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Materials 2017, 10(10), 1150; https://doi.org/10.3390/ma10101150

Comparison of a Material Point Method and a Galerkin Meshfree Method for the Simulation of Cohesive-Frictional Materials

1
International Center for Numerical Methods in Engineering (CIMNE), Edificio C1, Campus Norte, Jordi Girona 1-3, 08034 Barcelona, Spain
2
Department of Civil and Environmental Engineering (DECA), Technical University of Catalonia (UPC), Edificio C1, Campus Norte, Jordi Girona 1-3, 08034 Barcelona, Spain
*
Author to whom correspondence should be addressed.
Received: 28 July 2017 / Revised: 21 September 2017 / Accepted: 25 September 2017 / Published: 30 September 2017
(This article belongs to the Special Issue Computational Mechanics of Cohesive-Frictional Materials)
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Abstract

The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literatrue are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences from “standard” Updated Lagrangian (UL) approaches commonly employed by the Finite Elements (FE) community. Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM. On the other hand, the mesh-based MPM is demonstrated to be more robust and reliable for extremely large deformation cases. View Full-Text
Keywords: particle methods; nonlinear finite element method; implicit MPM; Galerkin Meshfree Method; cohesive-frictional materials particle methods; nonlinear finite element method; implicit MPM; Galerkin Meshfree Method; cohesive-frictional materials
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Iaconeta, I.; Larese, A.; Rossi, R.; Guo, Z. Comparison of a Material Point Method and a Galerkin Meshfree Method for the Simulation of Cohesive-Frictional Materials. Materials 2017, 10, 1150.

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