INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2002; 53:2701–2720 (DOI: 10.1002/nme.410) Implicit stress integration procedure for small and large strains of the Gurson material model Milos Kojic ∗; † , Ivo Vlastelica and Miroslav Zivkovic Faculty of Mechanical Engineering; University of Kragujevac; 34000 Kragujevac; Serbia SUMMARY The Gurson material model has broad applications in fracture mechanics, large strain deformations and failure of metals. Void growth and void nucleation are included in the model considered in this paper. An implicit stress integration procedure with calculation of the consistent tangent moduli is developed for the Gurson model. The general 3D deformations and the plane stress conditions are considered. The procedure is robust, simple and computationally ecient, suitable for use within the nite element method (FEM). It represents an application of the governing parameter method (GPM) for stress integration in case of inelastic material deformation. A large strain formulation, based on the multiplicative decomposition of the deformation gradient for material with plastic change of volume and logarithmic strains, is used in the paper. The developed numerical procedure for stress integration is applicable to small and large strains conditions. Solved examples illustrate the main features of the developed numerical algorithm. Copyright ? 2002 John Wiley & Sons, Ltd. KEY WORDS: stress calculation; Gurson model; large strains; nite element method 1. INTRODUCTION A commonly used assumption in metal plasticity is that plastic deformation is volume pre- serving. Material models representing this behaviour are of the von Misses and Hill’s type for isotropic and orthotropic material, described for example, in Mendelson [1] and Hill [2]. However, in case of large local plastic ow occurring in, for instance, processes of ductile fracture, void nucleation and void growth is observed. Then, permanent volumetric plastic strain develops and the hydrostatic stress independent plasticity models are not adequate to describe behaviour of the porous metals. 1.1. Model formulation The basic plasticity rate-independent model for porous metal was formulated by Gurson [3]. The yield criterion is developed by considering some simplied physical models of aggregates ∗ Correspondence to: M. Kojic, Faculty of Mechanical Engineering, University of Kragujevac, 34000 Kragujevac, Serbia † E-mail: kojic@knez.uis.kg.ac.yu Received 12 January 2000 Copyright ? 2002 John Wiley & Sons, Ltd. Revised 4 June 2001