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A discrete system constituted of particles interacting by means of acentroid-based law is numerically investigated. The elements of the system movein the plane, and the range of the interaction can be varied from a more localform (first-neighbours interaction) up to a generalized nth order interaction.The aim of the model is to reproduce the behaviour of deformable bodies withstandard (Cauchy model) or generalized (second gradient) deformation energydensity. The numerical results suggest that the considered discrete system caneffectively reproduce the behaviour of first and second gradient continua.Moreover, a fracture algorithm is introduced and some comparison betweenfirstand second-neighbour simulations are provided.

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