一种用于大应变岩土建模的无隐式体积锁定的B样条物质点法
An implicit locking-free B-spline Material Point Method for large strain geotechnical modelling
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中文总结 AI 辅助
本文提出一种无隐式体积锁定的B样条物质点法，通过新颖的形函数实现和锁定缓解策略，有效控制应力振荡，适用于大应变岩土问题，并经三个数值案例验证。
中文摘要 AI 辅助
物质点法（MPM）在大变形岩土问题的数值模拟中引起了广泛关注。MPM之所以流行，主要是因为其公式与有限元方法有显著相似之处。在MPM中，迭代点可以独立于网格移动，从而能够解决大变形问题。然而，正因如此，原始MPM公式存在众所周知的单元穿越噪声和体积锁定不稳定性，导致应力场强烈振荡。本文提出了一种新颖的无隐式体积锁定B样条MPM，可将应力振荡控制在可忽略的水平。一种新颖但非常直接的B样条形函数实现程序，避免了复杂物质点搜索算法的需求，实现了从原始MPM到这种稳健的B样条MPM的无缝转换，旨在模拟大应变岩土问题。新提出的体积锁定缓解策略也非常易于实现，这促进了本研究的可复现性。所提出的方法通过三个数值研究进行了验证：颗粒柱坍塌实验、边坡破坏和大贯入量基础。所提出的数值方法与文献中报道的实验和先前的数值研究结果吻合良好。此外，这些数值示例表明，所提出的方法比其他现有方法提供了更突出的应力场。
英文摘要
The Material Point Method (MPM) has drawn great attention in the numerical modelling of large deformation, geotechnical problems. The popularity of MPM is mainly because its formulation shares significant similarities with the Finite Element Method. In MPM, the iteration points can move independently from the mesh, allowing for the resolution of large deformation problems. However, because of this, the original MPM formulation suffers from the well-known cell-crossing noise and volumetric-locking instabilities, resulting in a strongly oscillated stress field. A novel implicit locking-free B-spline MPM that controls stress oscillations to a negligible level is proposed in this paper. A novel, but very straightforward B-spline shape function implementation procedure, avoids the need for a complex material point searching algorithm, providing seamless transformation from the original MPM to this robust B-spline MPM, aiming at modelling large-strain geotechnical problems. The newly proposed volumetric locking mitigation strategy is also very easy to implement, which facilitates the reproducibility of this research. The proposed method is validated against three numerical studies: granular column collapse experiment, slope failure and footing with large penetration. The proposed numerical method agrees well with experiments reported in the literature and previous numerical studies. Also, these numerical examples show that the proposed method provides a more prominent stress field than other available methodologies.
发表机构
- University College London.（伦敦大学学院）
- Universidad Politécnica de Madrid.（马德里理工大学）
机构由 AI 辅助整理，请以论文原文为准。
