Monolithic coupling of the implicit material point method with the finite element method
Monolithic coupling of the implicit material point method with the finite element method
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DOI：
10.1016/j.compstruc.2019.04.006
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发表时间：
2018-11
影响因子：
4.7
通讯作者：
E. Aulisa;Giacomo Capodaglio
中科院分区：
文献类型：
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作者：
E. Aulisa;Giacomo Capodaglio
提出了材料点法与有限元法的整体耦合。所描述的MPM公式是隐式的，并且最小化了粒子和背景网格之间的信息交换。减少了从粒子到网格的信息传递，提高了方法的稳定性。残差组装完成后，通过自动微分得到系统矩阵。通过这种方式，不需要显式的计算，并且大大简化了实现。当点阵与有限元耦合时，点阵背景网格附着在有限元体上，耦合是整体的。利用该策略，任何MPM粒子都不能穿透有限元单元，并且消除了现有耦合过程中使用的计算昂贵的接触搜索算法的需要。耦合系统可以用有限元法逐个单元的单一装配程序进行装配。数值结果显示了所讨论方法的性能和优点。
A monolithic coupling between the material point method (MPM) and the finite element method (FEM) is presented. The MPM formulation described is implicit, and the exchange of information between particles and background grid is minimized. The reduced information transfer from the particles to the grid improves the stability of the method. Once the residual is assembled, the system matrix is obtained by means of automatic differentiation. In such a way, no explicit computation is required and the implementation is considerably simplified. When MPM is coupled with FEM, the MPM background grid is attached to the FEM body and the coupling is monolithic. With this strategy, no MPM particle can penetrate a FEM element, and the need for computationally expensive contact search algorithms used by existing coupling procedures is eliminated. The coupled system can be assembled with a single assembly procedure carried out element by element in a FEM fashion. Numerical results are reported to display the performances and advantages of the methods here discussed.