Abstract The total Lagrangian Material Point Method (TLMPM) is an efficient formulation of the well known Material Point Method (MPM). Unlike the MPM, it is not subject to cell-crossing instabilities or numerical failure, and features better quadrature. However, the TLMPM is unable to model (no-slip) contacts seamlessly as the standard updated Lagrangian MPM. This paper presents a contact algorithm for the TLMPM able to model contacts with or without friction. Its performance is tested and compared to the standard MPM using five different tests that are popular problems from the MPM literature. Even when using simple hat weighting functions, and unlike in the MPM, the stress field in the TLMPM is fairly smooth and with this algorithm, there is no gap between two surfaces in contact. Moreover, there are less energy losses, and less error in the predicted forces.

中文翻译：

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用全拉格朗日材料点法模拟接触

摘要 总拉格朗日质点法 (TLMPM) 是众所周知的质点法 (MPM) 的有效公式。与 MPM 不同，它不受单元交叉不稳定性或数值失败的影响，并具有更好的正交性。然而，TLMPM 无法像标准更新的拉格朗日 MPM 那样无缝地建模（无滑动）接触。本文提出了一种 TLMPM 的接触算法，能够对有或没有摩擦的接触进行建模。使用 MPM 文献中常见的五种不同测试，测试其性能并与标准 MPM 进行比较。即使使用简单的帽子加权函数，与 MPM 不同，TLMPM 中的应力场也相当平滑，并且使用此算法，两个接触表面之间没有间隙。此外，能量损失更少，