Abstract
Abstract In this contribution we compare the yield function of Gurson (Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth—I. Yield criteria and flow rules for porous ductile media. Engineering Materials Technology 99, 2–15), its extensions by Tvergaard (Tvergaard, V., 1981. Influence of voids on shear band instabilities under plane strain conditions. Int. J. Fract. 17, 389–407) and Tvergaard and Needleman (Tvergaard, V. Needleman, A., 1984. Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica 32, 157–169), and the yield function by Rousselier (Rousselier, G., 1987. Ductile fracture models and their potential in local approach of fracture. Nuclear Engineering and Design 105, 97–111), formulated for modeling metallic materials with varying induced porosity, with the single-surface model of Ehlers (Ehlers, W., 1995. A single-surface yield function for geomaterials. Archive of Applied Mechanics 65, 246–259), formulated for modeling geomaterials with constant porosity. It is shown, that though obtained from rather different perspectives, all formulations can be casted into a similar mathematical structure. Based on this analogy a new model class of yield functions for simulating isotropic ductile damage is proposed. As a special case the model structure of Green's (Green, R.J., 1972. A plasticity theory for porous solids. Int. J. Mech. Sci. 14, 215–224) ellipsoid is considered, with coefficients dependent on the void volume fraction. The formulation of the rate equations is performed in the spatial configuration based on the multiplicative decomposition of the deformation gradient. Furthermore numerical aspects are addressed concerning the integration of the constitutive relations and the finite element equilibrium iteration, and additionally the sensitivity terms for parameter identification are derived. Two examples illustrate the performance of the proposed strategy.
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