Extension of B-spline Material Point Method for unstructured triangular grids using Powell–Sabin splines

Extension of B-spline Material Point Method for unstructured triangular grids using Powell–Sabin splines

de Koster, P.B.J. (TU Delft Team Raf Van de Plas)
Tielen, R.P.W.M. (TU Delft Numerical Analysis)
Wobbes, Elizaveta (TU Delft Numerical Analysis)
Möller, M. (TU Delft Numerical Analysis)

2020

The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of the piecewise-linear basis functions lead to the so-called grid-crossing errors when particles cross element boundaries. Previous research has shown that B-spline MPM (BSMPM) is a viable alternative not only to MPM, but also to more advanced versions of the method that are designed to reduce the grid-crossing errors. In contrast to many other MPM-related methods, BSMPM has been used exclusively on structured rectangular domains, considerably limiting its range of applicability. In this paper, we present an extension of BSMPM to unstructured triangulations. The proposed approach combines MPM with C¹-continuous high-order Powell–Sabin spline basis functions. Numerical results demonstrate the potential of these basis functions within MPM in terms of grid-crossing-error elimination and higher-order convergence.

B-splines
Grid-crossing error
Material Point Method
Powell–Sabin splines
Unstructured grids

http://resolver.tudelft.nl/uuid:8948f7c2-7c6a-447e-98e5-4b250087a263

https://doi.org/10.1007/s40571-020-00328-3

2196-4378

Computational Particle Mechanics, 8 (2021) (2), 273-288

Institutional Repository

journal article

© 2020 P.B.J. de Koster, R.P.W.M. Tielen, Elizaveta Wobbes, M. Möller