Abstract
SummaryThe discrete element method, developed by Cundall and Strack, typically uses some variations of the central difference numerical integration scheme. However, like all explicit schemes, the scheme is only conditionally stable, with the stability determined by the size of the time‐step. The current methods for estimating appropriate discrete element method time‐steps are based on many assumptions; therefore, large factors of safety are usually applied to the time‐step to ensure stability, which substantially increases the computational cost of a simulation. This work introduces a general framework for estimating critical time‐steps for any planar rigid body subject to linear damping and forcing. A numerical investigation of how system damping, coupled with non‐collinear impact, affects the critical time‐step is also presented. It is shown that the critical time‐step is proportional to if a linear contact model is adopted, where m and k represent mass and stiffness, respectively. The term which multiplies this factor is a function of known physical parameters of the system. The stability of a system is independent of the initial conditions. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.
Highlights
Contact mechanics primarily involves the analysis of the impulses and reaction forces that develop as a result of two or more bodies colliding or being in contact, and the governing dynamics which ensues [1,2,3,4]
The overall objective of this work is to improve upon existing guidelines for choosing appropriate time-steps for discrete element method (DEM) simulations using linear contact models
NUMERICAL RESULTS Here, we will focus on the numerical analysis of how the critical time-steps calculated in Section 4 are affected by the system parameters
Summary
Contact mechanics primarily involves the analysis of the impulses and reaction forces that develop as a result of two or more bodies colliding or being in contact, and the governing dynamics which ensues [1,2,3,4]. The understanding of the mechanics of contact has far-reaching applications in areas such as civil engineering, mechanical engineering, vehicle collision analysis and sport science [7]. One such method for modelling contact problems is the discrete element method (DEM) [8]. Using Newton’s second law together with Euler’s second law, the contact process can be described mathematically as a system of second-order differential equations (ODEs)
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