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UMAT_F_3D_PLASTICITY_VM.f
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!! !!!
!!! Created by Martin Genet, 2008-2016 !!!
!!! !!!
!!! Laboratoire de Mécanique et de Technologie (LMT), Cachan, France !!!
!!! Lawrence Berkeley National Laboratory, California, USA !!!
!!! University of California at San Francisco, USA !!!
!!! Swiss Federal Institute of Technology (ETH), Zurich, Switzerland !!!
!!! École Polytechnique, Palaiseau, France !!!
!!! !!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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,KSTEP,KINC)
C
#include 'ABA_PARAM.INC'
C
CHARACTER*80 CMNAME
C
DIMENSION STRESS(NTENS),STATEV(NSTATV),DDSDDE(NTENS,NTENS),
2 STRAN(NTENS),DSTRAN(NTENS),PROPS(NPROPS)
C
DIMENSION STRESSOLD(NTENS),DSTATEV(NTENS)
C
real E, nu, G, lambda, mu, dlambda
C
PRINT *, "\n INPUT VALUES"
PRINT *, "NOEL (element number) = ", NOEL
PRINT *, "NPT (integration point number) = ", NPT
PRINT *, "KSTEP (step number) = ", KSTEP
PRINT *, "KINC (increment number) = ", KINC
PRINT *, "NSTATV (number of state variables) = ", NSTATV
PRINT *, "STATEV (state variables)"
DO I = 1, NSTATV
PRINT *, STATEV(I)
END DO
PRINT *, "STRAN (total strain)"
DO I = 1, NTENS
PRINT *, STRAN(I)
END DO
PRINT *, "DSTRAN (total strain increment)"
DO I = 1, NTENS
PRINT *, DSTRAN(I)
END DO
C
! E1 = PROPS(1)
! E2 = PROPS(2)
! E3 = PROPS(3)
! nu12 = PROPS(4)
! nu13 = PROPS(5)
! nu23 = PROPS(6)
! G12 = PROPS(7)
! G13 = PROPS(8)
! G23 = PROPS(9)
! sigmac = PROPS(10)
C
! epsilonp11 = STATEV(1)
! epsilonp22 = STATEV(2)
! epsilonp33 = STATEV(3)
! epsilonp12 = STATEV(4)
! epsilonp13 = STATEV(5)
! epsilonp23 = STATEV(6)
C
E = PROPS(1)
PRINT *, "E = ", E
nu = PROPS(2)
PRINT *, "nu = ", nu
G = PROPS(1) / 2 / (1 + PROPS(2))
PRINT *, "G = ", G
sigmac = PROPS(3)
C
lambda = (E * nu) / ((1 + nu) * (1 - (2*nu)))
PRINT *, "lambda = ", lambda
mu = E / (2 * (1 + nu))
PRINT *, "mu = ", mu
C
DDSDDE(1,1) = lambda + 2 * mu
DDSDDE(1,2) = lambda
DDSDDE(1,3) = lambda
DDSDDE(1,4) = 0.
DDSDDE(1,5) = 0.
DDSDDE(1,6) = 0.
DDSDDE(2,1) = lambda
DDSDDE(2,2) = lambda + 2 * mu
DDSDDE(2,3) = lambda
DDSDDE(2,4) = 0.
DDSDDE(2,5) = 0.
DDSDDE(2,6) = 0.
DDSDDE(3,1) = lambda
DDSDDE(3,2) = lambda
DDSDDE(3,3) = lambda + 2 * mu
DDSDDE(3,4) = 0.
DDSDDE(3,5) = 0.
DDSDDE(3,6) = 0.
DDSDDE(4,1) = 0.
DDSDDE(4,2) = 0.
DDSDDE(4,3) = 0.
DDSDDE(4,4) = 2 * mu
DDSDDE(4,5) = 0.
DDSDDE(4,6) = 0.
DDSDDE(5,1) = 0.
DDSDDE(5,2) = 0.
DDSDDE(5,3) = 0.
DDSDDE(5,4) = 0.
DDSDDE(5,5) = 2 * mu
DDSDDE(5,6) = 0.
DDSDDE(6,1) = 0.
DDSDDE(6,2) = 0.
DDSDDE(6,3) = 0.
DDSDDE(6,4) = 0.
DDSDDE(6,5) = 0.
