正交各向异性损伤材料的Mohr-Coulomb条件

:0253-9993(2003)01-0026-05Mohr-Coulomb1,2,Zenon1Mroz3(11,110023;21,056038;31IFTR,PolishAcademyofSciences,Warsaw00-049,Poland):Mohr-Coulomb.,(Homogenization),Mohr-Coulomb,..,Mohr-Coulomb,-,.(c3,ct).:;;Mohr-Coulomb;;:TU459:A:2002-06-05:(1999363),;.,..:();..,Mohr-Coulomb,Mohr-Coulomb.,Mohr-Coulomb.Mohr-Coulomb,,.,[14],.,:,Mohr-Coulomb[5],,[6,7];,,Mohr-Coulomb[8,9].,(Homogenization),Mohr-Coulomb.1[10].N,DD=Ni=1iniáni,(1),ni,i.,D[10].,,.[10]281Vol.28No.120032JOURNALOFCHINACOALSOCIETYFeb.2003©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.D=P+()D,(2)Pijkl=Q+ikQ+jl,Q+=3i=1h(i)piápi,+=3i=1ipiápi,,P+;Q+;h(i)Heaviside;pii;ii.,.2Mohr-Coulomb(Homogenization)[10],.,Mohr-Coulomb.1Fig11Theslidingcriticalplaneofarepresentativeelementwithmicro-racks1.12,AFMohr-Coulomb.,AF,,,adn;,,idn.n;t.()(2)n=12(1-2)sin2,n=1cos2+2sin2.(3)AFMohr-Coulombn=c+n.,F=n-c-n=0.2Fig12Thestressdistributionovertheslidingcriticalplane0,,adn=0,tn=idn=n(1-adn)-1.(4),AF(AB,CD,EF),Mohr-CoulombFPt=tn-ttn-ct=0.(5)t.AFDE,,Mohr-CoulombFPid=idn-ididn-cid,(6),idcid.AFBC,,.,.AF,AFnnn=tn(1-adn-idn)+idnidn,n=tn(1-adn-idn)+idnidn,(7),adn,idn,adn=Dijninj,idn=(Dij-Dij)ninj.(7)Mohr-Coulomb(5),(6),tn,idn,(7),Mohr-Coulomb.n=c3+3n,(8)721:Mohr-Coulomb©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,n,n;3,3=(1-adn)[t(1-adn-idn)+ididn],(9)c3=ct(1-adn-idn)+cididn.(10)(8)(10),(10)c3,ct.,,N,Mohr-CoulombN.ivi(i=1,N),N.(8)ni=c3i+3ini,(11),ii.Mohr-CoulombF(n,n,3,c3)=1-22sin2-31+22+1-22cos2-c30.(12),adn=D11sin2+D22cos2+D12sin2,n=D11sin2+D22cos2+D12sin2,idn=n-adn.(13)D,(12)5F5=0,5F5=(1-2)cos2+3(1-2)sin2-5351+22+1-22cos2-5c35=0,(14),535=5adn5[idn(id-t)]+5idn5(id-t+tadn);5c35=cid5idn5-ct5idn5+5adn5;5idn5=(D11-D22-D11+D22)sin2+2(D12-D12)cos2;5adn5=(D11-D22)sin2+2D12cos2;5n5=(D11-D22)sin2+2D12cos2.DAF;,()(,),(8)(10)Mohr-Coulomb.3Fig13Stratifiedrockwithjointofangle3n-n,[5].,Mohr-Coulomb[8,11].,AF.Mohr-Coulomb((9)).3.,()-1,=45,id=tan40,(8)(13)adn+idn=1,c3=cididn,3=id(idn)2.4.3,82200328©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.D.,2,(9)(11)1.(3)n-n5,,[5,8].4DDFig14DandDontheslidingcriticalplane5n-nFig15Then-nresultsobtainedwiththemodelpresentedhere4(1),(Homogenization),Mohr-Coulomb,Mohr-Coulomb.,,Mohr-Coulomb,,.(2),(10)c3,ct.ct.Mohr-Coulomb,-[8,10],.(2)Mohr-Coulomb,,.:[1]LemaitreJ.Acourseondamagemechanics,2nded.[M].Berlin:Springer,1990.[2]HansenNR,SchreyerHL.Athermodynamicallyconsistentframeworkfortheoriesofelastoplasticitycoupledwithdamage[J].Int.J.SolidsStructures,1994,31(2):359389.