Full Text:   <3026>

CLC number: O33

On-line Access: 2021-11-17

Received: 2020-09-06

Revision Accepted: 2021-01-07

Crosschecked: 2021-10-20

Cited: 0

Clicked: 5500

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

You-kou Dong

https://orcid.org/0000-0002-7354-6464

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2021 Vol.22 No.11 P.870-881

http://doi.org/10.1631/jzus.A2000399


Implementation of absorbing boundary conditions in dynamic simulation of the material point method


Author(s):  Zhi-gang Shan, Zhe-xian Liao, You-kou Dong, Dong Wang, Lan Cui

Affiliation(s):  Zhejiang Huadong Construction Engineering Corporation Limited, Hangzhou 310014, China; more

Corresponding email(s):   dongyk@cug.edu.cn

Key Words:  Material point method (MPM), Absorbing boundary condition (ABC), Submarine landslide, Impact


Zhi-gang Shan, Zhe-xian Liao, You-kou Dong, Dong Wang, Lan Cui. Implementation of absorbing boundary conditions in dynamic simulation of the material point method[J]. Journal of Zhejiang University Science A, 2021, 22(11): 870-881.

@article{title="Implementation of absorbing boundary conditions in dynamic simulation of the material point method",
author="Zhi-gang Shan, Zhe-xian Liao, You-kou Dong, Dong Wang, Lan Cui",
journal="Journal of Zhejiang University Science A",
volume="22",
number="11",
pages="870-881",
year="2021",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A2000399"
}

%0 Journal Article
%T Implementation of absorbing boundary conditions in dynamic simulation of the material point method
%A Zhi-gang Shan
%A Zhe-xian Liao
%A You-kou Dong
%A Dong Wang
%A Lan Cui
%J Journal of Zhejiang University SCIENCE A
%V 22
%N 11
%P 870-881
%@ 1673-565X
%D 2021
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2000399

TY - JOUR
T1 - Implementation of absorbing boundary conditions in dynamic simulation of the material point method
A1 - Zhi-gang Shan
A1 - Zhe-xian Liao
A1 - You-kou Dong
A1 - Dong Wang
A1 - Lan Cui
J0 - Journal of Zhejiang University Science A
VL - 22
IS - 11
SP - 870
EP - 881
%@ 1673-565X
Y1 - 2021
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2000399


Abstract: 
Outgoing waves arising from high-velocity impacts between soil and structure can be reflected by the conventional truncated boundaries. Absorbing boundary conditions (ABCs), to attenuate the energy of the outward waves, are necessary to ensure the proper representation of the kinematic field and the accurate quantification of impact forces. In this paper, damping layer and dashpot ABCs are implemented in the material point method (MPM) with slight adjustments. Benchmark scenarios of different dynamic problems are modelled with the ABCs configured. Feasibility of the ABCs is assessed through the velocity fluctuations at specific observation points and the impact force fluctuations on the structures. The impact forces predicted by the MPM with ABCs are verified by comparison with those estimated using a computational fluid dynamics approach.

吸收边界在物质点法动力模拟中的实现

目的:在材料高速冲击结构物的过程中引起的应力波往往在材料中向边界逐渐传播,并在传统固定或自由边界处反射回材料内部,造成结构物附件的应力场和接触力数值的扰动.本文旨在在物质点法模拟中实现吸收边界的应用,在模型边界处吸收材料中的应力波,减少其反射及其对中心区域的干扰.
创新点:1. 对不同条件处的边界分别采用黏壶和阻尼层的吸收边界,优化边界处应力波的吸收效果;2. 建立物质点法分析模型,对吸收边界的效果进行量化评估.
方法:1. 在边界网格节点上采用黏壶吸收边界,并通过数学推导,确定不同时刻对节点处速度的调整量,以实现对应力波的充分吸收;2. 在距离边界一定距离的厚度内,设置阻尼层,对材料瞬态速度进行一定程度的调整,使其达到所需的稳态值,即对应力波完成吸收;3. 采用物质点法建立一维压缩、海底滑坡冲击管线和管线贯入模型,对吸收边界的使用效果进行评估,并对两种吸收边界的使用场景进行分析.
结论:1. 黏壶吸收边界通过对波动方程的推导,使其在自由边界处的使用更加灵活;2. 阻尼层吸收边界需要在计算区域外侧设置一定厚度的阻尼层,且阻尼值不宜过大;3. 在一定条件下,两种吸收边界组合使用可以优化对应力波的吸收.

关键词:物质点法;吸收边界;海底滑坡;冲击

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

Reference

[1]Altomare C, Domínguez JM, Crespo AJC, et al., 2017. Long-crested wave generation and absorption for SPH-based DualSPHysics model. Coastal Engineering, 127:37-54.

[2]ANSYS, 2011. ANSYS FLUENT Theory Guide, Release 14.0. ANSYS, Inc., Canonsburg, USA.

[3]Astley RJ, Gerdes K, Givoli D, et al., 2000. Finite elements for wave propagation–special issue of the Journal of Computational Acoustics. Journal of Computational Acoustics, 8(1):257.

[4]Bardenhagen SG, Kober EM, 2004. The generalized interpolation material point method. Computer Modeling in Engineering and Sciences, 5(6):477-495.

[5]Bécache E, Fauqueux S, Joly P, 2003. Stability of perfectly matched layers, group velocities and anisotropic waves. Journal of Computational Physics, 188(2):399-433.

[6]Berenger JP, 1994. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics, 114(2):185-200.

[7]Bisht V, Salgado R, 2018. Local transmitting boundaries for the generalized interpolation material point method. International Journal for Numerical Methods in Engineering, 114(11):1228-1244.

