On the micromorphic thermoelasticity without energy dissipation

The linear dynamic theory of micromorphic thermoelasticity without energy dissipation is considered. First, we establish a reciprocity relation which involves thermoelastic processes at different instants. We show that this relation can be used to establish a uniqueness theorem and a reciprocal theorem. The uniqueness result is derived with no definiteness assumption on elastic constitutive coefficients. The reciprocal theorem avoids both the use of the Laplace transform and the incorporation of initial conditions into the equations of motion. Then, a variational theorem for the first boundary-initial value problem is established. The effect of a concentrated heat supply in an unbounded body is also investigated.