Study of laws governing the elastoplastic deformation of transversely isotropic bodies

Equations of the theory of plasticity of anisotropic media were constructed earlier with the assumption of the existence of a plastic potential. We will examine a method of constructing the governing relations of the strain theory of elastoplastic deformation of transversely isotropic bodies without using the condition of the existence of a plastic potential and transverse incompressibility of the material. We will study a certain uniform orthotropic body connected with the orthogonal coordinate system 1, 2, 3, which coincides with the principal axes of anisotropy of the material. Let the components of the stress tensor σ be connected with the components of the strain tensor Ε by tensor-linear relations in the form of Hooke's law. The coefficients in these relations are variable.