A second-gradient model for porous ductile materials extending the standard GTN first-gradient model (Gurson, 1977; Tvergaard, 1981; Tvergaard and Needleman, 1984) was proposed by Gologanu et al. (1997), with the aim of solving the problem of potentially unlimited lo-calization of strain and damage resulting in mesh sensitivity in finite element computations. An efficient numerical implementation of Gologanu et al. (1997)'s model has been proposed by Bergheau et al. (2014), using an innovative procedure of elimination of the additional nodal degrees of freedom representing the strains ("nodal strains"). The aim of this paper is to present some new applications of the model and associated numerical algorithm. The first, relatively simple application consists of 2D numerical simulations of an experiment of ductile rupture of some pre-notched and pre-cracked CT specimen. The goal here is essentially to illustrate one major advantage of the procedure of elimination of the nodal strains, the possibility of easily mixing elements obeying first-and second-gradient models, and thus using the latter type of model only in those limited zones where it is really needed. The second, more complex application , concerns the 3D numerical simulation of crack propagation over a long distance in a multiphase material. The aim here is to illustrate the possibility of using the model, in spite of its sophistication, for the study of complex fracture problems of practical, industrial interest.