力學(xué)大會(huì)2015集離散元模擬中顆粒材料阻尼參數(shù)的選取及試驗(yàn)

周偉*，+，馬幸*，+，馬剛*，+，*（大學(xué)水資源與水電工程科學(xué)國(guó)家，+（水工巖石力學(xué)教育部β值對(duì)物理試驗(yàn)進(jìn)行數(shù)值模擬并進(jìn)行對(duì)比分析。研究結(jié)果表明：由于β影響了顆粒碰撞前后的速度從而影響了顆粒動(dòng)能與其他能量之間的轉(zhuǎn)化，β的增大會(huì)減小顆粒體動(dòng)能的轉(zhuǎn)化速率。β對(duì)顆≤800mm時(shí)，β0.2%時(shí)，hf隨著β的增大而增大，0.2β0.5%時(shí)，hf隨β的變化不明顯；hd1000mm較好的吻合，為數(shù)值試驗(yàn)中β的取值提供了有效參考。 數(shù)值模擬能否較好的實(shí)現(xiàn)顆粒材料實(shí)際的物理力學(xué)行為至關(guān)重要[1]DEM模型的細(xì)觀參數(shù)取值通常是顆粒振蕩阻尼器[7-8]，研究方向主要集中于顆粒之間的摩擦對(duì)多顆粒碰撞時(shí)系統(tǒng)能量耗散的影響[9-10]，而對(duì)于阻尼系數(shù)在多顆粒碰撞過程中的影響則研究較少。相同的效果，并且建議在DEM數(shù)值試驗(yàn)中，阻尼系數(shù)的取值為0.2%，但這一取值尚 本文采用基于離散單元法的ELLIPS3H程序[12]，對(duì)重力作用下生成試樣的下落試驗(yàn)進(jìn)行了數(shù)值1置示意1顆粒材料物理特顆粒直徑鋁試驗(yàn)進(jìn)行三種不同下落高度（225,425800mm）的多組、多次試驗(yàn)，研究顆粒體在重力作用下自由下落并堆積的過程，通過分析最終堆積高度（hf）與下落高度（h0）的關(guān)系來阻尼的影度（如圖。試驗(yàn)結(jié)果如圖4所示。圖2密實(shí)后的顆粒試 圖3顆粒最終堆積狀4理實(shí)驗(yàn)結(jié)個(gè)接觸顆粒的剪切模量G和泊松比ν。顆粒間接觸的法向剛度通過Hertzian理論定義為：

