Elastoplastic model and theory of slipping for the three-dimensional stress state

On the basis of concepts of the Batdorf-Budyanskii theory of slipping, we construct a model of elastoplastic medium for the case of three-dimensional stress state. The slipping conditions on the unit site take into account the local yield criterion and the local loading criterion. Under certain assumptions, one can integrate the increments of plastic shears over all possible sites of slipping in the case of an arbitrary three-dimensional stress state and obtain the constitutive relations for the elastoplastic model, which is a version of the theory of plastic flow.