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A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics / M. Franke, Rogelio Ortigosa Martinez, J. Martínez-Frutos, Antonio Gil, P. Betsch

Computer Methods in Applied Mechanics and Engineering, Volume: 389, Start page: 114298

Swansea University Authors: Rogelio Ortigosa Martinez, Antonio Gil

  • Accepted Manuscript under embargo until: 11th December 2022

Abstract

The aim of this paper is the design of a new one-step implicit and thermodynamically consistentEnergy-Momentum (EM) preserving time integration scheme for the simulation of thermoelectro-elastic processes undergoing large deformations. The time integration scheme takes advantageof the notion of poly...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2022
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa58544
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Abstract: The aim of this paper is the design of a new one-step implicit and thermodynamically consistentEnergy-Momentum (EM) preserving time integration scheme for the simulation of thermoelectro-elastic processes undergoing large deformations. The time integration scheme takes advantageof the notion of polyconvexity and of a new tensor cross product algebra. These twoingredients are shown to be crucial for the design of so-called discrete derivatives fundamental forthe calculation of the second Piola-Kirchhoff stress tensor, the entropy and the electric field. Inparticular, the exploitation of polyconvexity and the tensor cross product, enable the derivationof comparatively simple formulas for the discrete derivatives. This is in sharp contrast to muchmore elaborate discrete derivatives which are one of the main downsides of classical EM timeintegration schemes. The newly proposed scheme inherits the advantages of EM schemes recentlypublished in the context of thermo-elasticity and electro-mechanics, whilst extending to the moregeneric case of nonlinear thermo-electro-mechanics. Furthermore, the manuscript delves intosuitable convexity/concavity restrictions that thermo-electro-mechanical strain energy functionsmust comply with in order to yield physically and mathematically admissible solutions. Finally, aseries of numerical examples will be presented in order to demonstrate robustness and numericalstability properties of the new EM scheme.
Keywords: finite element method, nonlinear thermo-electro-elastodynamics, energy-momentumscheme, tensor cross product, polyconvexity, dielectric elastomers, electro active polymers
College: College of Engineering
Start Page: 114298