A Slip Model for Finite-Element Plasticity

Abstract

Conventional finite-element models are based on displacement or velocity fields which are at least continuous. However, it is known that perfectly plastic materials may exhibit discontinuities of the tangential velocity component along certain lines. In this investigation, a two-dimensional finite-element model is proposed which will allow for such discontinuities. A regular pattern of triangular elements is assumed. The elements are assumed to be rigid, and across the line separating any two adjoining elements the normal displacement component is continuous, but a discontinuity may exist in the tangential component. The defining equations—compatibility, equilibrium, and constitutive—are developed with the aid of the Principle of Virtual Work. Prandtl’s punch problem for contained flow is solved under plane strain conditions. Comparison is made with existing analytical and other numerical solutions, in order to evaluate the merits of allowing for discontinuities.