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Variational Treatment and Stability Analysis of Coupled Electro‐Mechanics
Author(s) -
Vallicotti Daniel,
Teichtmeister Stephan,
Keip MarcAndré,
Miehe Christian
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610189
Subject(s) - homogenization (climate) , finite element method , buckling , computation , instability , stability (learning theory) , bifurcation , coulomb , coulomb's law , actuator , materials science , structural engineering , computer science , mechanics , mechanical engineering , classical mechanics , physics , composite material , engineering , algorithm , nonlinear system , biodiversity , ecology , quantum mechanics , machine learning , artificial intelligence , biology , electron
Dielectric materials such as electro‐active polymers (EAPs) belong to the class of functional materials which are used in advanced industrial environments as sensors or actuators and in other innovative fields of research. Driven by Coulomb‐type electrostatic forces EAPs are theoretically able to withstand deformations of several hundred percents. However, large actuation fields and different types of instabilities prohibit the ascend of these materials. One distinguishes between global structural instabilities such as buckling and wrinkling of EAP devices, and local material instabilities such as limit‐ and bifurcation‐points in the constitutive response. We outline variational‐based stability criteria in finite electro‐elastostatics and design algorithms for accompanying stability checks in typical finite element computations. These accompanying stability checks are embedded into a computational homogenization framework to predict the macroscopic overall response and onset of local material instability of particle filled composite materials. Application and validation of the suggested method is demonstrated by a representative model problem. © 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)