VUMAT基本知识

NBLOCK: 在调用Vumat时需要用到的材料点的数量Ndir：对称张量中直接应力的数量（sigma11,sigma22,sigma33）Nshr：对称张量中间接应力的数量(sigma12, sigma13, sigma23)Nstatev:与材料类型相关联的用户定义的状态变量的数目Nfieldv：用户定义的外场变量的个数Nprops:用户自定义材料属性的个数Lanneal：指示是否在退火过程中被调用例程的标志。

Lanneal=0，指示在常规力学性能增量，例程被调用。

Lanneal=1表示，这是退火过程，你应该重新初始化内部状态变量，stepTime：步骤开始后的数值totalTime：总时间Dt：时间增量值Cmname：用户自定义的材料名称，左对齐。

它是通过字符串传递的。

一些内部材料模型是以“ABQ_”字符串开头给定的名称。

为了避免冲突，你不应该在“cmname”中使用“ABQ_”作为领先字符串。

coordMp(nblock,*)：材料点的坐标值。

它是壳单元的中层面材料点，梁和管（pipe）单元的质心。

charLength(nblock)：特征元素长度，是基于几何平均数的默认值或用户子程序VUCHARLENGTH中定义的用户特征元长度。

props(nprops)：用户使用的材料属性density(nblock)：中层结构的物质点的当前密度strainInc (nblock, ndir+nshr)：每个物质点处的应变增量张量relSpinInc (nblock, nshr)：在随转系统中定义的每个物质点处增加的相对旋转矢量tempOld(nblock)：物质点开始增加时的温度。

