Comparison of the quasi-static method and the dynamic method

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1、ComputMechDOI10.1007/s00466-007-0221-7ORIGINALPAPERComparisonofthequasi-staticmethodandthedynamicmethodforsimulatingfractureprocessesinconcreteJ.X.Liu·S.C.Deng·N.G.LiangReceived:15January2007/Accepted:24September2007©Springer-Verlag2007AbstractConcreteisheterogeneo

2、usandusuallydescribedconcreteisverydifficulttointerpretwithoutappealingtoasathree-phasematerial,wherematrix,aggregateandinter-theirmicro-structure(seeforinstance[9]).Concreteisusu-facearedistinguished.Totakethisheterogeneityintoconsid-allydescribedasathree-phasemate

3、rial,wherematrix,aggre-eration,theGeneralizedBeam(GB)latticemodelisadopted.gateandinterfacezonesaredistinguished(seeforinstanceTheGBlatticemodelismuchmorecomputationallyeffi-[11,13,14,17,19,20]).Amongdifferentkindsofmicrostruc-cientthanthebeamlatticemodel.Numericalp

4、roceduresofturalmodels,latticetypemodelsarebeingappliedbymorebothquasi-staticmethodanddynamicmethodaredevelopedandmoreinvestigators.Oneimportantreasonisthatthelat-tosimulatefractureprocessesinuniaxialtensiletestscon-ticemodelallowsastraightforwardimplementationofth

5、eductedonaconcretepanel.Casesofdifferentloadingratesmaterialheterogeneity[13].Latticetypematerialmodelingarecomparedwiththequasi-staticcase.Itisfoundthatthehasbeensuccessfullyusedforsolvingclassicalproblemsofinertiaeffectduetoloadincreasingbecomeslessimportantelast

6、icity[7].Morerecently,ithasbeenemployedforsimu-andcanbeignoredwiththeloadingratedecreasing,butthelatingtheprogressivefailureinheterogeneousmedia,espe-inertiaeffectduetounstablecrackpropagationremainscon-ciallybytheoreticalphysicists[5,6].Toinvestigatefracturesidera

7、blenomatterhowlowtheloadingrateis.Therefore,processesinconcrete,manydifferenttypesofmeso-levelanunrealisticresultwillbeobtainedifafractureprocesslatticemodelshavebeendevelopedinthepast.Ashasbeenincludingunstablecrackingissimulatedbythequasi-staticgenerallyaccepted,

8、itisnecessarytoprojectthematerialprocedure.structuredirectlyontothelatticeinordertoobtainmorerealisticresults[11,13,20].Schornetal.[18]andBazante