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A hybrid material-point spheropolygon-element method for solid and granular material interaction. (English) Zbl 07863269

Summary: Capturing the interaction between objects that have an extreme difference in Young’s modulus or geometrical scale is a highly challenging topic for numerical simulation. One of the fundamental questions is how to build an accurate multiscale method with optimal computational efficiency. In this work, we develop a material-point-spheropolygon discrete element method (MPM-SDEM). Our approach fully couples the material point method (MPM) and the spheropolygon discrete element method (SDEM) through the exchange of contact force information. It combines the advantage of MPM for accurately simulating elastoplastic continuum materials and the high efficiency of DEM for calculating the Newtonian dynamics of discrete near-rigid objects. The MPM-SDEM framework is demonstrated with an explicit time integration scheme. Its accuracy and efficiency are further analyzed against the analytical and experimental data. Results demonstrate this method could accurately capture the contact force and momentum exchange between materials while maintaining favorable computational stability and efficiency. Our framework exhibits great potential in the analysis of multi-scale, multi-physics phenomena.
{© 2020 John Wiley & Sons, Ltd.}

MSC:

74Sxx Numerical and other methods in solid mechanics
76Mxx Basic methods in fluid mechanics
74Lxx Special subfields of solid mechanics

References:

[1] AndradeJE, AvilaCF, HallSA, LenoirN, ViggianiG. Multiscale modelling and characterization of granular matter from grain kinematics to continuum mechanics. J Mech Phys Solid. 2011;59:237‐250. · Zbl 1270.74049
[2] SalotC, GottelandP, VillardP. Influence of relative density on granular materials behavior: DEM simulations of triaxial tests. Granul Matter. 2009;11:221‐236. · Zbl 1258.74047
[3] KruytNP. Micromechanical study of fabric evolution in quasi‐static deformation of granular materials. Mech Mater. 2012;44:120‐129.
[4] UtiliS, ZhaoT, HoulsbyGT. 3D DEM investigation of granular column collapse: evaluation of debris motion and its destructive power. Engrg Geol. 2015;186:3‐16.
[5] DaiZ, HuangY, ChengH, XuQ. SPH model for fluid‐structure interaction and its application to debris flow impact estimation. Landslides. 2017;14:917‐928.
[6] TeufelsauerH, WangY, PudasainiSP, BorjaRI, WuW. DEM simulation of impact force exerted by granular flow on rigid structures. Acta Geotech. 2011;6:119‐133.
[7] GaoM, TampubolonAP, JiangC, SifakisE. An adaptive generalized interpolation material point method for simulating elastoplastic materials. ACM Trans Graph. 2017;36(6):233:1‐233:12.
[8] TampubolonAP, GastT, KlárG, et al. Multi‐species simulation of porous sand and water mixtures. ACM Trans Graph. 2017;36(4):105:2‐105:11.
[9] HuangH, TutumluerE, DombrowW. Laboratory characterization of fouled railroad ballast behavior. Transp Res Rec. 2009;2117:93‐101.
[10] Sol‐SánchezM, ThomNH, Moreno‐NavarroF, Rubio‐GámezMC, AireyGD. A study into the use of crumb rubber in railway ballast. Construct Build Mater. 2015;75:19‐24.
[11] KwanSHJ, SzeHYE, LamC. Finite element analysis for rockfall and debris flow mitigation works. Can Geotech J. 2019;56:1225‐1250.
[12] ImseehWH, AlshibliKA. 3D finite element modelling of force transmission and particle fracture of sand. Comput Geotech. 2018;94:184‐195.
[13] LeeNS, BatheKJ. Error indicators and adaptive remeshing in large deformation finite element analysis. Finite Elem Anal Des. 1994;16:99‐139. · Zbl 0804.73064
[14] BardenhagenSG, BrackbillJU, SulskyD. The material‐point method for granular materials. Comput Methods Appl Mech Eng. 2000;187:529‐541. · Zbl 0971.76070
[15] GaumeJ, GastT, TeranJ, HerwijnenAV, JiangC. Dynamic anticrack propagation in snow. Nat Commun. 2018;9:3047.
[16] WolperJ, FangY, LiM, LuJ, GaoM, JiangC. CD‐MPM: continuum damage material point methods for dynamic fracture animation. ACM Trans Graph. 2019;119:1‐15.
[17] BardenhagenSG, GuilkeyJE, RoessigKM, BrackbillJU, WitzelWM, FosterJC. An improved contact algorithm for the material point method and application to stress propagation in granular material. Comput Model Engrg Sci. 2001;2(4):509‐522. · Zbl 1147.74375
[18] HuW, ChenZ. A multi‐mesh MPM for simulating the meshing process of spur gears. Comput Struct. 2003;81:1991‐2002.
