The material point method (MPM) has demonstrated itself as an effective numerical method to simulate extreme events with large deformations including fracture problems. However, the traditional MPM encounters difficulties in simulating discontinuities due to its continuous nodal shape function. In this paper, The eXtended Material Point Method (XMPM) is proposed to simulate the three‐dimensional (3D) crack propagation. The XMPM modifies the particle displacement approximation by introducing the local enrichment functions based on the partition of unity into the MPM framework. To accurately trace the evolution of the crack surface, the XMPM employs both the level set method and an extra set of crack surface mesh, which is independent of the background grid. Only locally enriching the nodes near the crack makes the XMPM efficient and able to multiple cracks without extra tricks. Besides, a series of adaptive crack front processing methods, including crack front splitting, merging and locking with its meeting the material boundary, are developed in the XMPM framework to ensure the continuity and smoothness of the crack surface. Numerical examples demonstrate the capability of XMPM to simulate the discontinuity, calculate the fracture parameters and handle the evolution of the crack surface growth in 3D dynamic crack propagation.

中文翻译：

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三维裂纹问题的扩展材料点法

物质点方法（MPM）已经证明是一种有效的数值方法，可以模拟具有变形等大变形的极端事件，包括断裂问题。但是，传统的MPM由于具有连续的节点形状功能，因此在模拟不连续性时会遇到困难。在本文中，提出了扩展材料点方法（XMPM）来模拟三维（3D）裂纹扩展。XMPM通过在MPM框架中引入基于单位划分的局部富集函数来修改粒子位移近似值。为了精确跟踪裂纹表面的演变，XMPM同时使用了水平集方法和额外的一组裂纹表面网格，这些网格独立于背景网格。只有局部填充裂纹附近的节点才能使XMPM高效，并且能够在没有额外技巧的情况下进行多个裂纹。此外，在XMPM框架中开发了一系列自适应的裂纹前处理方法，包括裂纹前裂，合并和锁定以满足其材料边界，以确保裂纹表面的连续性和平滑性。数值算例说明了XMPM在3D动态裂纹扩展中模拟不连续性，计算断裂参数以及处理裂纹表面扩展的能力。是在XMPM框架中开发的，以确保裂纹表面的连续性和平滑性。数值算例说明了XMPM在3D动态裂纹扩展中模拟不连续性，计算断裂参数以及处理裂纹表面扩展的能力。是在XMPM框架中开发的，以确保裂纹表面的连续性和平滑性。数值算例说明了XMPM在3D动态裂纹扩展中模拟不连续性，计算断裂参数以及处理裂纹表面扩展的能力。