The large deformation and fluidization process of a solid–fluid mixture includes significant changes to the temporal scale of the phenomena and the shape and properties of the mixed material. This paper presents an extended B‐spline (EBS)‐based implicit material point method (EBS‐MPM) for the coupled hydromechanical analysis of saturated porous media to enhance the overall versatility of MPM in addressing such diverse phenomena. The proposed method accurately represents phenomena such as high‐speed motion in both the quasi‐static and dynamic states by employing a full formulation of coupled hydromechanical modeling. The weak imposition of boundary conditions based on Nitsche's method allows representing the boundary conditions independent of the relative position of the particles and computational grid. In addition, it enables dynamic changes in the boundary domain based on the deformation. The robustness of this boundary representation is reinforced using EBS basis functions, which prevent the degradation of the condition number of the system matrices regardless of the position of the boundary domain with respect to the computational grid. Furthermore, a stabilization method based on a variational multiscale method (VMS) approach is employed to provide the flexibility in choosing arbitrary basis functions for spatial discretization, facilitating the effective construction of EBS. Numerical examples including comparisons between a full formulation and a simplified formulation are presented to demonstrate the performance of the developed method under various boundary conditions and loading states across different time scales.

中文翻译：

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基于扩展B样条的饱和多孔介质隐式材料点法


固液混合物的大变形和流化过程包括现象的时间尺度以及混合材料的形状和性质的显着变化。本文提出了一种基于扩展 B 样条 (EBS) 的隐式质点方法 (EBS-MPM)，用于饱和多孔介质的耦合流体力学分析，以增强 MPM 在解决此类不同现象时的整体多功能性。该方法通过采用耦合流体力学建模的完整公式，准确地表示了准静态和动态下的高速运动等现象。基于尼采方法的边界条件的弱施加允许独立于粒子和计算网格的相对位置来表示边界条件。此外，它还可以根据变形实现边界域的动态变化。使用 EBS 基函数增强了这种边界表示的鲁棒性，无论边界域相对于计算网格的位置如何，该函数都可以防止系统矩阵的条件数退化。此外，采用基于变分多尺度方法（VMS）的稳定方法可以灵活地选择任意基函数进行空间离散，从而促进EBS的有效构建。给出了包括完整公式和简化公式之间的比较在内的数值示例，以证明所开发的方法在不同时间尺度的各种边界条件和加载状态下的性能。