An Extended B‐Spline‐Based Material Point Method for Contact Problems

ABSTRACT A novel Material Point Method (MPM) is introduced for addressing contact problems. In contrast to the standard multi‐velocity field approach, this method employs a penalty method to evaluate contact forces at the discretised boundaries of their respective physical domains. This enhances simulation fidelity by accurately considering the deformability of the contact surface and preventing fictitious gaps between bodies in contact. Additionally, the method utilises the Extended B‐Splines (EBSs) domain approximation, providing two key advantages. First, EBSs robustly mitigate grid cell‐crossing errors by offering continuous gradients of the basis functions on the interface between adjacent grid cells. Second, numerical integration errors are minimised, even with small physical domains in occupied grid cells. The proposed method's robustness and accuracy are evaluated through benchmarks, including comparisons with analytical solutions, other state‐of‐the‐art MPM‐based contact algorithms, and experimental observations from the literature. Notably, the method demonstrates effective mitigation of stress errors inherent in contact simulations.