DDSDDE(6,6) = 2 * mu
sigmac = PROPS(3)
C
! DDSDDE(1,1) = (nu23**2*E1**2*E3**2-E1**2*E2*E3)/(nu23**2*E1*
! 1 E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*
! 2 E3+nu13**2*E1**2*E2)
! DDSDDE(1,2) = -((nu12*E1*E2**2+nu13*nu23*E1**2*E2)*E3)/(nu23**2*
! 1 E1*E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*
! 2 E3+nu13**2*E1**2*E2)
! DDSDDE(1,3) = -(nu12*nu23*E1*E2*E3**2+nu13*E1**2*E2*E3)/(nu23**2*
! 1 E1*E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*E3+nu13**2*
! 2 E1**2*E2)
! DDSDDE(1,4) = 0.
! DDSDDE(1,5) = 0.
! DDSDDE(1,6) = 0.
!
! DDSDDE(2,1) = -((nu12*E1*E2**2+nu13*nu23*E1**2*E2)*E3)/(nu23**2*
! 1 E1*E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*E3+nu13**2*
! 2 E1**2*E2)
! DDSDDE(2,2) = -(E1*E2**2*E3-nu13**2*E1**2*E2**2)/(nu23**2*E1*
! 1 E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*E3+nu13**2*
! 2 E1**2*E2)
! DDSDDE(2,3) = -(nu23*E1*E2*E3**2+nu12*nu13*E1*E2**2*E3)/(nu23**2*
! 1 E1*E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*E3+nu13**2*
! 2 E1**2*E2)
! DDSDDE(2,4) = 0.
! DDSDDE(2,5) = 0.
! DDSDDE(2,6) = 0.
!
! DDSDDE(3,1) = -(nu12*nu23*E1*E2*E3**2+nu13*E1**2*E2*E3)/(nu23**2*
! 1 E1*E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*E3+nu13**2*
! 2 E1**2*E2)
! DDSDDE(3,2) = -(nu23*E1*E2*E3**2+nu12*nu13*E1*E2**2*E3)/(nu23**2*
! 1 E1*E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*E3+nu13**2*
! 2 E1**2*E2)
! DDSDDE(3,3) = ((nu12**2*E2**2-E1*E2)*E3**2)/(nu23**2*E1*
! 1 E3**2+(nu12**2*E2**2+(2*nu12*nu13*nu23-1)*E1*E2)*E3+nu13**2*
! 2 E1**2*E2)
! DDSDDE(3,4) = 0.
! DDSDDE(3,5) = 0.
! DDSDDE(3,6) = 0.
!
! DDSDDE(4,1) = 0.
! DDSDDE(4,2) = 0.
! DDSDDE(4,3) = 0.
! DDSDDE(4,4) = 2 * G12
! DDSDDE(4,5) = 0.
! DDSDDE(4,6) = 0.
!
! DDSDDE(5,1) = 0.
! DDSDDE(5,2) = 0.
! DDSDDE(5,3) = 0.
! DDSDDE(5,4) = 0.
! DDSDDE(5,5) = 2 * G13
! DDSDDE(5,6) = 0.
!
! DDSDDE(6,1) = 0.
! DDSDDE(6,2) = 0.
! DDSDDE(6,3) = 0.
! DDSDDE(6,4) = 0.
! DDSDDE(6,5) = 0.
