Analysis and mitigation of spatial integration errors for the material point method
The material point method (MPM) is a robust numerical simulation approach for continuum mechanics problems involving large material deformations coupled to changing surface topographies. These types of problems are present in many different engineering contexts, from understanding the failure proces...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2024
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| Online Access: | https://hdl.handle.net/1721.1/153533 |
| _version_ | 1810987658472587264 |
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| author | Baumgarten, Aaron S. Kamrin, Ken |
| author_facet | Baumgarten, Aaron S. Kamrin, Ken |
| author_sort | Baumgarten, Aaron S. |
| collection | MIT |
| description | The material point method (MPM) is a robust numerical simulation approach for continuum mechanics problems involving large material deformations coupled to changing surface topographies. These types of problems are present in many different engineering contexts, from understanding the failure processes of earthen slopes to predicting the strengths and failure mechanisms of body armor to modeling the impact forces of waves in fluid tanks. By using a set of persistent material point tracers to follow the motion and deformation of the continuum material while solving the equations of motion on a static simulation grid, the MPM avoids several shortcomings of more traditional numerical approaches including blurring of material surfaces — as in Eulerian finite element or finite volume methods (FEMs or FVMs) — and mesh tangling — as in Lagrangian FEMs. Despite its robustness, MPM is known to develop significant numerical errors: namely, (i) the particle ringing instability and (ii) solution dependent discretization and integration errors. In this work, we present an analysis of local‐in‐time, spatial integration errors in the MPM and several techniques designed to mitigate these errors. Error mitigation approaches previously described in the literature are compared to a new method we propose for problems involving very large material deformations. The proposed method is shown to offer substantial improvement over standard MPM for simulations of fluid‐like materials without requiring significant augmentation of existing MPM frameworks. |
| first_indexed | 2024-09-23T11:53:37Z |
| format | Article |
| id | mit-1721.1/153533 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:53:37Z |
| publishDate | 2024 |
| publisher | Wiley |
| record_format | dspace |
| spelling | mit-1721.1/1535332024-02-16T03:39:19Z Analysis and mitigation of spatial integration errors for the material point method Baumgarten, Aaron S. Kamrin, Ken Applied Mathematics General Engineering Numerical Analysis The material point method (MPM) is a robust numerical simulation approach for continuum mechanics problems involving large material deformations coupled to changing surface topographies. These types of problems are present in many different engineering contexts, from understanding the failure processes of earthen slopes to predicting the strengths and failure mechanisms of body armor to modeling the impact forces of waves in fluid tanks. By using a set of persistent material point tracers to follow the motion and deformation of the continuum material while solving the equations of motion on a static simulation grid, the MPM avoids several shortcomings of more traditional numerical approaches including blurring of material surfaces — as in Eulerian finite element or finite volume methods (FEMs or FVMs) — and mesh tangling — as in Lagrangian FEMs. Despite its robustness, MPM is known to develop significant numerical errors: namely, (i) the particle ringing instability and (ii) solution dependent discretization and integration errors. In this work, we present an analysis of local‐in‐time, spatial integration errors in the MPM and several techniques designed to mitigate these errors. Error mitigation approaches previously described in the literature are compared to a new method we propose for problems involving very large material deformations. The proposed method is shown to offer substantial improvement over standard MPM for simulations of fluid‐like materials without requiring significant augmentation of existing MPM frameworks. 2024-02-15T22:05:07Z 2024-02-15T22:05:07Z 2023-02-28 2024-02-15T21:59:00Z Article http://purl.org/eprint/type/JournalArticle 0029-5981 1097-0207 https://hdl.handle.net/1721.1/153533 Baumgarten AS, Kamrin K. Analysis and mitigation of spatial integration errors for the material point method. Int J Numer Methods Eng. 2023; 124(11): 2449–2497. en 10.1002/nme.7217 International Journal for Numerical Methods in Engineering Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ application/pdf Wiley Wiley |
| spellingShingle | Applied Mathematics General Engineering Numerical Analysis Baumgarten, Aaron S. Kamrin, Ken Analysis and mitigation of spatial integration errors for the material point method |
| title | Analysis and mitigation of spatial integration errors for the material point method |
| title_full | Analysis and mitigation of spatial integration errors for the material point method |
| title_fullStr | Analysis and mitigation of spatial integration errors for the material point method |
| title_full_unstemmed | Analysis and mitigation of spatial integration errors for the material point method |
| title_short | Analysis and mitigation of spatial integration errors for the material point method |
| title_sort | analysis and mitigation of spatial integration errors for the material point method |
| topic | Applied Mathematics General Engineering Numerical Analysis |
| url | https://hdl.handle.net/1721.1/153533 |
| work_keys_str_mv | AT baumgartenaarons analysisandmitigationofspatialintegrationerrorsforthematerialpointmethod AT kamrinken analysisandmitigationofspatialintegrationerrorsforthematerialpointmethod |