Some new applications of a second-gradient model for porous ductile materials

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 localization 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. •This paper presents two new applications of a second-gradient extension of the famous GTN model for porous ductile solids, aimed at solving the issue of potentially unlimited localization of strain and damage, resulting in dependence of finite element results upon the mesh size.•The first application consists of 2D numerical simulations of an experiment of ductile rupture of some pre-notched and pre-cracked CT specimen. The goal is to illustrate 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 application concerns the 3D numerical simulation of crack propagation over a long distance in a multiphase material. The aim 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.