CLC number: TU431
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2021-10-25
Cited: 0
Clicked: 5374
Citations: Bibtex RefMan EndNote GB/T7714
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.
@article{title="Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method",
author="Wei-hai Yuan, Hao-cheng Wang, Kang Liu, Wei Zhang, Ding Wang, Yuan Wang",
journal="Journal of Zhejiang University Science A",
volume="22",
number="11",
pages="909-923",
year="2021",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A2100219"
}
%0 Journal Article
%T Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method
%A Wei-hai Yuan
%A Hao-cheng Wang
%A Kang Liu
%A Wei Zhang
%A Ding Wang
%A Yuan Wang
%J Journal of Zhejiang University SCIENCE A
%V 22
%N 11
%P 909-923
%@ 1673-565X
%D 2021
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2100219
TY - JOUR
T1 - Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method
A1 - Wei-hai Yuan
A1 - Hao-cheng Wang
A1 - Kang Liu
A1 - Wei Zhang
A1 - Ding Wang
A1 - Yuan Wang
J0 - Journal of Zhejiang University Science A
VL - 22
IS - 11
SP - 909
EP - 923
%@ 1673-565X
Y1 - 2021
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2100219
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.
[1]Abe K, Soga K, Bandara S, 2014. Material point method for coupled hydromechanical problems. Journal of Geotechnical and Geoenvironmental Engineering, 140(3):04013033.
[2]Bandara S, Soga K, 2015. Coupling of soil deformation and pore fluid flow using material point method. Computers and Geotechnics, 63:199-214.
[3]Bardenhagen SG, Kober EM, 2004. The generalized interpolation material point method. Computer Modeling in Engineering & Sciences, 5(6):477-495.
[4]Bardenhagen SG, Brackbill JU, Sulsky D, 2000. The material-point method for granular materials. Computer Methods in Applied Mechanics and Engineering, 187(3-4):529-541.
[5]Bathe KJ, 1996. Finite Element Procedures. Prentice Hall, Englewood Cliffs, USA.
[6]Beuth L, Więckowski Z, Vermeer PA, 2011. Solution of quasi-static large-strain problems by the material point method. International Journal for Numerical and Analytical Methods in Geomechanics, 35(13):1451-1465.
[7]Charlton TJ, Coombs WM, Augarde CE, 2017. iGIMP: an implicit generalised interpolation material point method for large deformations. Computers & Structures, 190: 108-125.
[8]Coetzee CJ, 2004. The Modelling of Granular Flow Using the Particle-in-cell Method. PhD Thesis, University of Stellenbosch, Stellenbosch, South Africa.
[9]Coetzee CJ, Vermeer PA, Basson AH, 2005. The modelling of anchors using the material point method. International Journal for Numerical and Analytical Methods in Geomechanics, 29(9):879-895.
[10]Coombs WM, Charlton TJ, Cortis M, et al., 2018. Overcoming volumetric locking in material point methods. Computer Methods in Applied Mechanics and Engineering, 333:1-21.
[11]Cummins SJ, Brackbill JU, 2002. An implicit particle-in-cell method for granular materials. Journal of Computational Physics, 180(2):506-548.
[12]Guilkey JE, Weiss JA, 2003. Implicit time integration for the material point method: quantitative and algorithmic comparisons with the finite element method. International Journal for Numerical Methods in Engineering, 57(9):1323-1338.
[13]Guilkey JE, Hoying JB, Weiss JA, 2006. Computational modeling of multicellular constructs with the material point method. Journal of Biomechanics, 39(11):2074-2086.
[14]Huang P, Zhang X, Ma S, et al., 2011. Contact algorithms for the material point method in impact and penetration simulation. International Journal for Numerical Methods in Engineering, 85(4):498-517.
[15]Hughes TJR, 1980. Generalization of selective integration procedures to anisotropic and nonlinear media. International Journal for Numerical Methods in Engineering, 15(9):1413-1418.
[16]Iaconeta I, Larese A, Rossi R, et al., 2019. A stabilized mixed implicit material point method for non-linear incompressible solid mechanics. Computational Mechanics, 63(6):1243-1260.
[17]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.
[18]Lemiale V, Nairn J, Hurmane A, 2010. Material point method simulation of equal channel angular pressing involving large plastic strain and contact through sharp corners. Computer Modeling in Engineering & Sciences, 70(1):41-66.
[19]Li F, Pan JZ, Sinka C, 2011. Modelling brittle impact failure of disc particles using material point method. International Journal of Impact Engineering, 38(7):653-660.
