簡單線性粘結(jié)材料

Example:Simplelinearviscoelasticmaterial簡單線性粘結(jié)材料AsasimpleexampleofthecodingofusersubroutineUMAT,considerthelinear,viscoelasticmodelshowninFigure1.1.41-.Althoughthisisnotaveryusefulmodelforrealmaterials,itservestoillustratehowtocodetheroutine.Figure1.1.41-Simplelinearviscoelasticmodel.Thebehavioroftheone-dimensionalmodelshowninthefigureisPl ■= 旳 丄 1 -°(Ei_砂廠[1—日/民廣(1/Ei—1/風(fēng)廠where二andarethetimeratesofchangeofstressandstrain.Thiscanbegeneralizedforsmallstrainingofanisotropicsolidas對于各向同性固體的小應(yīng)變，可以概括為

andwhereandwhereand兒.■'；，壷and：''arematerialconstants and：■aretheLameconstaNts).Asimple,stableintegrationoperatorforthisequationisthecentraldifferenceoperator:此方程式的一個簡單，穩(wěn)定的積分算子是中央差分算子：wherefissomefunction,?：isitsvalueatthebeginningoftheincrement,A：isthechangeinthefunctionovertheincrement,and△■'isthetimeincrement.Applyingthistotherateconstitutiveequationsabovegives將其應(yīng)用于上面的速率本構(gòu)方程可得出( =(△方77—1)漁Ey—(△fp—ZX"j.j.———^.v.r)￡7andsothattheJacobianmatrixhastheterms日△巨2；2；and坐*巧［△亡（弓+F）+X+蚩詞）日△巨2；2；andThetotalchangeinspecificenergyinanincrementforthismaterialis該材料的單位比能量總變化為whilethechangeinspecificelasticstrainenergyis而比彈性應(yīng)變能的變化是whereDistheelasticitymatrix:A—2^1AA0D0-AA-A0D0入AA—000D0000D0000_D000D4-Nostatevariablesareneededforthismaterial,sotheallocationofspaceforthemisnotnecessary.Inamorerealisticcaseasetofparallelmodelsofthistypemightbeused,andthestresscomponentsineachmodelmightbestoredasstatevariables.該材料不需要狀態(tài)變量，因此不需要為它們分配空間。在更實際的情況下，可以使用一組這種類型的并行模型，并且每個模型中的應(yīng)力分量都可以存儲為狀態(tài)變量。Foroursimplecaseausermaterialdefinitioncanbeusedtoreadinthefiveconstantsintheorder，八，門,and；■sothatPROPS⑴=XPROPS⑵=?,PROPSC3)=XPROPS(4)-認(rèn)PROPSC5)=ijTheroutinecanthenbecodedasfollows:SUBROUTINEUMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,RPL,DDSDDT,DRPLDE,DRPLDT,STRAN,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,CMNAME,NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,JSTEP,KINC)CINCLUDE'ABA_PARAM.INC'CCHARACTER*80CMNAMEDIMENSIONSTRESS(NTENS),STATEV(NSTATV),DDSDDE(NTENS,NTENS),DDSDDT(NTENS),DRPLDE(NTENS),STRAN(NTENS),DSTRAN(NTENS),TIME(2),PREDEF(1),DPRED(1),PROPS(NPROPS),COORDS(3),DROT(3,3),DFGRD0(3,3),DFGRD1(3,3),JSTEP(4)DIMENSIONDSTRES(6),D(3,3)CCEVALUATENEWSTRESSTENSORCEV=0.(體積應(yīng)變)DEV=0.DOK1=1,NDIEV=EV+STRAN(K1)DEV=DEV+DSTRAN(K1)ENDDOCTERM1=.5*DTIME+PROPS(5)TERM1I=1./TERM1TERM2=(.5*DTIME*PROPS(1)+PROPS(3))*TERM1I*DEVTERM3=(DTIME*PROPS(2)+2.*PROPS(4))*TERM1ICDOK1=1,NDIDSTRES(K1)=TERM2+TERM3*DSTRAN(K1)1 +DTIME*TERM1I*(PROPS(1)*EV2 +2.*PROPS(2)*STRAN(K1)-STRESS(K1))STRESS(K1)=STRESS(K1)+DSTRES(K1)ENDDOCTERM2=(.5*DTIME*PROPS(2)+PROPS(4))*TERM1II1=NDIDOK1=1,NSHRI1=I1+1DSTRES(I1)=TERM2*DSTRAN(I1)+1DTIME*TERM1I*(PROPS(2)*STRAN(I1)-STRESS(I1))STRESS(I1)=STRESS(I1)+DSTRES(I1)ENDDOCCCREATENEWJACOBIANCTERM2=(DTIME*(.5*PROPS(1)+PROPS(2))+PROPS(3)+12.*PROPS(4))*TERM1ITERM3=(.5*DTIME*PROPS(1)+PROPS(3))*TERM1IDOK1=1,NTENSDOK2=1,NTENSDDSDDE(K2,K1)=0.ENDDOENDDOCDOK1=1,NDIDDSDDE(K1,K1)=TERM2ENDDOCDOK1=2,NDIN2=Kl-lDOK2=1,N2DDSDDE(K2,Kl)=TERM3DDSDDE(Kl,K2)=TERM3ENDDOENDDOTERM2=(.5*DTIME*PROPS(2)+PROPS(4))*TERMlIIl=NDIDOKl=l,NSHRIl=Il+lDDSDDE(Il,Il)=TERM2ENDDOCCTOTALCHANGEINSPECIFICENERGYCTDE=0.DOKl=l,NTENSTDE=TDE+(STRESS(Kl)-.5*DSTRES(Kl))*DSTRAN(Kl)ENDDOCCCHANGEINSPECIFICELASTICSTRAINENERGYCTERMl=PROPS(l)+2.*PROPS(2)DOKl=l,NDID(K1,K1)=TERM1ENDDODOK1=2,NDIN2=K1-1DOK2=1,N2D(K1,K2)=PROPS(1)D(K2,K1)=PROPS(1)ENDDOENDDODEE=0.DOK1=1,NDITERM1=0.TERM2=0.DOK2=1,NDITERM1=TERM1+D(K1,K2)*STRAN(K2)TERM2=TERM2+D(K1,