On thermostatics of non-simple materials with memory

This paper deals with the thermostatics of materials with memory whose stress and free energy depend on histories of higher deformation gradients. The materials are fully compatible with the Clausius-Duhem inequality and with the balance equations in their most conventional forms without additional terms such as the couple-stresses etc. The consequences of the energy criterion of stability of equilibrium states are discussed. It is shown that at stable equilibrium the equilibrium stress relation holds and that the derivatives of the equilibrium free energy with respect to the higher deformation gradients vanish. This implies the Eshelby conservation law for stable states. Also various forms of the quasiconvexity properties of the free energy are proved. The results can be applied in a discussion of phase transitions modelled in terms of smooth stable configurations which are asymptotically homogeneous at infinity, and generalizations of the results of Gibbsian thermostatics are obtained in this way.