Coupling the Material Point Method (MPM) with the Finite Element Method (FEM) provides a powerful approach for addressing problems characterized by the coexistence of large and small deformations. The majority of existing MPM-FEM methods, which operate within the updated Lagrangian framework, introduce inherent issues, such as cell-crossing noise and numerical fracture, compromising the overall accuracy of the coupled method. This paper presents a coupled MPM-FEM method under a hybrid updated and total Lagrangian framework (HLFEMP). Within the HLFEMP, updated Lagrangian FEM is employed to handle small deformations, while total Lagrangian MPM is adopted to model large deformations. A particle-to-surface contact algorithm with auxiliary thickness layer is utilized to couple both methods. Notably, by imposing the weak form of total Lagrangian MPM in the undeformed configuration, HLFEMP is rendered free from cell-crossing noise and numerical fracture, resulting in better computational stability. The performance of HLFEMP in terms of energy behavior, accuracy, efficiency and stability under large elastic and elasto-plastic deformations are investigated through a series of numerical simulations.

中文翻译：

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HLFEMP：混合更新和总拉格朗日框架下的耦合 MPM-FEM 方法


将质点法 (MPM) 与有限元法 (FEM) 相结合，提供了一种强大的方法来解决大变形和小变形共存的问题。大多数现有的 MPM-FEM 方法在更新的拉格朗日框架内运行，会引入固有问题，例如单元交叉噪声和数值断裂，从而损害耦合方法的整体精度。本文提出了混合更新总拉格朗日框架（HLFEMP）下的耦合 MPM-FEM 方法。在 HLFEMP 中，采用更新的拉格朗日 FEM 来处理小变形，而采用总拉格朗日 MPM 来模拟大变形。利用具有辅助厚度层的颗粒与表面接触算法来耦合这两种方法。值得注意的是，通过在未变形配置中施加总拉格朗日 MPM 的弱形式，HLFEMP 不受单元交叉噪声和数值断裂的影响，从而获得更好的计算稳定性。通过一系列数值模拟研究了 HLFEMP 在大弹性和弹塑性变形下的能量行为、精度、效率和稳定性方面的性能。