, Volume 53, Issue 6, pp 1357–1401 | Cite as

A discontinuous Galerkin method for non-linear electro-thermo-mechanical problems: application to shape memory composite materials

  • Lina Homsi
  • Ludovic NoelsEmail author
Novel Computational Approaches to Old and New Problems in Mechanics


A coupled electro-thermo-mechanical discontinuous Galerkin (DG) method is developed considering the non-linear interactions of electrical, thermal, and mechanical fields. In order to develop a stable discontinuous Galerkin formulation the governing equations are expressed in terms of energetically conjugated fields gradients and fluxes. Moreover, the DG method is formulated in finite deformations and finite fields variations. The multi-physics DG formulation is shown to satisfy the consistency condition, and the uniqueness and optimal convergence rate properties are derived under the assumption of small deformation. First the numerical properties are verified on a simple numerical example, and then the framework is applied to simulate the response of smart composite materials in which the shape memory effect of the matrix is triggered by the Joule effect.


Discontinuous Galerkin method Electro-thermo-mechanics Non-linear elliptic problems Smart composites 



This project has been funded with support of the European Commission under the grant number 2012-2624/001-001-EM. This publication reflects the view only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein. Computational resources have been provided by the supercomputing facilities of the “Consortium des Équipements de Calcul Intensif en Fédération Wallonie Bruxelles (CÉCI)” funded by the “Fond de la Recherche Scientifique de Belgique (FRS-FNRS)”.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Aerospace and Mechanical Engineering, Computational and Multiscale Mechanics of Materials (CM3)University of Liège, Quartier Polytech 1LiègeBelgium

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