defgradOld (nblock,ndir+2*nshr)：在增量开始时，每个物质点出的变形梯度张量，在3d中形为（F11, F22，F33，F12，F23，F31，F21，F32，F13）,在2d中形为（F11，F22，F33，F12，F21）stretchOld (nblock, ndir+nshr)fieldOld (nblock, nfieldv)：在增量开始时，每个物质点处用户定义场变量的值stressOld (nblock, ndir+nshr)：在增量开始时，每个物质点处的应力张量：stateOld (nblock, nstatev)：在增量开始时，每个物质点处的状态变量：tempNew(nblock)：在增量结束时，每个物质点处的温度defgradNew (nblock,ndir+2*nshr)：在增量结束时，每个物质点出的变形梯度张量，在3d中形为（F11, F22，F33，F12，F23，F31，F21，F32，F13）,在2d中形为（F11，F22，F33，F12，F21）fieldNew (nblock, nfieldv)：在增量开始时，每个物质点处用户定义长变量的值Example: Elastic/plastic material with kinematic hardeningAs a simple example of the coding of subroutine VUMAT, consider the generalized plane strain case for an elastic/plastic material with kinematic hardening. The basic assumptions and definitions of the model are as follows.Let be the current value of the stress, and define to be the deviatoric part of the stress. The center of the yield surface in deviatoric stress space is given by the tensor , which has initial values of zero. Thestress difference, , is the stress measured from the center of the yield surface and is given byThe von Mises yield surface is defined aswhere is the uniaxial equivalent yield stress. The von Mises yield surface is a cylinder in deviatoric stress space with a radius ofFor the kinematic hardening model, R is a constant. The normal to the Mises yield surface can be written asWe decompose the strain rate into an elastic and plastic part using an additive decomposition:The plastic part of the strain rate is given by a normality conditionwhere the scalar multiplier must be determined. A scalar measure of equivalent plastic strain rate is defined byThe stress rate is assumed to be purely due to the elastic part of the strain rate and is expressed in terms of Hooke's law bywhere and are the Lamés constants for the material.The evolution law for is given aswhere H is the slope of the uniaxial yield stress versus plastic strain curve.During active plastic loading the stress must remain on the yield surface, so thatThe equivalent plastic strain rate is related to byThe kinematic hardening constitutive model is integrated in a rate form as follows. A trial elastic stress is computed aswhere the subscripts and refer to the beginning and end of the increment, respectively. If the trial stress does not exceed the yieldstress, the new stress is set equal to the trial stress. If the yield stress is exceeded, plasticity occurs in the increment. We then write the incremental analogs of the rate equations aswhereFrom the definition of the normal to the yield surface at the end of the increment, ,This can be expanded using the incremental equations asTaking the tensor product of this equation with , using the yield condition at the end of the increment, and solving for :The value for is used in the incremental equations to determine ,, and .subroutine vumat(C Read only -1 nblock, ndir, nshr, nstatev, nfieldv, nprops, lanneal,2 stepTime, totalTime, dt, cmname, coordMp, charLength,3 props, density, strainInc, relSpinInc,4 tempOld, stretchOld, defgradOld, fieldOld,3 stressOld, stateOld, enerInternOld, enerInelasOld,6 tempNew, stretchNew, defgradNew, fieldNew,C Write only -5 stressNew, stateNew, enerInternNew, enerInelasNew )Cinclude 'vaba_param.inc'CC J2 Mises Plasticity with kinematic hardening for planeC strain case.C Elastic predictor, radial corrector algorithm.CC The state variables are stored as:C STATE(*,1) = back stress component 11C STATE(*,2) = back stress component 22C STATE(*,3) = back stress component 33C STATE(*,4) = back stress component 12C STATE(*,5) = equivalent plastic strainCCC All arrays dimensioned by (*) are not used in this algorithm dimension props(nprops), density(nblock),1 coordMp(nblock,*),2 charLength(*), strainInc(nblock,ndir+nshr),3 relSpinInc(*), tempOld(*),4 stretchOld(*), defgradOld(*),5 fieldOld(*), stressOld(nblock,ndir+nshr),6 stateOld(nblock,nstatev), enerInternOld(nblock),7 enerInelasOld(nblock), tempNew(*),8 stretchNew(*), defgradNew(*), fieldNew(*),9 stressNew(nblock,ndir+nshr), stateNew(nblock,nstatev), 1 enerInternNew(nblock), enerInelasNew(nblock)Ccharacter*80 cmnameCparameter( zero = 0., one = 1., two = 2., three = 3.,1 third = one/three, half = .5, twoThirds = two/three,2 threeHalfs = 1.5 )Ce = props(1)xnu = props(2)yield = props(3)hard = props(4)Ctwomu = e / ( one + xnu )thremu = threeHalfs * twomusixmu = three * twomualamda = twomu * ( e - twomu ) / ( sixmu - two * e )term = one / ( twomu * ( one + hard/thremu ) )con1 = sqrt( twoThirds )Cdo 100 i = 1,nblockCC Trial stresstrace = strainInc(i,1) + strainInc(i,2) + strainInc(i,3) sig1 = stressOld(i,1) + alamda*trace + twomu*strainInc(i,1) sig2 = stressOld(i,2) + alamda*trace + twomu*strainInc(i,2) sig3 = stressOld(i,3) + alamda*trace + twomu*strainInc(i,3) sig4 = stressOld(i,4) + twomu*strainInc(i,4) CC Trial stress measured from the back stresss1 = sig1 - stateOld(i,1)s2 = sig2 - stateOld(i,2)s3 = sig3 - stateOld(i,3)s4 = sig4 - stateOld(i,4)CC Deviatoric part of trial stress measured from the back stresssmean = third * ( s1 + s2 + s3 )ds1 = s1 - smeands2 = s2 - smeands3 = s3 - smeanCC Magnitude of the deviatoric trial stress differencedsmag = sqrt( ds1**2 + ds2**2 + ds3**2 + 2.*s4**2 )CC Check for yield by determining the factor for plasticity,C zero for elastic, one for yieldradius = con1 * yieldfacyld = zeroif( dsmag - radius .ge. zero ) facyld = oneCC Add a protective addition factor to prevent a divide by zeroC when dsmag is zero. If dsmag is zero, we will not have exceededC the yield stress and facyld will be zero.dsmag = dsmag + ( one - facyld )CC Calculated increment in gamma (this explicitly includes theC time step)diff = dsmag - radiusdgamma = facyld * term * diffCC Update equivalent plastic straindeqps = con1 * dgammastateNew(i,5) = stateOld(i,5) + deqpsCC Divide dgamma by dsmag so that the deviatoric stresses areC explicitly converted to tensors of unit magnitude in theC following calculationsdgamma = dgamma / dsmagCC Update back stressfactor = hard * dgamma * twoThirdsstateNew(i,1) = stateOld(i,1) + factor * ds1stateNew(i,2) = stateOld(i,2) + factor * ds2stateNew(i,3) = stateOld(i,3) + factor * ds3stateNew(i,4) = stateOld(i,4) + factor * s4CC Update the stressfactor = twomu * dgammastressNew(i,1) = sig1 - factor * ds1stressNew(i,2) = sig2 - factor * ds2stressNew(i,3) = sig3 - factor * ds3stressNew(i,4) = sig4 - factor * s4CC Update the specific internal energy -stressPower = half * (1 ( stressOld(i,1)+stressNew(i,1) )*strainInc(i,1)1 + ( stressOld(i,2)+stressNew(i,2) )*strainInc(i,2) 1 + ( stressOld(i,3)+stressNew(i,3) )*strainInc(i,3) 1 + two*( stressOld(i,4)+stressNew(i,4) )*strainInc(i,4) ) CenerInternNew(i) = enerInternOld(i)1 + stressPower / density(i)CC Update the dissipated inelastic specific energy -plasticWorkInc = dgamma * half * (1 ( stressOld(i,1)+stressNew(i,1) )*ds11 + ( stressOld(i,2)+stressNew(i,2) )*ds2 1 + ( stressOld(i,3)+stressNew(i,3) )*ds3 1 + two*( stressOld(i,4)+stressNew(i,4) )*s4 ) enerInelasNew(i) = enerInelasOld(i)1 + plasticWorkInc / density(i)100 continueCreturnend。