On the requirement that material symmetries shall preserve density

Abstract

A material symmetry transformation may be described as a change of reference configuration such that no measurement of stress corresponding to the response of the material can distinguish the configurations before and after this change. One usually requires that such a change of reference configuration be density-preserving ([1], [2]) since otherwise the material could suffer arbitrarily large dilatation with no change in material r e s p o n s e a conclusion that seems physically unacceptable. GURTIN & WILLIAMS ([33) showed earlier that the second law of thermodynamics (in the form of the Clausius-Duhem inequality) reinforces this physical prejudice under certain assumptions. In this paper I derive this same conclusion from a different point of view, one which is simpler in its physical interpretation and more general in its consequences. Roughly speaking, the basic assumption is that one be able to do the same experiment starting from either reference configuration, as would be necessary if we were in fact to compare their corresponding material responses. This assumption leads to the requirement that material symmetry transformation be density-preserving.