On the response of non-dissipative solids

In addition to being incapable of dissipation, in any process that it is subject to, there are other tacit requirements that a classical elastic body has to meet. The class of solids that are incapable of dissipation is far richer than the class of bodies that is usually understood as being elastic. We show that, unlike the case of a classical elastic body, the stress in non-dissipative bodies is not necessarily derivable from a stored energy that depends only on the deformation gradient.