Analysis and mitigation of spatial integration errors for the material point method
Name
Numerical Meth Engineering - 2023 - Baumgarten - Analysis and mitigation of spatial integration errors for the material.pdf
Size
11.86 MB
Format
Adobe PDF
Checksum (MD5)
1ad9dd63138cb0b9a73590a7586ae142
Author(s)
Baumgarten, Aaron S.
Kamrin, Ken
Date Issued
February 28, 2023
Journal
International Journal for Numerical Methods in Engineering
Publisher
Wiley
Citation
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.
Version
Final published version
Abstract
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.
Subjects
Applied Mathematics
General Engineering
Numerical Analysis
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1002/nme.7217
