Multiplicative electro-elasticity of electroactive polymers accounting for micromechanically-based network models
Electro-active polymers are materials which exhibit coupled electro-mechanical behavior at large strains. They respond by a deformation to an applied electrical field and are applied in advanced industrial environments as sensors and actuators, for example in robotics, biomimetics and smart structures. A predictive modeling of these materials must account for characteristic features of their microstructure, consisting of an amorphous matrix of cross-linked polymer chain matrix and possibly a fraction of crystalline particles. The polymer network has an important effect on the electro-mechanical overall response, in particular in the large strain regime. The key intention of this work is to outline a general modeling structure for electroactive polymers on the macroscopic continuum level, that incorporates existing micromechanically-based network models for cross-linked polymers in a modular format. In order to account for electric dipoles associated with crystalline particle aggregates embedded into the polymer network, we consider a link to the network model based on multiplicative decompositions of the deformation gradient into electrically-induced and stress-producing parts. This includes a separate constitutive modeling of an electrically-induced stretch driven by the particle dipoles. Here, we incorporate Lee- and Clifton-type right and left decompositions, where the latter seems more appropriate for the modeling of electroactive polymers due to its dependence on the true electric field. Furthermore, micromechanical structures for a deformation-dependent permittivity of the polymer chain matrix are taken into account. We develop details of a unified modeling structure and its numerical implementation for those alternative kinematic assumptions, and combine it with the so-called microsphere network model of rubber elasticity, that exploits a homogenization over a chain orientation space. This provides an advanced model problem for the application of the proposed constitutive framework for EAPs.
electroactive polymers micromechanics electro-mechanics finite strains variational principles coupled problems