On necessary and sufficient conditions of strong ellipticity of equilibrium equations for certain classes of anisotropic linearly elastic materials

Abstract

Within the framework of linear elasticity of anisotropic solids, the strong ellipticity (SE) condition is discussing. In this paper, the SE‐condition is deriving for 19 classes of 32 known ones of anisotropy. For each class SE‐condition reduces to a finite set of elementary inequalities. As a special case, incompressible materials are also considered.