abaqus中UMAT子程序编写方法

1、abaqus中UMAT子程序编写方法UMATUSer subrouti ne to defi ne a material's mecha ni Cal behavior.Product: AbaqUS/Sta ndardWarning: The USe of this SUbrOUt ine gen erally requires COn SiderabIe expertise. You are CaUti Oned that the impleme ntati On Of any realistic COn StitUtiVe model requires exte nsive de

2、velopme nt and test ing. In itial testing On a Single-element model With PreSCribed traction IOading is stro ngly recomme nded.Refere nces,“ User-defined mechanical material behavior, ” SeCtiOn 25.7.1 oftheAbaqUS An alysis User's ManUal,“ User-defined thermal material behavior, ” SeCtiOn 25.7.2

3、of theAbaqUS An alysis User's ManUal,*USER MATERIAL,“SDVlNI,” SeCtiOn 4.1.11 of the AbaqUS VerifiCatiOn ManUal,“ UMAT and UHYPER, SeCtiO n 4.1.21 of the AbaqUS VerifiCatiOnMan UalOVerVieWUSer SUbrOUt ine UMAT:,Can be USed to define the mechanical conStitUtiVe behavior of amaterial;,Will be calle

4、d at all material CalCUlatiOn POints Of elements forWhiCh the material definition inCIUdeS a user-defined materialbehavior;,Can be USed With any PrOCedUre that inCIUdeS mechanical behavior;,Can USe soluti on-depe ndent State Variables;,must UPdate the StreSSeS and soluti on-depe ndent State VariabIe

5、S totheir VaIUeS at the end of the inCrement for WhiCh it is called; 陋,must PrOVide the material JaCObian matrix, , for themecha ni cal con StitUtiVe model;,Can be USed in conjUnCtion With USer SUbrOUtine USDFLD to redefineany field VariabIeS before they are PaSSed in; and,is described further in“ U

6、ser-defi ned mecha ni cal materialbehavior, ” SeCtion 25.7.1 of the AbaqUS Analysis User's ManUal. StOrage of StreSS and Strain comp OnentSIn the StreSS and Strain arrays and in the matrices DDSDDE, DDSDDT, and DRPLDE, direct comp OnentS are StOred first, followed by Shear comp onen ts. There ar

7、e NDI direct and NSHR engin eeri ng Shear comp Onents. The order of“COnVentions, ” SeCtion 1.2.2 of the AbaqUS the compOnentS isdefi ned inAn alysis User's ManU al. SinCe the nu mber of active StreSS and Stra in comp OnentS VarieS betwee n eleme nt types, the routi ne must be coded toPrOVide for

8、 all element types With WhiCh it WiIl be used. Defining localOrie ntatio nsIf a local orientation (“Orientations,” SeCtion 2.2.5 of theAbaquSAnalysis User's Manual) is USed at the Same point as USer SUbrOUtineUMAT, the StreSS and Strain compOnentS will be in the local orientation;and, in the CaS

9、e of finite-strain analysis, the basis SyStem in WhiChStreSS and Strain comp OnentS are StOred rotates With the material.StabiIityYou should en SUre that the in tegrati on SCheme coded in this rout ineis StabIe no direct PrOViSion is made to include a StabiIity limit inthe time StePPing SCheme based

10、 on the calculations in UMAT.Conv erge nce rateDDSDDE anfor coupled temperature-displaceme nt and coupledthermal-electrical-structural a nalyses DDSDDT, DRPLDE, and DRPLDTmustbe defi ned accurately if rapid conv erge nce of the overall NeWt onSCheme is to be achieved. In most CaSeS the accuracy of t

11、his defi niti onis the most importa nt factor gover ning the conv erge nce rate. SinCenonSymmetriC equation solution is as much as four times as expensive as the COrreSP Onding SymmetriC system, if the con StitUtiVe JaCObia n (DDSDDE)is OnIy SlightIy nonSymmetriC (for example, a frictional material

