Vector-based model of elastic bonds for DEM simulation of solids

TL;DR

This paper introduces a vector-based elastic bond model for discrete element method simulations, enabling accurate representation of bond stiffnesses and flexible calibration for various bond geometries and behaviors.

Contribution

The paper presents a novel vector-based bond model with explicit formulas linking model parameters to physical bond stiffnesses, allowing precise simulation of elastic bonds in DEM.

Findings

Model accurately describes bond stiffnesses in simulations.

Calibration procedures adapt to bond length/thickness ratios.

Simulations demonstrate effectiveness in buckling problems.

Abstract

A new model for computer simulation of solids, composed of bonded rigid body particles, is proposed. Vectors rigidly connected with particles are used for description of deformation of a single bond. The expression for potential energy of the bond and corresponding expressions for forces and moments are proposed. Formulas, connecting parameters of the model with longitudinal, shear, bending and torsional stiffnesses of the bond, are derived. It is shown that the model allows to describe any values of the bond stiffnesses exactly. Two different calibration procedures depending on bond length/thickness ratio are proposed. It is shown that parameters of model can be chosen so that under small deformations the bond is equivalent to either Bernoulli-Euler rod or Timoshenko rod or short cylinder connecting particles. Simple expressions, connecting parameters of V-model with geometrical and mechanical characteristics of the bond, are derived. Computer simulation of dynamical buckling of the straight discrete rod and half-spherical shell is carried out.