Extended B-spline-based implicit material point method for saturated porous media

IF 3.4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL
Yuya Yamaguchi, Shuji Moriguchi, Kenjiro Terada
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引用次数: 0

Abstract

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.

饱和多孔介质的基于 B 样条的扩展隐式材料点法
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著变化。本文提出了一种基于扩展 B-样条曲线(EBS)的隐式材料点方法(EBS-MPM),用于饱和多孔介质的耦合水力学分析,以增强 MPM 在处理此类不同现象时的整体通用性。所提出的方法通过采用完整的耦合水力学建模公式,准确地表示了准静态和动态状态下的高速运动等现象。基于 Nitsche 方法的弱边界条件强加,使得边界条件的表示不受粒子和计算网格相对位置的影响。此外,它还能根据变形情况动态改变边界域。使用 EBS 基函数加强了这种边界表示法的稳健性,无论边界域相对于计算网格的位置如何,它都能防止系统矩阵的条件数下降。此外,基于变异多尺度方法(VMS)的稳定方法为空间离散化提供了选择任意基函数的灵活性,从而促进了 EBS 的有效构建。研究还给出了一些数值示例,包括完整公式和简化公式之间的比较,以展示所开发的方法在不同边界条件和不同时间尺度的加载状态下的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
6.40
自引率
12.50%
发文量
160
审稿时长
9 months
期刊介绍: The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.
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