12、With a small frictio nan gle), it may be less expe nsive COmPUtati on ally to USe a SymmetriC approximatio n and accept a slower conv erge nce rate.An in COrreCt defi niti on of the material JaCObia n affects only theconv erge nce rate; the results (if obta in ed) are Un affected. SPeCiaI con Sidera

13、ti ons for VariOUS eleme nt typesThere are SeVeraI SPeCiaI con Siderati ons that n eed to be no ted. AVaiIabiIity of deformati on gradie ntThe deformatio n gradie nt is available for solid (COntinUUm) eleme nts, membra nes, and fin ite-strain shells (S3S3R, S4, S4R, SAXs, and SAXAs). It is not avail

14、able for beams or small-strain shells. It is StOred as a 3 × 3 matrix With component equivalence DFGRDo(I,J) . For fullyQ GJlin tegrated first-order isoparametric eleme nts (4-node quadrilaterals in two dime nsions and 8-node hexahedra in three dime nsions) the SeIeCtiVeIy reduced integration t

15、echnique is USed (also known as the tech niq ue).Bl“SolidSeCtiO n 3.2.4 of theis PaSSed into USer SUbrOUt ine UMAT. For more details, See isop arametric quadrilaterals and hexahedra,AbaqUSTheOry Manu al.BeamS and shells that calculate tran SVerSe Shear en ergyIf USer SUbrOUt ine UMAT is USed to desc

16、ribe the material of beams orshells that calculate tran SVerSe Shear en ergy, you must SPeCify thetran SVerSe Shear Stiff ness as Part of the beam or shell SeCti ondefi niti on to defi ne the tran SVerSe Shear behavior. See“ Shell SeCt ionbehavior, ” SeCtion2864 of the AbaqUS An alysis User's Ma

17、nU al, and“ Choos ing a beamelement, ”SeCtiO n 28.3.3 of the AbaqUS An alysis User's ManU al, for in formatio nonSPeCify ing this Stiff ness.OPen-SeCt ion beam eleme ntsWhe n USer SUbrOUt ine UMAT is USed to describe the material resp onseof beams With open SeCtions (for example, an I-SeCtiOn),

18、the torsionalStiff ness is obta ined asWhere J is the torsional conStant, A is the SeCtion area, k is aShear factor,and is the USer-SPeCified tran SVerSe Shear Stiff ness (Seea -I-Shear Stiffness definitionin“Choosing a beam element, ” SeCtion28.3.3of the AbaqUS An alysis User's ManU al).Element

19、s with hourglassing modesIf this capability is used to describe the material of elements with hourglassing modes, you must define the hourglass stiffness factor for hourglass control based on the total stiffness approach as part of the element section definition. The hourglass stiffness factor is no

20、t required for enhanced hourglass control, but you can define a scaling factor for the stiffness associated with the drill degree of freedom (rotation a bout the surface normal). See“Section controls, ” Section26.1.4 of the AbaqusAnalysis User's Manual, for information on specifying the stiffnes

21、sfactor.Pipe-soil interaction elementsThe constitutive behavior of the pipe-soil interaction elements (see “Pipe - soil interaction elements,” Section 31.12.1 of the AbaqusAnalysisUser's Manual) is defined by the force per unit length caused by relative displacement between two edges of the elem

22、ent. The relativedisplacements are available as“strains ” (STR AN and DSTRAN). Thecorresponding forces per unit length must be defined in the STRESS array. The Jacobian matrix defines the variation of force per unit length with respect to relative displacement.For two-dimensional elements two in-pla

23、ne components of “stress ” andstrain ” exist (NTENS=NDI=2, and NSHR=0). For three-dimensionaleleme nts three COmP OnentS Of“丄”I X”丄StreSS and Strain exist(NTENS=NDI=3,and NSHR=0).Large volume Cha nges With geometric non Ii nearityIf the material model allows large volume Cha nges and geometric nonIi

