A generalized projection algorithm for overcoming volumetric locking in explicit material point method

doi:10.1016/j.compgeo.2025.107391

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A generalized projection algorithm for overcoming volumetric locking in explicit material point method

2025-06-06

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陈祥胜 (Xiangsheng Chen)

DOI：10.1016/j.compgeo.2025.107391

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Abstract

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The Material Point Method (MPM) frequently encounters volumetric locking when simulating nearly incompressible materials, primarily due to an improper discretization strategy. For example, the combination of a low-order grid with numerous material points (used to enhance integration accuracy) results in a mismatch between the integration points and the grid degrees of freedom, leading to an over-constrained system. Existing mitigation approaches are typically limited by specific material models, applicable only to certain MPM formulations, or require significant modifications to current MPM algorithms. To address this issue, this study proposes a generalized projection algorithm that performs exceptionally well for explicit MPM. The proposed algorithm requires only minimal modifications to the original MPM formulation by introducing an additional sparse projection grid and performing mapping and remapping corrections of the material points’ volumetric strains on this grid. The projection process imposes no restrictions on the choice of basis functions (i.e., the MPM versions used) and, for different material models, only requires the extraction and projection of volumetric strain components. The proposed method is not only applicable to any form of MPM but also suitable for a variety of material models, including small deformations, finite deformations, and weakly compressible fluids. Compared to previous standard MPM, a slight increase in computational cost caused by grid projection is acceptable. The accuracy of projection algorithm is investigated, and the optimal configuration of the projection grid is discussed via a series of benchmark examples. Additionally, aspects such as computational efficiency and broad applicability are thoroughly examined. All results demonstrate that the proposed method can predict accurate displacement and stress fields in the simulation of incompressible materials, confirming that the proposed MPM method effectively mitigates volumetric locking.