[19] ZhangHW, WangKP, ChenZ. Material point method for dynamic analysis of saturated porous media under external contact/impact of solid bodies. Comput Methods Appl Mech Eng. 2009;198:1456‐1472. · Zbl 1227.74024
[20] GuilkeyJE, HarmanT, XiaA, KashiwaB, McMurtryP. An Eulerian‐Lagrangian approach for large deformation fluid structure interaction problems, part 1: algorithm development. WIT Trans Built Environ. 2003;17:1‐14.
[21] CundallPA, StrackODL. A discrete numerical model for granular assemblies. Geotechnique. 1979;29(1):47‐65.
[22] MichaelM, VogelF, PetersB. DEM‐FEM coupling simulations of the interactions between a tire tread and granular terrain. Comput Methods Appl Mech Eng. 2015;289:227‐248. · Zbl 1423.74673
[23] FengYT, HanK, OwenDRJ. Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: computational issues. Int J Numer Methods Eng. 2007;72:1111‐1134. · Zbl 1194.76230
[24] ZhongW, YuA, LiuX, TongZ, ZhangH. DEM/CFD‐DEM modelling of non‐spherical particulate systems: theoretical developments and applications. Powder Tech. 2016;302:108‐152.
[25] LiuC, SunQ, ZhouGGD. Coupling of material point method and discrete element method for granular flows impacting simulations. Int J Numer Methods Eng. 2018;115:172‐188. · Zbl 07864833
[26] YueY, SmithB, ChenPY, ChantharayukhonthornM, KamrinK, GrinspunE. Hybrid grains: adaptive coupling of discrete and continuum simulations of granular media. ACM Trans Graph. 2018;37(6):283:1‐283:18.
[27] Alonso‐marroquínF, WangY. An efficient algorithm for granular dynamics simulations with complex‐shaped objects. Granul Matter. 2009;11:317‐329. · Zbl 1258.74208
[28] JiangY, HerrmannHJ, Alonso‐MarroquinF. A boundary‐spheropolygon element method for modelling sub‐particle stress and particle breakage. Comput Geotech. 2019;103087:1‐14.
[29] Galindo‐TorresSA. A coupled discrete element lattice Boltzmann method for the simulation of fluid‐solid interaction with particles of general shapes. Comput Method Appl Mech Eng. 2013;265:107‐119. · Zbl 1286.76116
[30] SulskyD, ZhouSJ, SchreyerHL. Application of a particle‐in‐cell method to solid mechanics. Comput Phys Commun. 1995;87:236‐252. · Zbl 0918.73334
[31] JiangC, SchroederC, TeranJ, StomakhinA, SelleA. The material point method for simulating continuum materials. ACM SIGGRAPH 2016 Courses. 2016;1‐52.
[32] GanY, SunZ, ChenZ, ZhangX, LiuY. Enhancement of the material point method using B‐spline basis functions. Int J Numer Methods Eng. 2018;113:411‐431. · Zbl 07874302
[33] BardenhagenSG, KoberEM. The generalized interpolation material point method. Comput Model Eng Sci. 2004;5(6):477‐496.
[34] JiangC, SchroederC, TeranJ. An angular momentum conserving affine‐particle‐in‐cell method. J Comput Phys. 2017;338:137‐164. · Zbl 1415.74052
[35] BardenhagenSG. Energy conservation error in the material point method. J Comp Phys. 2002;180:383‐403. · Zbl 1061.74057
[36] EvansMW, HarlowF. The particle‐in‐cell method for hydrodynamic calculation. Los Alamos Sci Lab Report. 1957.
[37] BrackbillJU, RuppelHM. FLIP: a method for adaptively zoned, particle‐in‐cell calculations of fluid flows in two dimensions. J Comput Phys. 1986;65:314‐343. · Zbl 0592.76090
[38] LoveE, SulskyDL. An unconditionally stable energy‐momentum consistent implementation of the material‐point method. Comput Methods Appl Mech Eng. 2006;195:3903‐3925. · Zbl 1118.74054
[39] ZhuY, BridsonR. Animation sand as fluid. ACM Trans Graph. 2005;24(3):965‐972.
[40] HammerquistCC, NairnJA. Anew method for material point method particle updates that reduces noise and enhances stability. Comput Methods Appl Mech Eng. 2017;318:724‐738. · Zbl 1439.65127
[41] KlárG, GastT, PradhanaA, et al. Drucker‐Prager elasto‐plasticity for sand animation. ACM Trans Graph. 2016;35(4):103:1‐103:12.
[42] MolenkampF. Limits to the Jaumann stress rate. Int J Numer Anal Method Geomech. 1986;10:151‐176. · Zbl 0579.73113
[43] CourantR, FriedrichsK, LewyH. On the partial difference equations of mathematical physics. IBM J. 1967;11(2):215‐234. · Zbl 0145.40402
[44] MankocC, JandaA, ArévaloR, et al. The flow rate of granular materials through an orifice. Granul Matter. 2007;9(6):407‐414.
[45] FuP, DafaliasYF. Study of anisotropic shear strength of granular materials using DEM simulation. Int J Numer Anal Method Geomech. 2011;35:1098‐1126.
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