Many body interaction and cauchy relation for elastic constants

Abstract

Every non-two body interaction does not lead to a violation of the Cauchy symmetry in elastic constants. The condition forM-body interaction to satisfy Cauchy symmetry is discussed. For this purpose a simple expression for the contribution to the Brugger elastic constants in terms of theM-body force constants is derived. The advantage of the expression is that the force constants have to satisfy only the rotational and translational invariance conditions but not the equilibrium conditions.