簡(jiǎn)化的Mindlin理論，與法向剛度的關(guān)系為：kt

ELLIPS3Hβ決定。在數(shù)值模擬過程中，阻尼僅在顆粒發(fā)130mm×130mm×154mm。細(xì)觀參數(shù)取值參照顆粒材料的實(shí)際力學(xué)特性確定（見表。2細(xì)觀參顆粒直徑試樣生成的過程分為三步（5所示。第一步，在相應(yīng)尺寸的棱柱內(nèi)隨機(jī)生成半徑較小的度。試樣在下落前的特征參數(shù)見表3。3試樣的特征參顆粒體初 圖5試樣生成過程6值試驗(yàn)過225m425m800mmβh0hfβ7所示（點(diǎn)代表數(shù)值計(jì)算結(jié)果，箱型代表物理實(shí)驗(yàn)結(jié)果。通過對(duì)比數(shù)值模擬與物理實(shí)驗(yàn)結(jié)果，發(fā)現(xiàn)當(dāng)0.002≤β≤0.003時(shí)兩者的結(jié)果吻合較好。βh0hf600mm,1000mm1200mm，β值分別為0.0005,0.001,0.002,0.0030.005。hfh08所示，從圖中可以看出，hfh0h0的增大而增大到h（β=0.0005h0≤225mm0.001,h0425mm)，h0hfhfβ9所示，從圖中可以看出，hfβ0.0005≤β≤0.002時(shí)，hf隨著β的增大而增大，這與Ng[11]0.002≤β≤0.005時(shí)，h0hfβ的增大而增大，h0較大時(shí)，hf變化不明顯。圖8hf隨h0的變化曲 圖9hf隨β的變化曲具，對(duì)該物理實(shí)驗(yàn)進(jìn)行了數(shù)值模擬，分析了β對(duì)試驗(yàn)的影響，得出了一些結(jié)論。因此有力的證明了離散元數(shù)值計(jì)算中β取值范圍為[0.002，0.003]。hfβ的函數(shù)，同時(shí)也是h0的函數(shù)。h0≤225mmhf隨著β的增大而增大；425mm≤h0≤800mm0.0005≤β≤0.002時(shí)，hf隨著β0.002<β≤0.005時(shí)，hfLandryH,LagueC,RobergeM.Discreteelementrepresentationofmanureproducts.ComputersandElectronicsinAgriculture,2006,51(1):17~34.周健，，池永.砂土雙軸試驗(yàn)的顆粒流模擬.巖土工程學(xué)報(bào),2000,22(6):PowderTechnology,1996,88(1):59~64.DurdaDD,MovshovitzN,RichardsonDC,AsphaugbE,MorganbA,RawlingsdAR,VestdC.Experimentaldeterminationofthecoefficientofrestitutionformeter-scalegranitespheres.Icarus,2011,211(1):ImreB,R?bsamenS,SpringmanSM.Acoefficientofrestitutionofrockmaterials.Computers&Geosciences,2008,34(4):339~350..GüttlerC,Hei?elmannD,BlumJ,KrijtS.NormalCollisionsofSpheres:Alituresurveyonavailableexperiments.arXivpreprintarXiv:1204.0001,2012.MaoK,WangMY,XuZ,ChenT.DEMsimulationofparticledam.PowderTechnology,2004,142(2):FangX,TangJ,LuoH.Granulardamysisusinganimproveddiscreteelementapproach.JournalofSoundandVibration,2007,308(1):112~131.SunQ,JinF,ZhouGGD.Energycharacteristicsofsimplesheargranularflows.GranularMatter,2013,15(1):119~128.compression.GranularMatter,2011,13(4):NgTT,ZhouW,MaG,XLChang.DamandparticlemassinDEMsimulationsundergravity.JournalofEngineeringMechanics,2014,141(6): NgTT.Triaxialtestsimulationswithdiscreteelementmethodandhydrostaticboundaries.JournalofEngineeringMechanics,2004,130(10):1188~1194.CundallPA,StrackODL.Adiscretenumericalmodelforgranularassemblies.Geotechnique,1979,29(1):47~65.ZhangD,WhitenWJ.Thecalculationofcontactsbetweenparticlesusingspringanddammodels.PowderTechnology,1996,88(1):59~64.DETERMINATIONOFTHEDAMPAREMETERUSEDINDEMANDITSZHOUWei1, MAGang1, CHANGXiaolin1,(2KeyLaboratoryofRockMechanicsinHydraulicStructuralEngineeringofEducationMinistry,WuhanUniversity,Wuhan)Thispaperpresentsastudyonthedamratio(β)usedinthediscreteelementsimulations.Itfocusesontheinfluenceofparticledamonsamplepreparationofgranularmaterialsundergravity.Physicalexperimentsareperformedbydropparticlesfromapredeterminedheight.Aluminumspheresareused.Discreteelementmethodisusedtosimulatetheprocessofparticledepositingundergravity.Theexperimentalresultiscomparedwiththenumericalresulttoidentifytheappropriateβ.TheresultindicatestheappropriatedamratiousedinDEMisbetween0.2%and0.3%.Variousβhavebeenusedinthesimulationswhileotherinputparametersareconstants.Damaffectsthevelocitiesofparticlesafterimpactwhichinturnaffectsthetransformationbetweenpotentialandkineticenergy.Differentβyielddifferentsampleheights.Fordropheightlessthan225mm,theeffectofβisobvious,thefinalheightofthesampleincreaseswithβ.For425mm≤dropheight≤800mm,thefinalheightofthesampleincrea