Controlling the onset of numerical fracture in parallelized implementations of the material point method (MPM) with convective particle domain interpolation (CPDI) domain scaling

Abstract

SummaryThe material point method is well suited for large‐deformation problems in solid mechanics but requires modification to avoid cell‐crossing errors as well as extension instabilities that lead to numerical (nonphysical) fracture. A promising solution is convected particle domain interpolation (CPDI), in which the integration domain used to map data between particles and the background grid deforms with the particle, based on the material deformation gradient. While eliminating the extension instability can be a benefit, it is often desirable to allow material separation to avoid nonphysical stretching. Additionally, large stretches in material points can complicate parallel implementation of CPDI if a single particle domain spans multiple computational patches. A straightforward modification to the CPDI algorithm allows a user‐specified scaling of the particle integration domain to control the numerical fracture response, which facilitates parallelization. Combined with particle splitting, the method can accommodate materials with arbitrarily large failure strains. Used with a smeared damage/softening model, this approach will prevent nonphysical numerical fracture in situations where the material should remain intact, but the effect of a single velocity field on localization may still produce errors in the post‐failure response. Details are given for both 2‐D and 3‐D implementations of the scaling algorithm. Copyright © 2015 John Wiley & Sons, Ltd.