24、nearity is conSidered, the exact definition of the conSiStent JaCObia n should be USed to en SUre rapid con Verge nce. TheSe con diti ons are most com monly encoun tered Whe n con Sideri ng either large elastic Strai ns or PreSSUre-depe ndent PIaStiCity .In the former case, total-formUtiVe equati on

25、s relat ing the CaUChy StreSS to the deformati on con Stitgradie nt are com mon Iy used; in the Iatter case, rate-form con StitUtiVe laws are gen erally used.CFor total-form con StitUtiVe laws, the exact con SiSte nt JaCObia n isdefined through the Variation in KirChhOff stress:(.) = J(C : $D + *W y

26、 < WHere, J is the determ inant of the deformati on gradie nt, is the CaUChyAmVVStreSs, is the VirtUaI rate of deformation, and is the VirtUaI SPintensor, defined asrD *=Ir HMn(? - F-IIand,W 怛何 IMF HuFOr rate-form COn StitutiVe laws, the exact COn SiSte nt JaCObia n is give n by I a(.jJ=尽'7 U

27、Se With in COmPreSSibIe elastic materialsFor user-defined inCOmPreSSibIe elastic materials, USer SUbrOUtine UHYPERshould be USed rather than USer SUbrOUt ine UMAT. In UMATin COmPreSSibIematerials must be modeled Via a Pen alty method; that is, you must enSUre that a finite bulk modulus is used. The

28、bulk modulus should be large eno Ugh to model in COmPreSSibiIity SUffiCie ntly but small eno Ugh to avoid loss of PreCiSi on. AS a gen eral guideli ne, the bulk modulus should be about - times the Shear modulus. The tangent bulk modulus Can be()1I(fcalculated from7<f =52 DUSDDE(L-I).11 J iIf a hy

29、brid element is USed With USer SUbrOUtine UMAT,AbaqUS/Sta ndard willreplace the PreSSUre StreSS calculated from your definition of STRESS With that derived from the Lagra nge multiplier and will modify the JaCObia n appropriately.For in COmPreSSibIe PreSSUre-Se nsitive materials the eleme nt ChOiCe

30、isUMAT. In particular, particularly importa nt Whe n USing USerSUbrOUti neBfirst-order Wedge eleme nts should be avoided. For these eleme nts thetech nique is not USed to alter the deformati On gradie nt that is PaSSedinto USer SUbrOUti ne UMAT, WhiCh in CreaSeS the risk of volumetricIOCk ing. In Cr

31、eme nts for WhiCh OnIy the JaCObia n Can be defi nedAbaqUS/Sta ndard PaSSeS zero Stra in in Creme nts into USer SUbrOUti neUMATto Start the first inCrement of all the StePS and all inCrements ofStePS for WhiCh you have SUPPreSSed extrapolatio n (See“ Procedures:Roverview,SeCt ion 6.1.1 of the AbaqUS

32、 An alysis User's ManU al). In this CaSeyou Candefi ne only the JaCObia n (DDSDDE).UtiIity rout inesSeVeraI UtiIity routi nes may help in codi ng USer SUbrOUt ine UMAT.Theirfun Cti ons in clude determ ining StreSS in Varia nts for a StreSS ten sorand calculat ing Prin cipal VaIUeS and direct ion

33、s for StreSS or Stra inten sors. TheSe UtiIity rout ines are discussed in detail in“ Obta iningStreSSin Varia nts, Prin CiPal StreSS/strain VaIueS and directi ons, androtating tensors in an AbaqUS/Standard analysis, ” SeCtiOn 2.1.11.USer SUbrOUt ine in terfaceSUBRoUTlNE UMAT(STRESS,STATEV,DDSDDE,SSE

34、,SPD,SCD,1 Rplqdsddtqrpldeqrpldt,2 stran,dstran,time,dtime,temp,dtemp,predef,dpred,cmname,3 NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,4 CELENT,DFGRDO,DFGRD1,NOEL,NPT,LAYER,KSPT,KSTEP,KINC)CINCLUDE 'ABA_PARA M.INC'CCHARACTER*80 CMNAMEDIMENSION STRESS(NTENS),STATEV(NSTATV),1 DDSDDE

