On bifurcation in elastic-plastic solids

In Shanley's model of bifurcation, a perturbed motion is assumed to occur with increasing co-axial load. In this paper a new approach is used to derive constitutive equations during perturbed motion of inelastic solids; specifically, the rotation of principal stress axes due to stress-increment is considered and its effect on subsequent plastic deformation is allowed for. The basis for the derivation is (i) Levy-von Mises flow rule, and (ii) the dependence of total plastic strain-increments on the loading path. It is found, as a result, that the incipient value of the shear modulus in the constitutive relation could be lower than the elastic value. (Auth.)