An Implicit Compact-Kernel Material Point Method for Computational Solid Mechanics
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| Format: | Preprint |
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2026
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| _version_ | 1866913050724925440 |
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| author | Fu, Qirui Jiang, Yupeng Li, Minchen |
| author_facet | Fu, Qirui Jiang, Yupeng Li, Minchen |
| contents | The numerical performance of the material point method (MPM) is strongly governed by the particle-grid kernel, which controls the trade-off among smoothness, locality, numerical diffusion, contact accuracy, and computational cost. Although wide-support smooth kernels can effectively suppress cell-crossing instability, they often introduce increased numerical diffusion, artificial contact gaps, and higher transfer cost. In contrast, the suitability of compact-kernel designs for implicit computational solid mechanics remains unclear. In this work, we develop an implicit formulation of the Compact-Kernel Material Point Method (CK-MPM) and assess its performance through benchmark problems in linear and nonlinear solid mechanics, including cantilever bending, Hertzian contact, narrow-clearance free fall, and colliding hyperelastic rings. The results show that implicit CK-MPM retains the advantages of compact support while preserving the smoothness required for robust large-deformation simulation. Compared with linear MPM, it reduces cell-crossing-induced stress noise and excessive numerical dissipation; compared with quadratic B-spline MPM, it improves contact locality and reduces artificial contact gaps and early-contact artifacts while maintaining comparable overall smoothness and accuracy. These results indicate that CK-MPM provides a viable implicit MPM framework for computational mechanics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_18917 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Implicit Compact-Kernel Material Point Method for Computational Solid Mechanics Fu, Qirui Jiang, Yupeng Li, Minchen Computational Engineering, Finance, and Science Numerical Analysis Computational Physics The numerical performance of the material point method (MPM) is strongly governed by the particle-grid kernel, which controls the trade-off among smoothness, locality, numerical diffusion, contact accuracy, and computational cost. Although wide-support smooth kernels can effectively suppress cell-crossing instability, they often introduce increased numerical diffusion, artificial contact gaps, and higher transfer cost. In contrast, the suitability of compact-kernel designs for implicit computational solid mechanics remains unclear. In this work, we develop an implicit formulation of the Compact-Kernel Material Point Method (CK-MPM) and assess its performance through benchmark problems in linear and nonlinear solid mechanics, including cantilever bending, Hertzian contact, narrow-clearance free fall, and colliding hyperelastic rings. The results show that implicit CK-MPM retains the advantages of compact support while preserving the smoothness required for robust large-deformation simulation. Compared with linear MPM, it reduces cell-crossing-induced stress noise and excessive numerical dissipation; compared with quadratic B-spline MPM, it improves contact locality and reduces artificial contact gaps and early-contact artifacts while maintaining comparable overall smoothness and accuracy. These results indicate that CK-MPM provides a viable implicit MPM framework for computational mechanics. |
| title | An Implicit Compact-Kernel Material Point Method for Computational Solid Mechanics |
| topic | Computational Engineering, Finance, and Science Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2604.18917 |