35、(NTENS,NTENS),DDSDDT(NTENS),DRPLDE(NTENS),2 STRAN(NTENS),DSTRAN(NTENS),TIME(2),PREDEF(1),DPRED(1),3 PROPS(NPROPS),COORDS(3),DROT(3,3),DFGRDO(3,3),DFGRD1(3,3)USer codi ng to defi ne DDSDDE, STRESS, STATEV, SSE, SPD, SCDan d, if n ecessary, RPL, DDSDDT, DRPLDE, DRPLDT, PNEWDTRETURNENDVariabIeS to be d

36、efi nedIn all SitUati OnSDDSDDE(NTENS,NTENS)JaCObian matrix Of the COnStitutiVe model, , Where are theStreSS in Creme nts and are the Strain in Creme nts. DDSDDE(I,J) defi nesthe Change in the Ith StreSS compOnent at the end of the time inCrementCaUSed by an infinitesimal PertUrbation of the Jth com

37、pOnent of theStrain in Creme nt array. Un IeSS you inv oke the Un SymmetriC equati on solution CaPabiIity for the user-defined material, AbaqUS/Standard willUSe on Iy the SymmetriC Part of DDSDDE. The SymmetriC Part of the matrixis calculated by taking one half the SUm of the matrix and its transpos

38、e.STRESS(NTENS)ThiS array is PaSSed in as the StreSS ten sor at the beg inning of thein Creme nt and must be UPdated in this rout ine to be the StreSS ten sor atthe end of the in Creme nt. If you SPeCified in itial Stresses ( “ In itialconditions in AbaqUS/Standard and AbaqUS/Explicit,” SeCtion 32.2

39、.1of theAbaqUS An alysis User's ManU al), this array will COntain the in itialStreSSeS at the Start of the an alysis. The SiZe of this arraydepends on the value of NTENS as defined below. Infinite-strainproblems the StreSS ten sor has already bee n rotated to acco Unt for rigid body moti on in t

40、hein Creme nt before UMAT is called, so that on Iy the corotati onal Partof the StreSS integration should be done in UMAT. The measure of StreSSUSed is“true ” (CaUChy) stress.STATEV(NSTATV)An array containing the solution-dependent state variables. These are passed in as the values at the beginning

41、of the increment unless they are updated in user subroutines USDFLD or UEXPAN, in which case the updatedvalues are passed in. In all cases STATEV must be returned as the values at the end of the increment. The size of the array is defined as described in “Allocating space ” in “User subroutines: ove

42、rview,”Section 17.1.1of the Abaqus Analysis User's Manual.In finite-strain problems any vector-valued or tensor-valued state variables must be rotated to account for rigid body motion of the material, in addition to any update in the values associated with constitutive behavior. The rotation inc

43、rement matrix, DROT, is provided for this purpose.SSE, SPD, SCDSpecific elastic strain energy, plastic dissipation, and“creepdissipation, respectively. These are passed in as the values at the start of the increment and should be updated to the corresponding specific energy values at the end of the

44、increment. They have no effect on the solution, except that they are used for energy output.Only in a fully coupled thermal-stress or a coupled thermal-electrical-structural analysisRPLVolumetric heat generatiOn Per Unit time at the end Of the inCrementCauSed by mecha ni Cal work ing of the material

45、.DDSDDT(NTENS)Variati on of the StreSS in Creme nts With respect to the temperature. DRPLDE(NTENS)VariatiO n of RPL With respect to the Strain in Creme nts.DRPLDTVariatiO n of RPL With respect to the temperature.On Iy in a geostatic StreSS PrOCedUre or a coupled pore fluiddiffusi on/stress an alysis

