Thermodynamically consistent derivation and computation of electro-thermo-mechanical systems for solid bodies

For electro-thermo-mechanical systems such as a piezoceramic transducer, pyroelectric energy harvester, or a magnetic sensor using a magnetoelectric coupling, there are various formulations in continuum mechanics. The consensus of a well-established formulation is still missing. In this work we try to shed light to varying formulations and develop a thermodynamically consistent derivation of field equations for electro-thermo-mechanical systems. In order to justify their feasibility and verify their strength of modeling a physical system, we present simulations of engineering applications by exploiting open-source packages and solving problems monolithically with finite difference method in time and finite element method in space.