Material point method with enriched shape function for crack problems
Material point method with enriched shape function for crack problems
复制标题
具有丰富形函数的裂纹问题质点法
DOI：
10.1016/j.cma.2017.05.012
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发表时间：
2017-08
影响因子：
7.2
通讯作者：
Liu Yan
中科院分区：
文献类型：
--
作者：
Liang Yong;Benedek Tamas;Zhang Xiong;Liu Yan
在MPM/GIMP框架下，提出了一种具有丰富形状函数的物质点法/广义插值物质点法（简称EMPM/EGIMP）。基于扩展有限元法（XFEM）思想的EMPM/EGIMP丰富了节点自由度。这种改进使得位移和速度不连续的裂纹问题只用一组背景网格来模拟，从而不需要多网格和多速度场。此外，我们开发的质量矩阵块化技术使得EMPM/EGIMP可以很容易地在传统的MPM/GIMP代码中实现。如果没有裂纹，则EMPM/EGIMP退化为常规的MPM/GIMP。在EMPM/EGIMP中，采用水平集法（LSM）方便地跟踪裂纹表面。裂纹随材料点的物理移动，使得LSM函数由粒子携带。在每个时间步，LSM函数值从粒子映射到网格节点，从网格节点LSM函数值可以方便地识别待富集的节点。通过应力场分布、断裂参数计算和裂纹扩展的数值实验验证了所提出的EMPM/EGIMP方法。
A material point method (MPM)/generalized interpolation material point method (GIMP) with enriched shape function (EMPM/EGIMP for short) is proposed for modelling crack problems in the MPM/GIMP framework. The EMPM/EGIMP enriches the nodal degrees of freedom based on the idea of the extended finite element method (XFEM). This improvement allows the crack problem, whose displacement and velocity are discontinuous, to be simulated by only one set of background grid meshes, so multigrid and multiple velocity fields are unnecessary. In addition, the technique we developed to lump the mass matrix makes the EMPM/EGIMP can be implemented easily in a conventional MPM/GIMP code. If there is no crack, the EMPM/EGIMP degenerates to the conventional MPM/GIMP. The Level Set Method (LSM) is employed in the EMPM/EGIMP for easily tracking crack surfaces. The crack moves with the material points physically, so that the LSM function is carried by particles. In each time step, the LSM function value is mapped to the grid nodes from the particles, and the nodes to be enriched can be identified conveniently from the grid nodal LSM function values. Numerical experiments for stress fields distribution, fracture parameters calculation and crack propagation are provided to validate the proposed EMPM/EGIMP.
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影响因子：
5.1
作者：
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通讯作者：
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影响因子：
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影响因子：
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影响因子：
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影响因子：
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