Applied and engineering versions of the theory of elastoplastic processes of active complex loading. Part 1: Conditions of mathematical well-posedness and methods for solving boundary value problems

In the proposed theory of plasticity, the deviator constitutive relation has a trinomial form (the vectors of stresses, stress rates, and strain rates, which are formed form the deviators, are coplanar) and contains two material functions; one of these functions depends on the modulus of the stress vector, and the other, on the angle between the stress vector and the strain rate, the length of the deformation trajectory arc, and the moduli of the stress and strain vectors. The spherical parts of the stress and strain tensors satisfy the relations of elastic variation in the volume.