An assessment of the Gurson yield criterion by a computational multi‐scale approach

Purpose Assess the Gurson yield criterion for porous ductile metals. Methodology A finite element procedure is used within a purely kinematical multi- scale constitutive modelling framework to determine estimates of extremal overall yield surfaces. The RVEs analysed consist of an elastic-perfectly plastic von Mises type matrix under plane strain conditions containing a single centered circular hole. Macroscopic yield surface estimates are obtained under three different RVE kine- matical assumptions: linear boundary displacements (an upper bound); periodic boundary displacement fluctuations (corresponding to periodically perforated me- dia); and, minimum constraint or uniform boundary traction (a lower bound). Findings The Gurson criterion predictions fall within the bounds obtained under relatively high void ratios - when the bounds lie farther apart. Under lower void ra- tios, when the bounds lie close together, the Gurson predictions of yield strength lie slightly above the computed upper bounds in regions of intermediate to high stress triaxiality. A modification to the original Gurson yield function is proposed that can capture the computed estimates under the three RVE kinematical constraints considered. Originality Assesses the accuracy of the Gurson criterion by means of a fully computational multi-scale approach to constitutive modelling. Provides an alterna- tive criterion for porous plastic media which encompasses the common microscopic