A finite strain modeling for electro-viscoelastic materials

Abstract

Of interest in this work is the multi-physics modeling of electrically sensitive materials known to have viscoelastic properties. We show how the current state of the art in the modeling of electro-mechanics in deformable media can easily be integrated within the unified framework of continuum thermodynamics, this latter being crucial in setting the convenient forms for the constitutive laws and evolution equations. The formulation is developed within the finite strain range and we adopt the nowadays well-accepted multiplicative decomposition of the deformation gradient into elastically relaxing and viscous parts giving rise to an intermediate configuration on which the electric field vectors can eventually be transported. The paper discusses in depth such a formulation. Among others, it is implicitly found that the electric displacement and polarization vectors can be split into equilibrium and non-equilibrium parts. A model example is proposed for the purpose of demonstration to study some phenomena qualitatively. The paper presents also the numerical design of a simplified version within the context of the finite element method to illustrate the effectiveness of the proposed framework for structural simulations.