On the Thermodynamic Stability of Elastic Heat-Conducting Solids Subject to a Deformation—Temperature Constraint

In this paper the thermoelastic stability of a three-dimensional body subject to a deformation—temperature constraint is examined with reference to Ericksen’s [7] theory for unconstrained materials. It is shown that sufficient conditions for infinitesimal stability are unattainable for finite bodies if the constraint is temperature dependent. This general result is illustrated by considering the infinitesimal dynamic stability of a slab, initially at rest at uniform temperature, in respect of one-dimensional thermomechanical perturbations satisfying ‘dead loading’ boundary conditions on its parallel faces. Results obtained by Manacorda [12] are extended to show that the slab is thermomechanically (linearly) unstable if the trace of the infinitesimal strain tensor is dependent on temperature. In the light of these results, it is shown that the instability can be removed on the basis of the conjecture that the constraint be independent of temperature, or equivalently that the entropy is uniquely determined. The conjecture is justified by considering a limiting form of a theory for almost constrained rubberlike elastic solids.