An approximate yield criterion for voided nonlinear materials

Abstract

An approximate yield criterion (Eq. (40)) for voided nonlinear materials is proposed in which the effect of material hardening is directly included. The matrix is assumed to be a power-law material and approximate velocity fields for the matrix are employed to derive the yield function. Analysis indicates that the shape of yield surface in stress space expands along with increasing strain-hardening exponent N. For N = 0, the Gurson yield function is derived. And as N = 1, an analytical expression of the yield function in the form of ellipsoid is obtained. Furthermore, as 0 < N < 1, an approximate expression for the yield function is suggested. A comparison between the approximate yield function and Cocks' model (1989) is carried out. The agreement of the two models is very good.