Il’yushin's particular postulate and nonlinear relations for anisotropic bodies

A review of the works devoted to the theoretical study and experimental verification of one of the fundamental hypotheses of the theory of processes by A. A. Ilyushin — a particular postulate of isotropy as well as the possibility of its generalization to initially anisotropic materials is fulfilled. A formulation of such a generalization is proposed using the concept of invariant subspaces of the symmetry group of an anisotropic material. As an example, within the framework of the proposed generalization, nonlinear constitutive relations for an elastic orthotropic material are constructed.