Basic Principles and the Limits of Applicability of the Theory of Plasticity Based on the Concept of Slip and Il’yushin’s Isotropy Postulate

We study a nonlinear differential version of the theory of plasticity satisfying the well-known fundamental principles and postulates of the mechanics of deformable body and taking into account the mechanism of inelastic deformation of materials. The results of analytic and numerical experiments demonstrate the possibility of application of the proposed theory of plasticity for the description of the inelastic deformation of polycrystalline materials under simple and complex loads. Special attention is given to the formulation and solution of the problems of stability of structural elements with regard for the memory of materials.