adina土的模型(双语)

13.9Geotechnicalmaterialmodels地质材料模型3.9.1Curvedescriptionmaterialmodel曲线描述的材料模型•Thecurvedescriptionmodelcanbeemployedwiththe2-Dsolid(planestrainandaxisymmetric)and3-Dsolidelements.曲线描述的材料模型可以用于二维实体（平面应变及轴对称的）和三维实体单元•Thecurvedescriptionmodelcanbeusedwiththesmalldisplacementandlargedisplacementformulations.Inallcases,smallstrainsareassumed.Whenusedwiththesmalldisplacementformulation,amaterially-nonlinear-onlyformulationisemployed,andwhenusedwiththelargedisplacementformulation,aTLformulationisemployed.曲线描述的材料模型可以用于大变形和小变形分析。在任何情况下都假设为小应变。当用于小应变分析时，使用材料非线性分析；当使用大应变分析时使用的是TL分析。•Thecurvedescriptionmodelisasimpleincrementalstressstrainlawusedtorepresenttheresponseofgeologicalmaterials.Themodeldescribestheinstantaneousbulkandshearmoduliaspiecewiselinearfunctionsofthecurrentvolumestrain,asshowninFig.3.9-1.Anexplicityieldconditionisnotusedandwhetherthematerialisloadingorunloadingisdeterminedbythehistoryofthevolumestrainonly.曲线描述模型是单值的应力应变规律，通常用来表示地质材料。模型用实时体积的分段线性函数描述了材料的瞬态体积和剪切模量，如图3.9.1所示。不需要直接的屈服条件并且是否受荷取仅仅取决于材料体积应变得历史。•Topresentthegoverningconstitutiverelations,letijet＝totalstrains(theleftsuperscripttalwaysreferstotimet)总应变（左上标t表示时间t）ije＝incrementalstrains应变增量met＝3iieit＝meanstrain(negativeincompression)平均应变（忽略压缩）me＝3iiie=incrementalmeanstrain平均应变增量ijgt＝ijmeeijtt=deviatoricstrains偏应变ijg＝incrementaldeviatoricstrains偏应变增量ijt＝totalstresses(negativeincompression)全应力2ij=incrementalstresses应力增量3mt＝3iiit=meanstress平均应力m＝3iii=incrementalmeanstress平均应力增量minp＝minimummeanstresseverreached曾经达到的最小平均应力ijt＝ijmijtt＝deviatoricstresses偏应力ijs=incrementaldeviatoricstresses偏应力增量,ttGK＝shearandbulkmoduli剪切及体积模量Theincrementalstress-strainrelationsusingthecurvedescriptionmodelarethen使用曲线描述的应力-应变增量关系是：ijs＝2tijGgm＝3tmKe•Theinstantaneousbulkandshearmoduli,tKandtG,arefunctionsoftheloadingcondition,andthevolumetricstrainvetisdefinedas瞬时体积及剪切模量tG和tK是荷载条件的函数，并且体积应变tve定义如下：(3)ttvgravmeeewheregraveisthevolumetricstrain(threetimesthemeanstrainandtakenpositiveincompression)duetothegravitypressureandtmeisthemeanstrainattimet.Definingeminastheminimummeanstraineverreachedduringthesolution,wehavethatthematerialisloadingifmintmee，andthematerialisunloadingifmintmeei.e.,式中grave是有重力引起的体积应变（3倍的平均应变并且压缩为正），tme是t时刻的平均应变，定义mine为求解过程中达到的最小平均应变，如果mintmee材料为受荷的，如果mintmee材料为不受荷的。例如：minminttLDmtttUNmKwheneeKKwhenee及minminttLDmtttUNmGwheneeGGwhenee•Notethattheloadingconditionsforboththebulkandtheshearmoduliaredeterminedbythehistoryoftmeonly.ThevaluesoftKLD,tKUN,andtGLDareobtainedusingthecurvesinFig.3.9-1,andthemodulustttUNUNLDtLDKGGK注意体积和剪切模量的荷载条件仅仅是由tme得历史绝定的。tLDK、tUNK及tLDG的值是通过图3.9.1的曲线获得，系数tttUNUNLDtLDKGGK•Theincrementalsolutionattimetisobtainedusingtheequationst时刻增加的结果通过下面的公式得到：2tttttttijijijijsGggs及3tttttttmmimmKeeToobtaintGandtK,wecheckwhethertheloadingorunloadingconditionsareactive4bycomparingthecurrentvolumetricstrainsandpreviousvolumetricstrains.Tostarttheprocedureattime0,loadingconditionsareassumed.Itshouldbenotedthatthestressesattimettarecalculatedusingthematerialmodulipertainingtotimet.为获得tG和tK，我们通过比较当时的和以前的体积应变来检查受荷和非受荷状况是否起作用。在时刻0开始程序，假定为受荷状况。可以注意到时刻tt的应力是通过t时刻的材料模量计算出来的。•Animportantadditionalanalysisoptionisthatthematerialcanweakenunderloadingconditionsiftensilestressesexceedpreassignedvalues.Sincethecurvedescriptionmodelhasbeendevelopedprimarilyfortheanalysisofgeologicalmaterials,thematerialweakeningisassumedtooccuroncetheprincipaltensilestressesduetotheappliedloadingexceedthein-situgravitypressurep(takenpositive).Thegravitypressurepiscalculatedas1Niiiphpwherehiaretheelementinterpolationfunctionsandpiisthepressureattheelementnodes.Thenodalpressurepiiscalculatedas.iipZ,whereisthematerialdensityandZithenodalZcoordinate,whichcoincideswiththeverticaldirection.Thematerialweakeningcanbeincludedusingatensioncut-offmodeloracrackingmodel.一个重要的附加分析选项是在荷载状态下如果拉应力超过许可值材料会被削弱。由于曲线描述的模型主要为地质材料的分析而发展起来的，假定一旦由效用荷载导致的主要拉应力超过in-situ自重压力p（取正）那么材料的削弱就会发生。自重压力p通过公式1Niiiphp计算得到。式中hi是单元的插值函数，pi是单元结点的压力。结点压力pi通过.iipZ计算：式中使材料的密度；Zi为结点Z的坐标，与垂直方向一致。使用tensioncut-off模式或cracking模式可以包含材料的削弱。Inbothmodesofbehavior(tensioncut-offandcracking)theprincipalstressesduetotheexternalloadingarecalculatedandcomparedwiththein-situgravitypressure.Oncetheprincipaltensilestressisequaltothein-situgravitypressure,thematerialistreatedasbeingorthotropic,withthemoduluscorrespondingtothedirectionoftheprincipaltensilestressbeingmultipliedbyastiffnessreductionfactor(aninputparameter).Anotherfactor,alsoaninputparameter,isappliedtoreducetheshearstiffness.在这两种模式(tensioncut-offandcracking)由外部荷载引起的主应力都将被计算出来，并且与初始重力相比较。一旦主要张应力等于初始重力，材料被认为是正交的，同时与主要张应力方向相应的系数通过刚度衰减系数（一个输入参数）被增加。另一个系数（也是一个输入参数）被用来减小剪切刚度。Inthetensioncut-offmode,thenormalandshearstiffnessescorrespondingtothedirectionofthemaximumprincipaltensilestressarereduced,butthestressesarefullyretained.Themodelthereforesimulateselastic-plasticflowofthematerial.在tensioncut-off模式中，与最大主要张应力方向相同的法向剪切刚度减小，但是应力被全部保留下来。模型可以用来模拟材料的弹塑性流Ontheotherhand,inthecrackingmodethestiffnessesare