Nonlinear constitutive relations for anisotropic elastic materials

Abstract

A general approach to constructing of nonlinear variants of connection between stresses and strains in anisotropic materials with different types of symmetry of properties is considered. This approach is based on the concept of elastic proper subspaces of anisotropic materials introduced in the mechanics of solids by J. Rychlewski and on the particular postulate of isotropy proposed by A. A. Il’yushin.The generalization of the particular postulate on the case of nonlinear anisotropic materials is formulated. Systems of invariants of deformations as lengths of projections of the strain vector into proper subspaces are developed.Some variants of nonlinear constitutive relations for anisotropic materials are offered. The analysis of these relations from the point of view of their satisfaction to general and limit forms of generalization of partial isotropy postulate on anisotropic materials is performed. The relations for particular cases of anisotropy are written.