Multiscale modeling of electroactive polymer composites

Abstract

Electroactive polymer composites are materials that consist of an elastomeric matrix and dispersed high-dielectric-modulus or metallic inclusions. The addition of the inclusions generally leads to a significant enhancement of the electrostatic actuation or, more generally, of the overall electro-mechanical coupling. This enhancement is mainly due to the contrast of dielectric moduli of the individual phases, which induces fluctuations of the electric field in the matrix material. The present contribution aims at the derivation and implementation of a multiscale homogenization framework for the macroscopic simulation of electroactive polymer composites with explicit consideration of their microscopic structure. This is achieved through the development of a two-scale computational homogenization approach for electro-mechanically coupled solids at finite deformations. The microscopic part of the problem is defined on a representative volume element that is attached at each integration point of the macroscopic domain. In order to derive energetically consistent transition conditions between the scales a generalized form of the Hill-Mandel condition extended to electro-elastic phenomena at large deformations is exploited. An efficient solution of the macroscopic boundary value problem is guaranteed by means of an algorithmically consistent tangent. The method is applied to the simulation of different dielectric polymer-ceramic composites, which are analzyed with regard to their effective actuation properties. In addition to that, an example of a multiscale electro-mechanical actuator at large deformations is presented.