Full Text:   <2040>

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CLC number: TU431

On-line Access: 2021-11-17

Received: 2021-05-11

Revision Accepted: 2021-06-20

Crosschecked: 2021-10-25

Cited: 0

Clicked: 3487

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Wei-hai Yuan

https://orcid.org/0000-0002-0732-4329

Wei Zhang

https://orcid.org/0000-0002-3933-0109

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Journal of Zhejiang University SCIENCE A 2021 Vol.22 No.11 P.909-923

http://doi.org/10.1631/jzus.A2100219


Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method


Author(s):  Wei-hai Yuan, Hao-cheng Wang, Kang Liu, Wei Zhang, Ding Wang, Yuan Wang

Affiliation(s):  College of Mechanics and Materials, Hohai University, Nanjing 210098, China; more

Corresponding email(s):   zhangwei@scau.edu.cn

Key Words:  Material point method (MPM), Large deformation, Implicit generalized interpolation material point method (iGIMP), Volumetric locking, B-bar method


Wei-hai Yuan, Hao-cheng Wang, Kang Liu, Wei Zhang, Ding Wang, Yuan Wang. Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method[J]. Journal of Zhejiang University Science A, 2021, 22(11): 909-923.

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author="Wei-hai Yuan, Hao-cheng Wang, Kang Liu, Wei Zhang, Ding Wang, Yuan Wang",
journal="Journal of Zhejiang University Science A",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A2100219"
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%T Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method
%A Wei-hai Yuan
%A Hao-cheng Wang
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%I Zhejiang University Press & Springer
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Abstract: 
This paper presents a quasi-static implicit generalized interpolation material point method (iGIMP) with B-bar approach for large deformation geotechnical problems. The iGIMP algorithm is an extension of the implicit material point method (iMPM). The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations. Where possible, the implementation procedure closely follows standard finite element method (FEM) approaches to allow easy conversion of other FEM codes. The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM. For the first time, the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics. The proposed iGIMP was tested and compared with iMPM and analytical solutions via a 1D column compression problem. Results highlighted the superiority of the iGIMP approach in reducing stress oscillations, thereby improving computational accuracy. Then, elasto-plastic slope stabilities and rigid footing problems were considered, further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility. Results showed that the proposed iGIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.

基于隐式广义插值物质点法的岩土工程大变形分析

目的:物质点法由于其不受网格畸变影响等特点被广泛应用于大变形问题的模拟,然而在使用物质点法模拟涉及不可压缩材料或不排水条件的问题时往往出现体积锁定现象而影响计算结果.同时,物质点法在计算过程中产生的网格穿透会造成应力震荡.为解决上述问题,本文在隐式广义插值物质点法的基础上,通过引入B-bar方法来解决体积锁定问题,提出使用B-bar方法的隐式广义插值物质点法.
创新点:首次提出在隐式广义插值物质点法中引入B-bar函数,以克服广义插值物质点法在模拟不可压缩材料时出现的体积锁定问题.
方法:1. 通过替换应变矩阵,构建使用B-bar方法的隐式广义插值物质点法,使其在不明显增加计算复杂程度的情况下,克服体积锁定的问题.2. 分别使用隐式物质点法(iMPM)、隐式广义插值物质点法(iGIMP)和使用B-bar方法的隐式广义插值物质点法对一维杆压缩、弹塑性边坡和刚性基础贯入进行数值模拟和对比研究,验证所提方法在减少网格穿透以及克服体积锁定方面的优势.
结论:1. 本文首次将B-bar方法引入隐式广义插值物质点算法,构造了使用B-bar方法的隐式广义插值物质点法;该方法能够有效减少网格穿透造成的计算误差并克服体积锁定问题,同时不需明显增加计算复杂程度.2. 分别使用iMPM算法与iGIMP算法对一维杆压缩以及弹塑性边坡稳定性进行模拟和对比的结果表明,iGIMP算法能有效减小网格穿透所造成的震荡.3. 对边坡稳定性问题以及刚性基础贯入问题进行数值模拟的结果表明,使用B-bar方法的隐式广义插值物质点法能有效处理体积锁定问题,因此可用于实际岩土工程的大变形分析.

关键词:物质点法;大变形;广义插值物质点法;体积锁定;网格穿透;B-bar

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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