme by employing discrete derivatives in the sense of Gonzalez. A one-step integration scheme of second-order accuracy is obtained which is shown to be stable even for large time steps. Eventually, the performance of the novel formulation is demonstrated in several numerical examples.
Keywords: Nonlinear thermo-electro-elastodynamics, polyconvexity, tensor cross product, non-potential mixed formulation, energy-momentum scheme
College: Faculty of Science and Engineering
Funders: DFG, German Research Foundation, project number 443238377 21132/SF/19, Fundación Séneca, Región de Murcia Fundación Séneca, grant 20911/PI/18, and PID2021-125687OA-I00
Issue: 10
Start Page: 2135
End Page: 2170