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An electromechanically coupled micro-sphere framework: application to the finite element analysis of electrostrictive polymers

The number of industrial applications of electroactive polymers (EAPs) is increasing and, consequently, the need for reliable modelling frameworks for such materials as well as related robust simulation techniques continuously increases. In this context, we combine the modelling of non-linear electroelasticity with a computational micro-sphere formulation in order to simulate the behaviour of EAPs. The micro-sphere approach in general enables the use of physics-based constitutive models like, for instance, the so-called worm-like chain model. By means of the micro-sphere formulation, scalar-valued micromechanical constitutive relations can conveniently be extended to a three-dimensional continuum setting. We discuss several electromechanically coupled numerical examples and make use of the finite element method to solve inhomogeneous boundary value problems. The incorporated material parameters are referred to experimental data for an electrostrictive polymer. The numerical examples show that the coupled micro-sphere formulation combined with the finite element method results in physically sound simulations that mimic the behaviour of an electrostrictive polymer.