The deformation theory of plasticity of anisotropic media
Mutually inverse defining equations of the deformation theory of plasticity of media with arbitrary anisotropy are written assuming the relations between the stresses and deformations to be quasilinear. The conditions of plasticity and unloading are considered. Theorems are proved on the existence and uniqueness of solutions of the quasistatic problem of the deformation theory of plasticity and of simple loading. The method of successive approximations for solving the problem is considered, and its convergence is proved. Various means of simplifying the theory are considered. Theorems of minimum Lagrangian and the maximum of the Castiglianian are proved.
relations between the stresses and deformations
scientific article; zbMATH DE number 3904072