Plain plastic strain for jump homogeneity (Q2541362)

In certain problems of plastic strain the material constants change in a jump-like fashion. The present paper is concerned with plane plastic strain where the yield limit changes across certain jump surfaces. The body is divided by a number of contact surfaces \(L\) into portions of varying yield limits. For example, two different materials are united by welding or by strong adhesion, etc.. The properties of the joints between the surfaces play a differentiating role. The usual set of equations is set up: incompressibility; coaxiality of stress deviator tensor and deformation rate tensor; the two Levy equations which take the place of two equilibrium conditions and a yield condition. The independent variables are orthogonal curvilinear coordinates with stress and velocity as dependent variables. The system is quasilinear with coefficients discontinuous across the \(L\)-lines. After a general analysis of the problem the case of a semi-infinite body acted on by a smooth rigid punch is considered as an example. The body is composed of two materials with different yield limits on the two sides of a straight separation line \(L\). The body is assumed so large that in the neighborhood of the punch the plastic flow can be treated as local.