Deviatoric and hydrostatic mode interaction in hard and soft tissue

Abstract

It has been established that many hard and soft tissues have anisotropic material symmetries. These materials are contrasted with traditional structural metals which have isotropic material symmetry. It is noted here that the deviatoric and hydrostatic modes interact with each other in a general anisotropic elastic material. In the special case of isotropic, linear elastic, materials these modes are non-interactive. As a consequence of the interaction of these modes encountered in anisotropic materials, the decomposition into hydrostatic and deviatoric modes, and deviatoric mode concepts such as the von Mises effective stress are not appropriate for anisotropic materials in general. The implications of this observation for the presentation of computationally generated stress contours for hard and soft tissues are discussed. It is also pointed out that the mode coupling and mode interaction raise the question of whether anisotropic living tissues respond directly to stress or to some other physical quantity such as strain or strain energy, in view of the recent hypothesis concerning the proliferation and ossification of cartilage.