On the numerical integration of an advanced Gurson model

This article is focused on a new extended version of Gurson's model (J. Eng. Mater. Technol. 1977; 99:2–15), its numerical integration scheme and its consistent tangent matrix being within an FE code. First, this new advanced Gurson model is proposed, which is an extension of the original to take into account plastic anisotropy and mixed (isotropic+kinematic) hardening. In this paper, only the growth phase of cavities is considered (the nucleation of new voids is ignored). Second, a new numerical algorithm for the integration of this new Gurson model is presented. The algorithm is implicit in all variables and is unconditionally stable. This algorithm is generic and could be used for other anisotropic yield functions and other hardening laws. Third, the consistent tangent matrix is computed in an explicit way by exact linearization of the constitutive equations. To check its efficiency and robustness, the proposed integration algorithm is compared, under some simplified assumptions and choices, with the algorithms of Aravas (Int. J. Numer. Meth. Engng 1987; 24:1395–1416) and Kojic (Int. J. Numer. Meth. Engng 2002; 53(12):2701–2720). The performance of the developed consistent modulus, compared to other techniques for the computation of the tangent matrix is assessed. The paper ends with numerical simulations of tensile tests on homogeneous and notched specimens.