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

Antonio Battista (1) , Luigi Rosa (2) , Ramiro Dell'Erba (3) , Leopoldo Greco (1)

1 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
2 Dipartimento di Scienze Fisiche [Naples]
3 ENEA - Agenzia Nazionale per le nuove Tecnologie, l’energia e lo sviluppo economico sostenibile = Italian National Agency for New Technologies, Energy and Sustainable Economic Development

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 first-and second-neighbour simulations are provided.

Mots clés: Discrete mechanical systems; second gradient continua; fracture; generalized continua

Domaines: Physique mathématique [math-ph]

Antonio Battista, Luigi Rosa, Ramiro Dell'Erba, Leopoldo Greco. Numerical investigation of a particle system compared with first and second gradient continua: Deformation and fracture phenomena*. Mathematics and Mechanics of Solids, 2016, 22 (11), pp.2120-2134. ⟨10.1177/1081286516657889⟩. ⟨hal-01998612⟩