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On The Formulatio and Numerical Implementation of Dissipative Electro‐Mechanics at Large Strains
Author(s) -
Rosato Daniele,
Miehe Christian
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910145
Subject(s) - dissipative system , constitutive equation , dissipation , nonlinear system , finite strain theory , homogeneous space , deformation (meteorology) , convexity , classical mechanics , metric tensor , finite element method , mathematics , mechanics , theoretical physics , physics , mathematical analysis , geometry , thermodynamics , quantum mechanics , meteorology , financial economics , economics , geodesic
In the last year an increasing interest in functional materials such as ferroelectric polymers and ceramics has been shown. For those materials viscous effects or electric polarizations cause hysteresis phenomena accompanied with possibly large remanent strains. This paper outlines aspects of the formulation and numerical implementation of dissipative electro‐mechanics at large strains. In the first part, we focus on the geometric nature of dissipative electro‐mechanics. In a second part, we discuss constitutive assumptions which account for specific problems arising in the geometric nonlinear setting. This concerns the definition of objective energy storage and dissipation functions with suitable symmetries and (weak) convexity properties. With regard to the choice of the internal variables entering these functions, a critical point are kinematic assumptions. Here, we investigate the multiplicative decomposition of the local deformation gradient into reversible and remanent parts as well as the introduction of a remanent metric. In a third part, we summarize details of the constitutive updates as well as the finite element formulations, both on the basis of compact incremental variational principles. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)