On the general theory of stability for elastic bodies

This paper deals with the stability of loaded equilibrium configuration of elastic bodies, within the framework of nonlinear thermoelasticity. Although most of the results are obtained in the context of thermo-mechanical stability, the parallel developments for the purely mechanical stability are also considered. By use of an appropriate thermodynamic restriction, several theorems are proved concerning a sufficient condition for stability of the equilibrium configuration. These theorems hold under a general class of motions and their validity is not limited to small motions and small temperature changes from a loaded equilibrium state. Various generalizations of our main results are discussed and the reasonableness of the proposed stability criterion is demonstrated.