TY - JOUR
T1 - A Convected Particle Least Square Interpolation Material Point Method
AU - Tran, Quoc Anh
AU - Sołowski, Wojciech Tomasz
AU - Berzins, Martin
AU - Guilkey, James
PY - 2020/3/30
Y1 - 2020/3/30
N2 - Applying the Convected Particle Domain Interpolation (CPDI) to the Material Point Method has many advantages over the original Material Point Method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The Convected Particle Least Square Interpolation (CPLS) Material Point Method assumes the velocity field inside the material point domain as non‐constant. This velocity field in the material point domain is mapped to the background grid nodes with a Moving Least Squares reconstruction. In this paper, we apply the Improved Moving Least Squares method to avoid the instability of the conventional Moving Least Squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the Method of Manufactured Solutions.
AB - Applying the Convected Particle Domain Interpolation (CPDI) to the Material Point Method has many advantages over the original Material Point Method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The Convected Particle Least Square Interpolation (CPLS) Material Point Method assumes the velocity field inside the material point domain as non‐constant. This velocity field in the material point domain is mapped to the background grid nodes with a Moving Least Squares reconstruction. In this paper, we apply the Improved Moving Least Squares method to avoid the instability of the conventional Moving Least Squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the Method of Manufactured Solutions.
KW - convected particle domain interpolation
KW - improved moving least squares
KW - material point method
KW - methods of manufactured solution
KW - moving least squares
KW - numerical convergence
UR - http://www.scopus.com/inward/record.url?scp=85075746103&partnerID=8YFLogxK
U2 - 10.1002/nme.6257
DO - 10.1002/nme.6257
M3 - Article
VL - 121
SP - 1068
EP - 1100
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 6
ER -