- Title
- A simple time stepping algorithm for material point method
- Creator
- Sołowski, Wojciech T.; Sheng, Daichao
- Relation
- 7th European Conference on Numerical Methods in Geotechnical Engineering, 2010 (NUMGE 2010). Proceedings of the 7th European Conference on Numerical Methods in Geotechnical Engineering (Trondheim, Norway 2-4 June, 2010) p. 157-162
- Relation
- http://www.crcpress.com/product/isbn/9780415592390
- Publisher
- CRC Press/Balkema
- Resource Type
- conference paper
- Date
- 2010
- Description
- The Material Point Method (MPM) is an emerging numerical method that provides a natural solution to dynamic problems involving large deformation and contact/impact. However, the method can be prohibitively time consuming because extremely small time steps often have to be used to obtain a reliable solution. The paper presents an adaptive time stepping algorithm with error control for the material point method. The proposed approach is based on an error estimate derived from the global energy. This error estimate is then used to control the time step size. The proposed algorithm is validated for a 1D dynamic problem involving impact of two elastic bars. The proposed time stepping algorithm seems to be able to recover the correct solution with arbitrary step sizes specified by the user. As such, it is hoped that the proposed algorithm may offer a way to overcome some of the shortcomings of the MPM. A conceptually similar algorithm may be used for 2D & 3D problems with more advanced boundary conditions and material models.
- Subject
- time stepping algorithm; material point method; large deformation solutions; impact problems solutions
- Identifier
- http://hdl.handle.net/1959.13/935840
- Identifier
- uon:12146
- Identifier
- ISBN:9780415592390
- Language
- eng
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