Some Theorems in the Theory of Microstretch Thermomagnetoelectroelasticity

The linear dynamic theory of microstretch thermomagnetoelectroelasticity is studied in this paper. First, a reciprocity relation which involves two processes at different instants is established to form the basis of a uniqueness result and a reciprocal theorem. The proof of the reciprocal theorem avoids both using the Laplace transform and incorporating the initial conditions into the equations of motion. The uniqueness theorem is derived with no definiteness assumption on the elastic constitutive coefficients. Then the continuous dependence theorem is discussed upon two external data systems. Finally, the variational principle of Hamilton type which fully characterizes the solution of the mixed boundary-initial-value problem (mixed problem) is obtained. These theorems lay a solid foundation for further theoretical and numerical studies on microstretch thermomagnetoelectroelastic materials.