Numerical implementation and assessment of a phenomenological nonlocal model of ductile rupture

Abstract

Just like all constitutive models involving softening, Gurson’s [A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: Part I – Yield criteria and flow rules for porous ductile media, ASME J. Engrg. Mater. Technol. 99 (1977) 2–15] model of ductile rupture predicts unlimited localization of strain and damage. Leblond et al.’s [J.B. Leblond, G. Perrin, J. Devaux, Bifurcation effects in ductile metals with nonlocal damage, ASME J. Appl. Mech. 61 (1994) 236–242] have proposed to solve this problem in a heuristic way by using a nonlocal evolution equation for the porosity, which expresses its time-derivative as a spatial convolution integral of some “local porosity rate”. This paper is devoted to the numerical implementation and assessment of this phenomenological variant of Gurson’s model. The numerical implementation proposed bears some resemblance to Aravas’s [N. Aravas, On the numerical integration of a class of pressure-dependent plasticity models, Int. J. Numer. Methods Engrg. 24 (1987) 1395–1416] classical one but departs from it through use of an explicit algorithm with respect to the porosity, if not with respect to other parameters. The main reason for this choice lies in the proof of existence and uniqueness, for such an algorithm, of the solution of the “projection problem” onto Gurson’s yield locus. The assessment of the model is based on two criteria, absence of mesh size effects in finite element computations and agreement of experimental and numerical results for some typical ductile fracture tests. Since the first topic has already been investigated by Tvergaard and Needleman’s [V. Tvergaard, A. Needleman, Effects of nonlocal damage in porous plastic solids, Int. J. Solids Struct. 32 (1995) 1063–1077], we concentrate on the second one. Unfortunately, numerical experience reveals that the modification of Gurson’s model envisaged degrades the agreement between experimental results and model predictions. A theoretical analysis of this phenomenon is presented. Although based on crude simplifying assumptions, this analysis suffices to qualitatively explain the failure of the model and suggest a simple remedy. Numerical experience confirms that this remedy considerably improves numerical predictions. Thus, with this modification, Leblond et al. (1994)’s proposal appears as a viable solution to the problem of unlimited localization of strain and damage in Gurson (1997)’s model.