A new numerical implementation of a second-gradient model for plastic porous solids, with an application to the simulation of ductile rupture tests

An interesting second-gradient model for plastic porous solids, extending Gurson (1977)'s standard first-gradient model, was proposed by Gologanu et al. (1997) in order to settle the issue of unlimited localization of strain and damage and the ensuing mesh sensitivity in finite element calculations. Gologanu et al. (1997)'s model was implemented in a finite element code by Enakoutsa (2007); Enakoutsa and Leblond (2009). The implementation however rose two difficulties: (i) the number of degrees of freedom per node was awkwardly large because of the introduction of extra nodal degrees of freedom representing strains; (ii) convergence of the global elastoplastic iterations was often very difficult. A new implementation solving these problems is presented in this work. An original procedure of elimination of the nodal degrees of freedom representing the strains permits to reduce the number of degrees of freedom per node to its standard value. Also, the convergence issue is solved through use of normally integrated linear elements instead of more customary subintegrated quadratic ones. As an application, 2D numerical simulations of experiments of ductile rupture of a pre-notched and pre-cracked axisymmetric specimen and a CT specimen are performed. The calculations are pursued without difficulties up to a late stage of the rupture process, and the results are mesh-independent. Also, a good agreement between experimental and computed load-displacement curves is obtained for values of the parameters governing void coalescence compatible with those suggested by micromechanical numerical simulations, which could never be achieved in calculations based on Gurson (1977)'s standard model.