An efficient and locking‐free material point method for three‐dimensional analysis with simplex elements

Abstract

The Material Point Method is a relative newcomer to the world of solid mechanics modelling. Its key advantage is the ability to model problems having large deformations while being relatively close to standard finite element methods, however its use for realistic engineering applications will happen only if the material point can be shown to be both efficient and accurate (compared to standard finite element methods), when modelling complex geometries with a range of material models. In this paper we present developments of the standard material point method aimed at realizing these goals. The key contribution provided here is the development of a material point method that avoids volumetric locking (arising from elastic or elasto-plastic material behavior) while using low-order tetrahedral finite elements for the background computational mesh, hence allowing unstructured background grids to be used for complex geometries. We also show that these developments can be effectively parallelized to improve computational efficiency.

Multiple‐GPU parallelization of three‐dimensional material point method based on single‐root complex

“…The explicit updated Lagrangian calculation in each incremental step was based on the uGIMP method 40,54 . Meshes with identical sizes of square elements were used, 18,41 and unstructured elements can be found in References 22 and 23. The definition of the stresses and strains followed finite strain theory taking account of the incremental rotation of the configurations between time steps for objectivity: the stresses were measured with the Cauchy stress and updated with the Jaumann rate, and the strains were calculated with the deformation gradient.…”

“…The MPM, introduced to solid mechanics 5 from computational fluid dynamics, 6 was used to simulate high explosive explosions, 7 propagation of wood cracks, 8 impact between solid bodies, 9–12 fluid–structure interactions, 13 and computer animations 14–16 . In the recent decade the MPM was applied to geotechnical engineering to investigate runout of submarine landslides, 17–20 penetration and pull‐out of structures 21–23 and flow of granular materials 24–26 . Coupling analysis of pore or free water and soil, mainly used in the analysis of slope stability, 27–30 is a new trend of the MPM simulations.…”

Ghost stabilisation of the material point method for stable quasi‐static and dynamic analysis of large deformation problems

“…35 This powerful combination is widely used in large deformation finite element methods 36 and several MPM implementations. 29,30,34,[37][38][39][40] These numerical implementations require the weak statement of equilibrium (1) to be discretised in space and time.…”

Overcoming Volumetric Locking in Three-Dimensional Material Point Analysis

“…The use of an unstructured background mesh increases the complexity (and potentially cost) of determining the element location of each material point. In this paper we adopt a modified version of the Walking-in-Triangulation (WiT) procedure of Devillers et al (2002) which, for an example problem containing 31,000 material points and elements, reduces the searching time to 0.054% of a naïve searching method based on local element positions (see Wang et al (2020) for details).…”