  A thermodynamically consistent model of non-classical coupled non-linear
thermoelasticity capable of accounting for thermal wave propagation is
proposed. The heat flux is assumed to consist of both additive energetic and
dissipative components. Constitutive relations for the stress, the entropy and
the energetic component of the heat flux are derived in a thermodynamically
consistent manner. A Lyapunov function for the dynamics is obtained for the
case in which the surface of the continuum body is maintained at a reference
temperature. It is shown that the system is non-linearly stable. The linearized
model is shown to be similar to the type III model of Green and Naghdi, except
for some minor differences in the interpretations of some of the parameters.
