A Path Criterion for Deformation Plasticity Theory

A loading path criterion is presented for total strain (or deformation) theory of plasticity based upon the associated loading function of Sanders. The considered state of stress is that corresponding to three-dimensional axisymmetric or plane strain problems. A simple geometric transformation of the yield surfaces enables the establishment of an analytic condition for determining the acceptability of stress paths predicted by the Hencky-Nadai total strain equations. The criterion is shown to be satisfied throughout the loading history of a longitudinally constrained, thermally loaded bar. A stiffness matrix iteration method is employed in the numerical solution.