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

TL;DR

This paper numerically investigates a particle system to model deformation and fracture phenomena, comparing it with first and second gradient continuum theories, and introduces a fracture algorithm for enhanced simulation accuracy.

Contribution

It presents a novel discrete particle model that effectively reproduces first and second gradient continuum behaviors, including fracture processes.

Findings

Discrete system reproduces continuum deformation behaviors

Model captures fracture phenomena effectively

Comparison between first- and second-neighbour interactions

Abstract

A discrete system constituted of particles interacting by means of a centroid-based law is numerically investigated. The elements 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 the behaviour of deformable bodies with standard (Cauchy model) or generalized (second gradient) deformation energy density. The numerical results suggest that the considered discrete system can effectively reproduce the behaviour of first and second gradient continua. Moreover, a fracture algorithm is introduced and some comparison between firstand second-neighbour simulations are provided.