On the computational modelling of nonlinear electro-elasticity in heterogeneous bodies at finite deformations

Abstract

Dielectric elastomer actuators (DEA) have been demonstrated to exhibit a quasi-immediate electro-mechanical actuation response with relatively large deformation capability. The properties of DEA make them suitable to be used in the form of major active components within soft robotics and biomimetic artificial muscles. However, some of the electro-active material properties impose limitations on its applications. Therefore, researchers attempt to modify the structure of the homogeneous DEA material by the incorporation of fillers that possess distinct electro-mechanical properties. This modification of the material’s structure leads to a fabricated inhomogeneous composite. From the point of mathematical material modelling and numerical simulation, we propose a material model and a computational framework using the finite element method, which is capable of emulating nonlinear electro-elastic interactions. We consider a coupled electro-mechanical description with the electric and the electro-mechanical properties of the material assumed to be nonlinearly dependent on the deformation. Furthermore, we demonstrate a coupled ansatz that expresses the electric response as dielectrically quasi-linear with only density-dependent electric permittivity. We couple the electro-mechanical models to the extended tube model, which is a suitable approach for the realistic emulation of the hyperelastic response of rubber-like materials. Thereafter, we demonstrate analytical and numerical solutions of a homogeneous electro-elastic body with the Neo-Hookean material model and the extended tube model to express the hyperelastic response. Finally, we use the finite element method to investigate several heterogeneous configurations consisting of soft DEA matrix filled with spherical stiff inclusions with changing volume fraction and ellipsoidal inclusions with varying aspect ratio.