Universal relations for a new class of elastic bodies

Abstract

Universal relations hold in all members that belong to a certain class of bodies, and they are therefore useful in designing experiments in which all members belonging to the particular class of bodies can be tested. It has been shown recently that the class of elastic bodies is much larger than the classical Cauchy elastic bodies. It has also been shown that such elastic bodies have firm thermodynamic underpinnings. In this short paper, we discuss universal relations that hold for a large sub-class of bodies which belong to this new class of elastic bodies. To be more precise, we consider a class of compressible isotropic elastic solids that are a sub-class of the new class of elastic bodies. We show that practically all the universal solutions which are possible in classical Cauchy elastic bodies are also possible within the context of the sub-class of elastic bodies that we consider.