On the influence of the coupled invariant in thermo-electro-elasticity

Electro-active polymers (EAPs) are a comparatively new class of smart materials that can change their properties and undergo large deformations as a result of an external electric excitation. These characteristics make them promising candidates in a wide range of applications, for example in sensor and actuator technology. As the experimental testing is both expensive and time consuming, simulation methods are developed in order to predict the material behavior. These simulations are based on well established energy formulation that are amended by additional coupling terms, often times in form of an invariant description. While the form of the purely mechanical and purely electric invariant quantities does not vary among the contributions of the electro-mechanical community, two different formulations for the coupling invariant can be found. In this contribution we demonstrate the influence of the selected coupling invariant on the material response. Therefore a thermo-electromechanically coupled constitutive model is derived based on the frequently used total energy approach.We devise the relevant constitutive equations starting from the basic laws of thermodynamics. Two distinctively different non-homogeneous boundary value problems are solved analytically in order to demonstrate the influence of the selected coupling invariant