Tensor-Nonlinear Constitutive Equations for an Elastic Body with Primary Anisotropy

A nonlinear elastic body with primary anisotropy is considered. It is assumed that the initial state of the body is equivalent to its natural state, while strains are small. The covariant components of the fourth rank anisotropy tensor are determined using the known dependences of all covariant components of the strain tensor on each contravariant component of the stress tensor. Relations between the covariant components of the strain tensor and the contravariant components of the stress tensor, which coincide with the Reiner relations in the case of an isotropic body are proposed. Based on these relations and Richter’s method, tensor-nonlinear constitutive equations are derived. Conditions defining the relations between the covariant components of the strain tensor and the contravariant components of the stress tensor are indicated.