This paper presents an enhanced coupled approach between the finite element method (FEM) and the discrete element method (DEM) in which an adaptive remeshing technique has been implemented. The remeshing technique is based on the computation of the Hessian of a selected nodal variable, i.e. the mesh is refined where the curvature of the variable field is greater. Once the Hessian is known, a metric tensor is defined node-wise that serves as input data for the remesher (MmgTools) that creates a new mesh. After remeshing, the mapping of the internal variables and the nodal values is performed and a regeneration of the discrete elements on the crack faces of the new mesh is carried out. Several examples of fracturing problems using the enhanced FEM–DEM formulation are presented. Accurate results in comparison with analytical and experimental solutions are obtained.

中文翻译：

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结合自适应有限元分析技术和FEM-DEM耦合方法来分析裂纹扩展问题

本文提出了一种在有限元方法（FEM）和离散元方法（DEM）之间的增强耦合方法，其中已实现了自适应重网格技术。重新网格化技术基于所选节点变量的Hessian的计算，即在变量场曲率较大的地方对网格进行细化。一旦知道了Hessian，就可以在节点上定义度量张量，该度量张量用作创建新网格的重网格（MmgTools）的输入数据。重新网格化后，执行内部变量和节点值的映射，并在新网格的裂纹面上进行离散元素的再生。给出了使用增强的FEM-DEM配方进行压裂问题的几个示例。