Moving least squares reconstruction for B-spline Material Point Method

Abstract

The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). B-spline MPM have shown to reduce the grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the grid-crossing occurs frequently, the B-spline MPM suffered from the reduction of spatial convergence rate of the numerical solution. In this paper, moving least squares reconstruction is employed to retrieve the expected convergence rate of the numerical solutions. The proposed formulation version is examined in terms of the spatial convergence using the method of manufactured solutions for large deformations.