Abstract
The author considers some versions of the deformation theory of plasticity, which takes into account the influence of hydrostatic stress and stress deviator type on the mechanical properties of a medium for the case of proportional loading. The emphasis is on the generalized statement of a nonlinear boundary-value problem and investigation of its solvability. Conditions have been determined that ensure the existence, uniqueness, and continuous dependence of the generalized solution on the loads applied.
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