[8]Boukpeti N, White DJ, Randolph MF, et al., 2012. Strength of fine-grained soils at the solid-fluid transition. Géotechnique, 62(3):213-226.

[9]Bui HH, Fukagawa R, Sako K, et al., 2008. Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model. International Journal for Numerical and Analytical Methods in Geomechanics, 32(12):1537-1570.

[10]Chern A, 2019. A reflectionless discrete perfectly matched layer. Journal of Computational Physics, 381:91-109.

[11]Dong Y, 2020. Reseeding of particles in the material point method for soil–structure interactions. Computers and Geotechnics, 126:103716.

[12]Dong YK, Grabe J, 2018. Large scale parallelisation of the material point method with multiple GPUs. Computers and Geotechnics, 101:149-158.

[13]Dong YK, Wang D, Randolph MF, 2015. A GPU parallel computing strategy for the material point method. Computers and Geotechnics, 66:31-38.

[14]Dong YK, Wang D, Randolph MF, 2017a. Investigation of impact forces on pipeline by submarine landslide using material point method. Ocean Engineering, 146:21-28.

[15]Dong YK, Wang D, Randolph MF, 2017b. Runout of submarine landslide simulated with material point method. Journal of Hydrodynamics, 29(3):438-444.

[16]Festa G, Delavaud E, Vilotte JP, 2005. Interaction between surface waves and absorbing boundaries for wave propagation in geological basins: 2D numerical simulations. Geophysical Research Letters, 32(20):L20306.

[17]Gao K, Huang LJ, 2018. Optimal damping profile ratios for stabilization of perfectly matched layers in general anisotropic media. Geophysics, 83(1):T15-T30.

[18]Gao M, Wang XL, Wu K, et al., 2018. GPU optimization of material point method. ACM Transactions on Graphics, 37(6):254.

[19]Hamad F, Stolle D, Vermeer P, 2015. Modelling of membranes in the material point method with applications. International Journal for Numerical and Analytical Methods in Geomechanics, 39(8):833-853.

[20]Hu Y, Randolph MF, 1998. A practical numerical approach for large deformation problems in soil. International Journal for Numerical and Analytical Methods in Geomechanics, 22(5):327-350.

[21]Huang P, Zhang X, Ma S, et al., 2008. Shared memory OpenMP parallelization of explicit MPM and its application to hypervelocity impact. Computer Modeling in Engineering & Sciences, 38(2):119-148.

[22]Jassim I, Stolle D, Vermeer P, 2013. Two-phase dynamic analysis by material point method. International Journal for Numerical and Analytical Methods in Geomechanics, 37(15):2502-2522.

[23]Kellezi L, 2000. Local transmitting boundaries for transient elastic analysis. Soil Dynamics and Earthquake Engineering, 19(7):533-547.

[24]Komatitsch D, Tromp J, 2003. A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation. Geophysical Journal International, 154(1):146-153.

[25]Komatitsch D, Martin R, 2007. An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation. Geophysics, 72(5):SM155-SM167.

[26]Kouroussis G, Verlinden O, Conti C, 2011. Finite-dynamic model for infinite media: corrected solution of viscous boundary efficiency. Journal of Engineering Mechanics, 137(7):509-511.

[27]Longuet-Higgins MS, Cokelet ED, 1976. The deformation of steep surface waves on water–I. A numerical method of computation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 350(1660):1-26.

[28]Lysmer J, Kuhlemeyer RL, 1969. Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division, 95(4):859-877.

[29]Ma J, Wang D, Randolph MF, 2014. A new contact algorithm in the material point method for geotechnical simulations. International Journal for Numerical and Analytical Methods in Geomechanics, 38(11):1197-1210.

[30]Meza-Fajardo KC, Papageorgiou AS, 2008. A nonconvolutional, split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media: stability analysis. Bulletin of the Seismological Society of America, 98(4):1811-1836.

[31]Oberai AA, Malhotra M, Pinsky PM, 1998. On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation. Applied Numerical Mathematics, 27(4):443-464.

[32]Rajagopal P, Drozdz M, Skelton EA, et al., 2012. On the use of absorbing layers to simulate the propagation of elastic waves in unbounded isotropic media using commercially available finite element packages. NDT & E International, 51:30-40.

[33]Sankaran K, Fumeaux C, Vahldieck R, 2006. Cell-centered finite-volume-based perfectly matched layer for time-domain Maxwell system. IEEE Transactions on Microwave Theory and Techniques, 54(3):1269-1276.

[34]Shen LM, Chen Z, 2005. A silent boundary scheme with the material point method for dynamic analyses. CMES-Computer Modeling in Engineering & Sciences, 7(3):305-320.

[35]Soga K, Alonso E, Yerro A, et al., 2016. Trends in large-deformation analysis of landslide mass movements with particular emphasis on the material point method. Géotechnique, 66(3):248-273.

[36]Sulsky D, Zhou SJ, Schreyer HL, 1995. Application of a particle-in-cell method to solid mechanics. Computer Physics Communications, 87(1-2):236-252.

[37]Wang PP, Zhang AM, Ming FR, et al., 2019. A novel non-reflecting boundary condition for fluid dynamics solved by smoothed particle hydrodynamics. Journal of Fluid Mechanics, 860:81-114.

[38]Yao G, da Silva NV, Wu D, 2018. An effective absorbing layer for the boundary condition in acoustic seismic wave simulation. Journal of Geophysics and Engineering, 15(2):495-511.

[39]Zhang X, Krabbenhoft K, Pedroso DM, et al., 2013. Particle finite element analysis of large deformation and granular flow problems. Computers and Geotechnics, 54:133-142.

[40]Zheng J, Hossain MS, Wang D, 2015. Numerical modeling of spudcan deep penetration in three-layer clays. International Journal of Geomechanics, 15(6):04014089.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE