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

Antonio Battista, Luigi Rosa+2 more|arXiv (Cornell University)|Apr 10, 2020

Nonlocal and gradient elasticity in micro/nano structuresMaterials Science55 references31 citations

TL;DR

The paper numerically analyzes a discrete particle system with centroid-based interactions to reproduce deformation energies of first and second gradient continua and introduces a fracture algorithm, comparing local and nonlocal interaction ranges.

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.

Motivation & Objective

• Motivate a discrete particle model that can reproduce deformation behavior of standard (Cauchy) and generalized (second gradient) continua.
• Explore how interaction range (from first-neighbours to higher-order) affects deformation and fracture phenomena.
• Assess the extent to which the discrete system can emulate first- and second-gradient continuum responses.

Proposed method

• Simulate a planar particle system with centroid-based interaction laws.
• Vary the interaction range from local (first-neighbours) to generalized nth-order interactions.
• Compare discrete results to predictions of first- and second-gradient continuum energy densities.
• Introduce a fracture algorithm for the discrete system and analyze fracture patterns.
• Perform comparisons between first- and second-neighbour simulations to evaluate nonlocal effects.

Experimental results

Research questions

• RQ1 Can a centroid-based discrete particle system reproduce the deformation behavior of first-gradient (Cauchy) continua?
• RQ2 Can it reproduce second-gradient (generalized) continuum deformation energy?
• RQ3 How does increasing interaction range influence deformation and fracture phenomena in the discrete model?
• RQ4 What fracture behavior emerges when applying the fracture algorithm to the discrete system, and how does it compare to continuum predictions?

Key findings

• The discrete particle system can effectively reproduce the behavior of first-gradient continua.
• The discrete system can also reproduce aspects of second-gradient continuum behavior.
• A fracture algorithm is successfully introduced for the particle system.
• Comparisons between first- and second-neighbour simulations illustrate the effects of interaction range on deformation and fracture.