The problem of multiphase materials (fluid or solid) interacting with the rigid body structure is studied by proposing a novel VMS-FEM (variational multi-scale finite element method) in the Eulerian framework using the fixed mesh. The incompressible N-S equation with high Reynolds number is stabilized using the idea of the VMS stabilization. To model the multiphase materials, a modified level set method is used to track the development of interfaces between different phases of materials. The interaction between the materials and the rigid body structure is realized using the Lagrangian multiplier method. The mesh of the rigid body structure domain is incompatible with the Eulerian fixed mesh for material domains. A cutting finite element scheme is used to satisfy the coupling condition between the rigid body structure boundary and the deformeable multiphase materials. A novel algorithm is proposed to track the stress history of the material point in the Eulerian fixed-mesh framework such that the stress-history-dependent fluid or solid materials (e.g. as soil) are also analysable using fixed-mesh. The non-local stress theory is used. To consider the stress-history-dependent material in the Eulerian fixed mesh, in the step of calculating the non-local relative-distance-based averaging treatment, the field point location is based on the updated material point position,rather than the spatial field point location. Thus, the convective effect of the previous stress history and the calculation of the non-local stress fields are realized in one shot. Thus, the proposed novel VMS-FEM can solve almost any history-dependent materials (fluid or solid) in the Eulerian framework (fixed mesh), where the distorted mesh problem is not existent.

翻译：针对多相材料（流体或固体）与刚体结构的相互作用问题，本文在欧拉框架下采用固定网格提出了一种新型VMS-FEM（变分多尺度有限元方法）。基于VMS稳定化思想对高雷诺数不可压缩N-S方程进行稳定化处理。为模拟多相材料，采用改进的水平集方法追踪不同材料相界面的演化过程。通过拉格朗日乘子法实现材料与刚体结构间的相互作用。刚体结构域网格与材料域的欧拉固定网格不兼容，采用切割有限元格式满足刚体结构边界与可变形多相材料间的耦合条件。提出了一种新颖算法在欧拉固定网格框架下追踪物质点的应力历史，使得采用固定网格同样可分析应力历史相关的流体或固体材料（如土体）。采用非局部应力理论。为在欧拉固定网格中考虑应力历史相关材料，在基于非局部相对距离的加权平均处理步骤中，场点位置基于更新后的物质点位置而非空间场点位置。由此，历史应力迁移效应与非局部应力场计算得以一次性实现。因此，本文提出的新型VMS-FEM可在欧拉框架（固定网格）中求解几乎所有的历史相关材料（流体或固体），从根本上避免了网格畸变问题。