A modified bond model for describing isotropic linear elastic material behaviour with the particle method

TL;DR

This paper introduces a modified bond model for particle-based methods that accurately describes isotropic linear elastic materials across a full range of Poisson's ratios by coupling shear strain energy of neighboring bonds.

Contribution

The paper proposes a new bond model with coupled shear strain energy, overcoming previous Poisson's ratio restrictions in particle methods.

Findings

Model accurately predicts behavior for 0 ≤ ν < 0.5

Strain energy function is positive definite

Validated through various mechanical tests

Abstract

Particle based methods such as the Discrete Element Method and the Lattice Spring Method may be used for describing the behaviour of isotropic linear elastic materials. However, the common bond models employed to describe the interaction between particles restrict the range of Poisson's ratio that can be represented. In this paper, to overcome the restriction, a modified bond model that includes the coupling of shear strain energy of neighbouring bonds is proposed. The coupling is described by a multi-bond term that enables the model to distinguish between shear deformations and rigid-body rotations. The positive definiteness of the strain energy function of the modified bond model is verified. To validate the model, uniaxial tension, pure shear, pure bending and cantilever bending tests are performed. Comparison of the particle displacements with continuum mechanics solution demonstrates the ability of the model to describe the behaviour of isotropic linear elastic material for values of Poisson's ratio in the range $0 \leq \nu < 0.5$.