Challenges and Innovations in Geomechanics - Proceedings of the 16th International Conference of IACMAG - Volume 1
Challenges and Innovations in Geomechanics - Proceedings of the 16th International Conference of IACMAG - Volume 1
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地质力学的挑战与创新 - 第 16 届 IACMAG 国际会议论文集 - 第 1 卷
DOI：
10.1007/978-3-030-64514-4_82
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Coombs W
中科院分区：
文献类型：
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作者：
Coombs W
材料点法非常适合于三维大变形问题的建模，特别是在有限元法由于网格变形而难以解决的情况下。然而，当该方法被用来分析问题与近不可压缩材料的行为，如在岩土工程中使用模型与等容塑性流动，它遭受严重的体积锁定。这导致该方法过度预测给定位移的力，并在问题域中引起虚假的应力振荡。在有限元文献中已经提出了几种方法，但其中很少有被应用到材料点法。在本文中，我们提出了一种方法，以避免体积锁定的三维物质点分析与单纯形元素（线性四面体）使用安巴尔补丁的方法。该技术不仅避免了与体积锁定相关的过刚性行为，而且还减少了该方法中的应力振荡，这通常归因于单元交叉不稳定性。两个三维基准问题的制定进行了验证。
The material point method is ideally suited to modelling large deformation problems in three dimensions, especially in cases where the finite element method struggles due to mesh distortion. However, when the method is used to analyse problems with near-incompressible material behaviour, such as in geotechnical engineering using models with isochoric plastic flow, it suffers from severe volumetric locking. This causes the method to over predict the forces for a given displacement and induces spurious stress oscillations through the problem domain. Several methods have been proposed in the finite element literature but few of these have been applied to the material point method. In this paper we present a way to avoid volumetric locking for three-dimensional material point analyses with simplex elements (linear tetrahedra) using anbar patch approach. Not only does the technique avoid the over-stiff behaviour associated with volumetric locking but it also reduces the stress oscillations in the method, which are often attributed to cell-crossing instabilities. The formulation is validated against two three-dimensional benchmark problems.