Is the elastic energy of amorphous materials rotationally invariant ?

Abstract

It is shown that scalar, stress induced contributions to the elastic energy, which are not explicitly rotationally invariant can play an important rôle in determining the elastic properties of tenuous structures. Recent scaling results are used to show that the scalar contributions tend to be dominant at criticality It is argued that liquid-like hydrostatic stresses are large and will tend to lead to dominant scalar elasticity in many situations as they are known to do for rubbers. Some new results on the elastic properties of a Sierpinski gasket are presented in an appendix