Connections between deformation-temperature and deformation-entropy constraints and near-constraints in thermoelasticity

Two types of thermomechanical constraint are known to the literature, the first consisting of a relation between the deformation and temperature, the second consisting of a relation between deformation and entropy. The first is known to be unstable in response to small disturbances and the second stable. Insight into these unphysical instabilities is sought by modelling each constraint as the limit of a nearly constrained thermoelastic material. It is found that each deformation-entropy near-constraint is equivalent to a corresponding deformation-temperature near-constraint. But the limit of the deformation-entropy constraint holding exactly is found to correspond to a situation where the limit of the deformation-temperature near-constraint has not been reached. Then this constraint holds only approximately and the need for unphysical instabilities is avoided.