Generalized solutions in the theory of plasticity
The present paper shows that certain generalization of the Mises principle makes it possible to impart to the inequality expressing it a divergent form and enables us to write it in integral form. From this it follows that in the incompressible plastic medium the surface of discontinuity in the tangential velocity component serves as the surface of maximum tangential stresses, with tangential stress directed along the velocity jump vector. In a compressible plastic medium the stress discontinuity is determined from the condition that the direction of the six-dimensional deformation velocity ``vector'' is continuous. The problem considered here is that of steady motion of a strip of finite thickness undergoing pure shear, in a rigid-plastic hardening medium. The emission of heat caused by plastic deformation and its effect on the functions of state and the forces of inertia are all taken into account. It is shown that under certain specified conditions the strip thickness may tend to zero, i.e. the appearance of isothermal velocity discontinuities is possible. The adiabatic and quasistatic cases are discussed.
scientific article; zbMATH DE number 4031130