Abstract
Abstract. We present an efficient MATLAB-based implementation of the material point method (MPM) and its most recent variants. MPM has gained popularity over the last decade, especially for problems in solid mechanics in which large deformations are involved, such as cantilever beam problems, granular collapses and even large-scale snow avalanches. Although its numerical accuracy is lower than that of the widely accepted finite element method (FEM), MPM has proven useful for overcoming some of the limitations of FEM, such as excessive mesh distortions. We demonstrate that MATLAB is an efficient high-level language for MPM implementations that solve elasto-dynamic and elasto-plastic problems. We accelerate the MATLAB-based implementation of the MPM method by using the numerical techniques recently developed for FEM optimization in MATLAB. These techniques include vectorization, the use of native MATLAB functions and the maintenance of optimal RAM-to-cache communication, among others. We validate our in-house code with classical MPM benchmarks including (i) the elastic collapse of a column under its own weight; (ii) the elastic cantilever beam problem; and (iii) existing experimental and numerical results, i.e. granular collapses and slumping mechanics respectively. We report an improvement in performance by a factor of 28 for a vectorized code compared with a classical iterative version. The computational performance of the solver is at least 2.8 times greater than those of previously reported MPM implementations in Julia under a similar computational architecture.
Highlights
The material point method (MPM), developed in the 1990s (Sulsky et al, 1994), is an extension of a particle-in-cell (PIC) method to solve solid mechanics problems involving massive deformations
It is an alternative to Lagrangian approaches that is well suited to problems with large deformations involved in geomechanics, granular mechanics or even snow avalanche mechanics
As MPM and finite element method (FEM) are similar in their structure, we aim to improve the performance of MATLAB up to the level reported by Sinaie et al (2017) using the Julia language environment
Summary
The material point method (MPM), developed in the 1990s (Sulsky et al, 1994), is an extension of a particle-in-cell (PIC) method to solve solid mechanics problems involving massive deformations. It is an alternative to Lagrangian approaches (updated Lagrangian finite element method) that is well suited to problems with large deformations involved in geomechanics, granular mechanics or even snow avalanche mechanics. Bandara et al (2016), Bandara and Soga (2015), and Abe et al (2014) proposed a poro-elastoplastic MPM formulation to study levee failures induced by pore pressure increases. Baumgarten and Kamrin (2019), Dunatunga and Kamrin (2017), Dunatunga and Kamrin (2015), and Wieckowski (2004) proposed a general numerical framework of granular mechanics, i.e. silo discharge or granular collapses. Gaume et al (2019, 2018) proposed a unified numerical model in the finite deformation framework to study the whole process (i.e. from failure to propagation) of slab avalanche releases
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