Numerical implementation and assessment of the GLPD micromorphic model of ductile rupture

Just like all constitutive models involving softening, Gursonʹs classical model for porous ductile solids predicts unrealistic, unlimited localization of strain and damage. An improved variant of this model aimed at solving this problem has been proposed by Gologanu, Leblond, Perrin and Devaux (GLPD) on the basis of some refinement of Gursonʹs original homogenization procedure. The GLPD model is of “micromorphic” nature since it involves the second gradient of the macroscopic velocity and generalized macroscopic stresses of “moment” type, together with some characteristic “microstructural distance”. This work is devoted to its numerical implementation and the assessment of its practical relevance. This assessment is based on two criteria: absence of mesh size effects in finite element computations and agreement of numerical and experimental results for some typical experiments of ductile fracture. The GLPD model is found to pass both tests. It is therefore concluded that it represents a viable, although admittedly complex solution to the problem of unlimited localization in Gursonʹs model of ductile rupture.