An improved moving least squares method for the Material Point Method

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Conference article in proceedings
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Date
2019-01-10
Major/Subject
Mcode
Degree programme
Language
en
Pages
8
Series
Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019)
Abstract
The paper presents an improved moving least squares reconstruction technique for the Material Point Method. The moving least squares reconstruction (MLS) can improve spatial accuracy in simulations involving large deformations. However, the MLS algorithm relies on computing the inverse of the moment matrix. This is both expensive and potentially unstable when there are not enough material points to reconstruct the high-order least squares function, which leads to a singular or an ill-conditioned matrix. The shown formulation can overcome this limitation while retain the same order of accuracy compared with the conventional moving least squares reconstruction. Numerical experiments demonstrate the improvements in the accuracy and comparison with the original Material Point Method and the Convected Particles Domain Interpolation method.
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Keywords
Material Point Method, Moving least square, CPDI, improved moving least squares
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Citation
Tran , Q , Berzins , M & Sołowski , W T 2019 , An improved moving least squares method for the Material Point Method . in D Liang , K Kumar & A Rohe (eds) , Proceedings of the 2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction (MPM 2019) . , mpm2019.06 , Ocean Press , International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction , Cambridge , United Kingdom , 08/01/2019 .