46、 for pore PreSSUre COheSiVe eleme nts RPLRPL is USed to in dicate Whether or not a COheSiVe eleme nt is ope n to the tangen tial flow of pore fluid. Set RPL equal to 0 if there is no tangen tial flow; otherwise, assig n a non zero value to RPL if an eleme nt is ope n. OnCe ope ned, a COheSiVe eleme

47、nt will rema in ope n to the fluid flow. VariabIe that Can be UPdatedPNEWDTRatio of SUggeSted new time in Creme nt to the time in Creme nt being USed (DTIME, See discussi on Iater in this SeCtiO n). ThiS VariabIe allows you to PrOVide inPUt to the automatic time inCrementation algorithms in AbaqUS/S

48、ta ndard (if automatic time in Creme ntatio n is chose n). For a quasi-static PrOCedUre the automatic time StePP ing that AbaqUS/Sta ndard uses, WhiCh is based on tech niq UeS for in tegrati ng Sta ndard CreeP laws (See “QUaSi- StatiC analysis, ” SeCtion 6.2.5 of the AbaqUS Analysis User'sManu a

49、l), CannOt be COn trolled from Within the UMAT SubrOut ine.PNEWDTiS Set to a large value before each call to UMAT.If PNEWDT is redefined to be less than 1.0, AbaqUS/Standard mustabandon the time inCrement and attempt it again With a smaller timein Creme nt. The SUggeSted new time in Creme nt PrOVide

50、d to the automatic time in tegrati on algorithms is PNEWDT × DTIME, Where the PNEWDT USed is the minimum valuefor all calls to USer SUbrOUtines that allow redefinition of PNEWDTfor this iterati on.If PNEWDT is given a value that is greater than 1.0 for all calls toUSer SUbrOUtines for this iter

51、ation and the inCrement converges in this iterati on, AbaqUS/Sta ndard may in CreaSe the time in Creme nt. The SUggeSted new time in Creme nt PrOVided to the automatic time in tegrati on algorithms is PNEWDT × DTIME, Where the PNEWDT USed is the mi nimum value for all calls to USer SUbrOUtines

52、for this iteration.If automatic time inCrementation is not SeIeCted in the analysisprocedure, VaIUeS of PNEWDT that are greater tha n 1.0 will be ignored and VaIUeS of PNEWDT that are less than 1.0 will CaUSe the job to termi nate. VariabIeS PaSSed in for in formatio nSTRAN(NTENS)An array COntaining

53、 the total Stra ins at the beg inning of theinCrement. If thermal expansion is inCIUded in the Same materialdefi niti on, the Strai ns PaSSed in to UMAT are the mecha ni cal Strai ns only (that is, the thermal Stra ins COmPUted based upon the thermal expa nsion coefficient have been subtracted from

54、the total strains). These strains are available for output as the “elastic ” strains.In finite-strain problems the strain components have been rotated to account for rigid body motion in the increment before UMAT is called and are approximations to logarithmic strain.DSTRAN(NTENS)Array of strain inc

55、rements. If thermal expansion is included in the same material definition, these are the mechanical strain increments (the total strain increments minus the thermal strain increments).TIME(1)Value of step time at the beginning of the current increment. TIME(2) Value of total time at the beginning of

56、 the current increment. DTIME Time increment.TEMPTemperature at the start of the increment.DTEMPIncrement of temperature.PREDEFArray of interpolated values of predefined field variables at this point at the start of the increment, based on the values read in at the nodes. DPREDArray of increments of

57、 predefined field variables.CMNAMEUser-defined material name, left justified. Some internal material models are given names starting with the“ABQ_” cha racter string. Toavoid conflict, you should not use“ABQ_” as the leading string forCMNAME.NDINumber of direct stress components at this point.NSHRNu

58、mber of engineering shear stress components at this point. NTENSSize of the stress or strain component array (NDI + NSHR). NSTATVNumber of solution-dependent state variables that are associated with this material type (defined as described in“Allocating space ” in“Usersubroutines: overview, ” Section 17.1.1 of the Abaqus Analysis User's Manual).PROPS(NPROPS)User-specified array of materia