Nonlinear effects at elastic deformation of cubic materials

Abstract

A variant of the relations of nonlinear elasticity is considered for anisotropic materials which are supposed to be crystals of cubic syngony with respect to the type of elastic symmetry. The proposed model takes into account the physical nonlinearity in the behavior of such materials under the condition of small deformations. Based on the representation of the elastic potential in the form of a tensor polynomial in third-order strains, relations for stresses with elastic constants of the second and third orders are obtained. On the basis of the concept of the elastic eigenstates of materials, in the case of a cubic material, representations for the elastic tensors of the fourth and sixth ranks in eigentensor bases are obtained. The proposed variant of constitutive relations takes into account the mutual influence of the processes occurring in various eigenspaces of cubic material.