On the coupled theory of thermo-magnetoelectroelasticity

Within the context of the coupled theory of thermo-magnetoelectroelasticity, we derive some variational principles which fully characterize the solution of the boundary-initial-value problem. Then we establish a reciprocity 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 and uniqueness theorems. The reciprocity 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 without making restrictions on the positive definiteness of the elastic moduli or the conductivity tensor. There are also no restrictions on piezoelectric moduli, piezomagnetic moduli and thermal coupling coefficients other than symmetry conditions. The results obtained are applicable for some special cases which can be deduced from our model.