[20]Li JG, Hamamoto Y, Liu Y, et al., 2014. Sloshing impact simulation with material point method and its experimental validations. Computers & Fluids, 103:86-99.
[21]Mast CM, Mackenzie-Helnwein P, Arduino P, et al., 2012. Mitigating kinematic locking in the material point method. Journal of Computational Physics, 231(16):5351-5373.
[22]Mieremet MMJ, Stolle DF, Ceccato F, et al., 2016. Numerical stability for modelling of dynamic two-phase interaction. International Journal for Numerical and Analytical Methods in Geomechanics, 40(9):1284-1294.
[23]Nair A, Roy S, 2012. Implicit time integration in the generalized interpolation material point method for finite deformation hyperelasticity. Mechanics of Advanced Materials and Structures, 19(6):465-473.
[24]Smith IM, Griffiths DV, Margetts L, 2014. Programming the Finite Element Method, 5th Edition. John Wiley & Sons, New York, USA.
[25]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.
[26]Sołowski WT, Sloan SW, 2015. Evaluation of material point method for use in geotechnics. International Journal for Numerical and Analytical Methods in Geomechanics, 39(7):685-701.
[27]Steffen M, Kirby RM, Berzins M, 2008. Analysis and reduction of quadrature errors in the material point method (MPM). International Journal for Numerical Methods in Engineering, 76(6):922-948.
[28]Sulsky D, Kaul A, 2004. Implicit dynamics in the material-point method. Computer Methods in Applied Mechanics and Engineering, 193(12-14):1137-1170.
[29]Sulsky D, Chen Z, Schreyer HL, 1994. A particle method for history-dependent materials. Computer Methods in Applied Mechanics and Engineering, 118(1-2):179-196.
[30]Sulsky D, Schreyer H, Peterson K, et al., 2007. Using the material-point method to model sea ice dynamics. Journal of Geophysical Research: Oceans, 112(C2):C02S90.
[31]Wang B, Hicks MA, Vardon PJ, 2016a. Slope failure analysis using the random material point method. Géotechnique Letters, 6(2):113-118.
[32]Wang B, Vardon PJ, Hicks MA, 2016b. Investigation of retrogressive and progressive slope failure mechanisms using the material point method. Computers and Geotechnics, 78:88-98.
[33]Wang B, Vardon PJ, Hicks MA, et al., 2016c. Development of an implicit material point method for geotechnical applications. Computers and Geotechnics, 71:159-167.
[34]Wang B, Vardon PJ, Hicks MA, 2018. Rainfall-induced slope collapse with coupled material point method. Engineering Geology, 239:1-12.
[35]Wiȩckowski Z, 2004. The material point method in large strain engineering problems. Computer Methods in Applied Mechanics and Engineering, 193(39-41):4417-4438.
[36]Yamaguchi Y, Takase S, Moriguchi S, et al., 2020. Solid–liquid coupled material point method for simulation of ground collapse with fluidization. Computational Particle Mechanics, 7(2):209-223.
[37]Yerro A, Alonso EE, Pinyol NM, 2015. The material point method for unsaturated soils. Géotechnique, 65(3):201-217.
[38]Yuan WH, Wang B, Zhang W, et al., 2019. Development of an explicit smoothed particle finite element method for geotechnical applications. Computers and Geotechnics, 106:42-51.
[39]Yuan WH, Liu K, Zhang W, et al., 2020. Dynamic modeling of large deformation slope failure using smoothed particle finite element method. Landslides, 17(7):1591-1603.
[40]Yuan WH, Wang HC, Zhang W, et al., 2021. Particle finite element method implementation for large deformation analysis using Abaqus. Acta Geotechnica, 16:2449-2462.
[41]Zhang DZ, Ma X, Giguere PT, 2011. Material point method enhanced by modified gradient of shape function. Journal of Computational Physics, 230(16):6379-6398.
[42]Zhang W, Zhong ZH, Peng C, et al., 2021. GPU-accelerated smoothed particle finite element method for large deformation analysis in geomechanics. Computers and Geotechnics, 129:103856.
[43]Zhao EJ, Dong YK, Tang YZ, et al., 2021. Numerical investigation of hydrodynamic characteristics and local scour mechanism around submarine pipelines under joint effect of solitary waves and currents. Ocean Engineering, 222:108553.
[44]Zheng XC, Pisanò F, Vardon PJ, et al., 2021. An explicit stabilised material point method for coupled hydromechanical problems in two-phase porous media. Computers and Geotechnics, 135:104112.
Open peer comments: Debate/Discuss/Question/Opinion
<1>