弹塑性线性强化常刚度Umat（1）
问题描述：假设一圆柱半径为5mm，拉伸50mm，弹性模量E=200e3Mpa，泊松比V=0.3，本构曲线取线性强化，圆柱一端约束Z向变形和周向变形，另一端拉伸0.9mm，试对比ABAQUS自带本构与UMAT子程序的计算结果。
对比结果：abaqus结果见图左，umat子程序结果见图右
通过对比发现，Umat子程序与Abaqus自带本构得出结果值完全一致。
umat源码如下：
SUBROUTINE UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD, 1 RPL,DDSDDT,DRPLDE,DRPLDT, 2 STRAN,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,CMNAME, 3 NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT, 4 CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,JSTEP,KINC)C INCLUDE 'ABA_PARAM.INC'C CHARACTER*80 CMNAME DIMENSION STRESS(NTENS),STATEV(NSTATV), 1 DDSDDE(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),DFGRD0(3,3),DFGRD1(3,3), 4 JSTEP(4) double precision E,V,yield0,H,lamdba,G,STATEV double precision hydroStaticPressure,misesEqualStress double precision dEqualPlasticStrain double precision, DIMENSION(NTENS)::deviatoricStress INTEGER i,jC Elastic properties E = PROPS(1) V = PROPS(2) yield0 = PROPS(3) H = (PROPS(5)-PROPS(3))/(PROPS(6)-PROPS(4)) lamdba = E*V/((1+V)*(1-2*V)) G = E/(2*(1+V)) C Calculate the material jacobian matrix do i=1, NTENS do j=1, NTENS DDSDDE(i,j)=0 end do end do do i=1,NDI do j=1,NDI DDSDDE(i,j)=lamdba end do DDSDDE(i,i)=lamdba+2*G DDSDDE(i+NDI,i+NDI)=G end do C Calculate stress-try do i=1,NTENS do j=1,NTENS stress(i)=stress(i)+DDSDDE(i,j)*DSTRAN(j) end do end do C Calculate hydroStaticPressure hydroStaticPressure=0 do i=1,NDI hydroStaticPressure=hydroStaticPressure+stress(i) end do hydroStaticPressure=hydroStaticPressure/3C Calculate the deviatoricStress-try do i=1,NDI deviatoricStress(i)=STRESS(i)-hydroStaticPressure end do do i=1+NDI,NTENS deviatoricStress(i)=stress(i) end do C Calculate misesEqualStress misesEqualStress=0 do i=1,NDI misesEqualStress=misesEqualStress+deviatoricStress(i)**2 end do misesEqualStress=sqrt(1.5*misesEqualStress)C get the nth equalPlasticStrain from STATEV equalPlasticStrain=STATEV(1)C Calculate the nth yield yieldn=yield0+H*equalPlasticStrain if (misesEqualStress>yieldn) then dEqualPlasticStrain=(misesEqualStress-yieldn)/(H+3*G) do i=1,NTENS deviatoricStress(i)=deviatoricStress(i)-3*G*dEqualPlasticStrain*deviatoricStress(i)/misesEqualStress end do do i=1,NDI stress(i)=deviatoricStress(i)+hydroStaticPressure end do do i=1+NDI,NTENS stress(i)=deviatoricStress(i) end do else dEqualPlasticStrain=0 end if STATEV(1)=equalPlasticStrain+dEqualPlasticStrain RETURN END
59~64：计算偏试应力： 67~71：计算Mises等效应力： 74：从STATEV状态变量中获取等效塑性应变 77：弹塑性线性强化本构关系， 79：判断是否屈服 80：计算等效塑性应变增量， 82~84：如果屈服，则更新偏试应力， 86~91：更新试应力 93：如果没有屈服，则不会发生塑性流动 96：将等效塑性应变储存在状态变量中 以上是我结合***论坛上SuperID大神的模型，进一步讨论对弹塑性线性强化常刚度Umat的理解，下节内容将更新弹塑性线性强化切线刚度Umat的相关内容
来源：易木木响叮当
