The Generalized Theory of Thermo-Magnetoelectroelasticity

Abstract

The governing equations for thermo-magnetoelectroelasticity are given for the heat-flux-dependent theory of Lebon. First, we establish a reciprocal relation using a new method of proof, which involves two thermoelastic processes at different instants. We show that this relation can be used to obtain reciprocity, uniqueness and continuous dependence theorems. The reciprocal theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. The uniqueness theorem is derived avoiding both the use of the definiteness assumption on the thermoelastic coefficients and the restriction that the conductivity tensor is positive definite. There are also no restrictions on the piezoelectric moduli, piezomagnetic moduli, and the thermal coupling coefficients other than symmetry conditions. We prove also that the reciprocal relation leads to a continuous dependence theorem studied on external body loads and heat supply, which ensures that the mathematical model for the generalized problem is well posed.