Deformational theory of plasticity of transversely isotropic media

We propose a version of the theory of plasticity of transversely isotropic media for the case of simple loading. Our version is based on the concept of yield surface. We use a quadratic condition of yield that takes into account the partial effects of equivalent stresses computed according to von Mises and Hill and according to Tresca on the plastic deformation of the material. In the general case, this condition can be interpreted as a singular surface in the space of stresses. On the basis of the assumptions concerning the linearity of trajectories of plastic deformation and their normality to the initial yield surface under simple loading as well as concerning the existence of a relationship between the introduced equivalent stresses and equivalent plastic strains independent of the type of the stressed state, we deduce reversible master equations of plasticity. The adequacy of the proposed model is confirmed by the good agreement between the results of numerical analysis and experimental data.