On Additional Tensor Symmetry Relation in the Mathematical Theory of Perfect Plasticity

The paper presents fundamental principles of the mathematical theory of plasticity for spatial states, corresponding to an edge of the Coulomb–Tresca prism, when the flow of a body is governed by generalized associated flow rule. A detailed analysis is provided for the relations resulting from the generalized flow rule for an isotropic body, associated with the Tresca yield condition, and restricting the freedom of plastic flow to the minimum extent for the specified states. It has been shown that the spatial relations of plasticity theory formulated by A.Yu. Ishlinskii in 1946 follow from the generalized version of the flow theory. It has been established that the constitutive relations of Ishlinskii for the states on the edge of the Coulomb–Tresca prism express the commutativity of the stress and plastic strain increment tensors. An additional tensor symmetry relation is obtained by applying this commutativity relation.