Coupling schemes for modeling hydraulic fracture using XFEM.pdf

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1、Comput.MethodsAppl.Mech.Engrg.253(2013)305–322ContentslistsavailableatSciVerseScienceDirectComput.MethodsAppl.Mech.Engrg.journalhomepage:www.elsevier.com/locate/cmaCouplingschemesformodelinghydraulicfracturepropagationusingtheXFEMElizavetaGordeliy,AnthonyPeirce⇑DepartmentofMathematics

2、,UniversityofBritishColumbia,Vancouver,BritishColumbia,CanadaV6T1Z2articleinfoabstractArticlehistory:WedescribecoupledalgorithmsthatusetheExtendedFiniteElementMethod(XFEM)tosolvetheelasticReceived9May2012crackcomponentoftheelasto-hydrodynamicequationsthatgovernthepropagationofhydrauli

3、cfrac-Receivedinrevisedform17August2012turesinanelasticmedium.Withappropriateenrichment,theXFEMresolvestheNeumanntoDirichletAccepted18August20122(ND)mapforcrackproblemswithOðhÞaccuracyandtheDirichlettoNeumann(DN)mapwithOðhÞAvailableonline15September2012accuracy.Forhydraulicfracturepro

4、blemswithalagseparatingthefluidfrontfromthefracturefront,2wedemonstratethatthefinitepressurefieldmakesitpossibletouseaschemebasedontheOðhÞXFEMKeywords:solutiontotheNDmap.Totreatproblemsinwhichthereisacoalescenceofthefluidandfracturefronts,XFEMresultinginsingulartippressures,wedevelopedano

5、velmixedalgorithmthatcombinesthetipwidthHydraulicfractures2FreeboundaryproblemsasymptoticsolutionwiththeOðhÞXFEMsolutionoftheNDmapawayfromthetips.Enrichmentbasisfunctionsrequiredforthesesingularpressurefieldscorrespondtowidthpowerlawindicesk>1,which2aredifferentfromtheindexk¼1oflineare

6、lasticfracturemechanics.Thesolutionsobtainedfromthe2newcoupledXFEMschemesagreeextremelywellwiththoseofpublishedreferencesolutions.Ó2012ElsevierB.V.Allrightsreserved.1.Introductioncanberepresentedbystandardpolynomialbasisfunctions.Thusfracturepropagationcanbecapturedevenonastructuredme

7、shHydraulicfractures(HFs)areaclassoffracturesthatoccurinbydynamicallyadjustingtheenrichmentprocesstoincorporatebrittlematerialsduetotheinjectionofaviscousfluid.HFoccurthelocationofthemovingfracturetips.Previousresearchonusingbothnaturallyandaredeliberatelycreatedforengineeringapplica-t

8、heXFE