Thermodynamics of Deformable Materials

Abstract

It is now a little over a hundred years that the conceptual basis of thermostatics has been laid. Clausius introduced the entropy concept and obtained the laws of thermostatics for fluids which are in internal equilibrium. Not much later, i.e. 94 years ago, Gibbs completed the formal mathematical structure of thermostatics and developed the minimum and maximum principles and the stability conditions for fluids. There came many applications of thermostatics, of which chemical reactions, blackbody radiation and the thermostatics of surface tension may be mentioned.

Thermostatics of solid deformable materials has been restricted to small strains and stresses for a long time. It is only through the last few decades that thermostatics of large deformations has found attention. And there are still some important problems which as yet have not found a satisfactory solution. The thermostatics of plastic deformation is, in my opinion, still in a very primitive state. But even if we confine our attention, as we shall do here, to deformations where plasticity does not yet occur, or more precisely, to simple deformable materials, no full thermostatic stability condition is known. It goes without saying that such stability conditions must exist. But none of the many inequalities in mechanics of deformable materials which have been postulated or motivated can be considered as such (or as the mechanical part thereof) because, when applied to fluids, they do not go over into the well-established stability conditions for fluids.