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A thermodynamically consistent model of non-classical coupled non-linearthermoelasticity capable of accounting for thermal wave propagation isproposed. The heat flux is assumed to consist of both additive energetic anddissipative components. Constitutive relations for the stress, the entropy andthe energetic component of the heat flux are derived in a thermodynamicallyconsistent manner. A Lyapunov function for the dynamics is obtained for thecase in which the surface of the continuum body is maintained at a referencetemperature. It is shown that the system is non-linearly stable. The linearizedmodel is shown to be similar to the type III model of Green and Naghdi, exceptfor some minor differences in the interpretations of some of the parameters.

A thermodynamically consistent formulation of generalized thermoelasticity at finite deformations