Numerical investigation of a particle system compared with first and second gradient continua: Deformation and fracture phenomena

A discrete system constituted of particles interacting by means of a centroid-based law is numerically investigated. Theelements of the system move in the plane, and the range of the interaction can be varied from a more local form(first-neighbours interaction) up to a generalized nth order interaction. The aim of the model is to reproduce thebehaviour of deformable bodies with standard (Cauchy model) or generalized (second gradient) deformation energydensity. The numerical results suggest that the considered discrete system can effectively reproduce the behaviour offirst and second gradient continua. Moreover, a fracture algorithm is introduced and some comparison between firstandsecond-neighbour simulations are provided.