[3]HayakawaK,MurakamiS.Thermodynamicmodelingofelastic-plasticdamageandexperimentalvalidationofdamagepo2tential[J].Int1J1DamaMech,1997,6(2):333363.[4]MariottideSciarraF.Anewvariationaltheoryandacomputationalalgorithmforcoupledelastoplasticdamagemodels[J].Int1J1SolidsStructures,1997,34(9):17611796.[5]VutukuriVS,LamaRD,SalujaSS.Handbookonmechanicalpropertiesofrocks,Vol.1[A].Berlin:TransTechPub2lisher,1974.[6]BasistaM,GrossD.Theslidingcrackmodelofbrittledeformation:aninternalvariableapproach[J].Int.J.SolidsStruc2tures,1998,35(3):487509.[7]DragonA,HalmD.Amesocrackdamageandfrictioncoupledmodelforbrittlematerials[A].In:DamageMechanicsinEn2gineeringMaterials[C].VoyiadjisGZ,JuJW,ChabocheJL,Editors.Amsterdam:ElsevierScience,1998.321336.921:Mohr-Coulomb©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.[8]DuveauG,ShaoJF.Amodifiedsingleplaneofweaknesstheoryforthefailureofhighlystratifiedrocks[J].Int.J.Rock.Mech.Min.Sci.,1998,35(6):807813.[9]HoekE,BrownET.Practicalestimationofrockmassstrength[J].Int.J.Rock.Mech.Min.Sci.,1997,34(8):11651186.[10]SwobodaG,ShenXP,RosasL.Damagemodelforjointedrockmassanditsapplicationtotunneling[J].ComputerandGeotechnics,1998,22(3/4):183203.[11]MullerD,KratochvilJ,BerveillerM.Nonlocalversuslocalelastoplasticbehaviorofheterogeneousmaterials[J].Int.J.Plasticity,1993,9(3):633645.[12]BasistaM,GrossD.Theslidingcrackmodelofbrittledeformation:aninternalvariableapproach[J].Int1J1SolidsStruc2tures,1998,35(3):487509.:(1963-),,,,,19939,,,40.Mohr2CoulombcriteriaassociatedwithmaterialsoforthotropicdamageSHENXin2pu1,WANGJian2xue2,ZenonMroz3(11CollegeofArchitecture,ShenyangPolytechnicUniversity,Shenyang110023,China;21HebeiInstituteofAchitectrualScienceandTechnology,Handan056038,China;31IFTR,PolishAcademyofScience,Warsaw,002049,Poland)Abstract:Mohr2Coulombcriterionassociatedwithmaterialsoforthotropicdamageispresentedinthispaper.Secondorderdamagetensorisadoptedandtheeffectofcrack2closureistakenintoaccount.Basedonthemicro2mechanicalanalysisofrepresentativeelementconsistingofcracks,theorthotropicdamagetensorisintroducedintotheMohr2Coulombcriterionthroughhomogenization.Boththedegradationofshearstrengthanddegrada2tionoffrictionanglecausedbydamageareincludedinthismodel.Withthetheoryestablishedinthispaper,thenonlineardiagramofpressurevsshearstrengthisobtained,andthenitisindicatedthattheshearstrengthre2portedinreferencesisonlyc3,avalueoccurredintheloadingprocess,butnotct,theexpectedmaterialparam2eter.Keywords:orthotropy;damage;Mohr2Coulombcriteria;homogeniz