TY - JOUR
T1 - Extension of B-spline Material Point Method for unstructured triangular grids using Powell–Sabin splines
AU - de Koster, Pascal
AU - Tielen, Roel
AU - Wobbes, Elizaveta
AU - Möller, Matthias
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - B-splines
KW - Grid-crossing error
KW - Material Point Method
KW - Powell–Sabin splines
KW - Unstructured grids
UR - http://www.scopus.com/inward/record.url?scp=85082929389&partnerID=8YFLogxK
U2 - 10.1007/s40571-020-00328-3
DO - 10.1007/s40571-020-00328-3
M3 - Article
AN - SCOPUS:85082929389
SN - 2196-4378
VL - 8 (2021)
SP - 273
EP - 288
JO - Computational Particle Mechanics
JF - Computational Particle Mechanics
IS - 2
ER -