CLC number: O33
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2021-10-20
Cited: 0
Clicked: 6002
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.
[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>