! DDSDDE(6,6) = 2 * G23
C
DO I = 1, NTENS
STRESSOLD(I) = STRESS(I)
DO J = 1, NTENS
STRESS(I)=STRESS(I)+DDSDDE(I,J)*DSTRAN(J)
ENDDO
ENDDO
C
! q = ((STRESS(3)+DSTRESS(3))-((STRESS(3)+DSTRESS(3))+
! 1 (STRESS(2)+DSTRESS(2))+(STRESS(1)+DSTRESS(1)))/3)**2
! q = q + ((STRESS(2)+DSTRESS(2))-((STRESS(3)+DSTRESS(3))+
! 1 (STRESS(2)+DSTRESS(2))+(STRESS(1)+DSTRESS(1)))/3)**2
! q = q + ((STRESS(1)+DSTRESS(1))-((STRESS(3)+DSTRESS(3))+
! 1 (STRESS(2)+DSTRESS(2))+(STRESS(1)+DSTRESS(1)))/3)**2
! q = q + (STRESS(6)+DSTRESS(6))**2+(STRESS(5)+DSTRESS(5))**2+
! 1 (STRESS(6)+DSTRESS(6))**2+(STRESS(4)+DSTRESS(4))**2+
! 2 (STRESS(5)+DSTRESS(5))**2+(STRESS(4)+DSTRESS(4))**2
! PRINT *, q
C
q = (STRESS(3)-(STRESS(3)+STRESS(2)+STRESS(1))/3)**2+
1 (STRESS(2)-(STRESS(3)+STRESS(2)+STRESS(1))/3)**2+
2 (STRESS(1)-(STRESS(3)+STRESS(2)+STRESS(1))/3)**2+
3 2*STRESS(6)**2+2*STRESS(5)**2+2*STRESS(4)**2
! PRINT *, q
C
IF (sqrt(3*q/2) - sigmac > 0) THEN
10 IF (abs(sqrt(3*q/2) - sigmac) / sigmac > 1e-6) THEN
PRINT *, "q = ", sqrt(3*q/2)
PRINT *, "sigmac = ", sigmac
dlambda = (sqrt(3*q/2) - sigmac) / 2 / G / sqrt(3*q/2)
PRINT *, "dlambda = ", dlambda
C
DSTATEV(1)=dlambda*(STRESSOLD(1)-(STRESSOLD(3)+
1 STRESSOLD(2)+STRESSOLD(1))/3)
DSTATEV(2)=dlambda*(STRESSOLD(2)-(STRESSOLD(3)+
2 STRESSOLD(2)+STRESSOLD(1))/3)
DSTATEV(3)=dlambda*(STRESSOLD(3)-(STRESSOLD(3)+
3 STRESSOLD(2)+STRESSOLD(1))/3)
DSTATEV(4)=dlambda*STRESSOLD(4)
DSTATEV(5)=dlambda*STRESSOLD(5)
DSTATEV(6)=dlambda*STRESSOLD(6)
C
! PRINT *, DSTATEV(1)
! PRINT *, DSTATEV(2)
! PRINT *, DSTATEV(3)
! PRINT *, DSTATEV(4)
! PRINT *, DSTATEV(5)
! PRINT *, DSTATEV(6)
C
! STATEV(1)=STATEV(1)+dlambda*(STRESSOLD(1)-(STRESSOLD(3)+
! 1 STRESSOLD(2)+STRESSOLD(1))/3)
! STATEV(2)=STATEV(2)+dlambda*(STRESSOLD(2)-(STRESSOLD(3)+
! 2 STRESSOLD(2)+STRESSOLD(1))/3)
! STATEV(3)=STATEV(3)+dlambda*(STRESSOLD(3)-(STRESSOLD(3)+
! 3 STRESSOLD(2)+STRESSOLD(1))/3)
! STATEV(4)=STATEV(4)+dlambda*STRESSOLD(4)
! STATEV(5)=STATEV(5)+dlambda*STRESSOLD(5)
! STATEV(6)=STATEV(6)+dlambda*STRESSOLD(6)
C
STATEV(1) = STATEV(1) + DSTATEV(1)
STATEV(2) = STATEV(2) + DSTATEV(2)
STATEV(3) = STATEV(3) + DSTATEV(3)
STATEV(4) = STATEV(4) + DSTATEV(4)
STATEV(5) = STATEV(5) + DSTATEV(5)
STATEV(6) = STATEV(6) + DSTATEV(6)
C
! PRINT *, STATEV(1)
! PRINT *, STATEV(2)
! PRINT *, STATEV(3)
! PRINT *, STATEV(4)
! PRINT *, STATEV(5)
! PRINT *, STATEV(6)
C
DO I = 1, NTENS
STRESSOLD(I) = STRESS(I)
DO J = 1, NTENS
STRESS(I) = STRESS(I)-DDSDDE(I,J)*DSTATEV(J)
ENDDO
ENDDO
C
q = (STRESS(3)-(STRESS(3)+STRESS(2)+STRESS(1))/3)**2+
1 (STRESS(2)-(STRESS(3)+STRESS(2)+STRESS(1))/3)**2+
2 (STRESS(1)-(STRESS(3)+STRESS(2)+STRESS(1))/3)**2+
3 2*STRESS(6)**2+2*STRESS(5)**2+2*STRESS(4)**2
C
GOTO 10
ENDIF
ENDIF
C
! PRINT *, "OUTPUT VALUES"
! PRINT *, "STRESS (stress at the end of the increment)"
! DO I = 1, NTENS
! PRINT *, STRESS(I)
! END DO
C
! PRINT *, "DDSDDE (jacobian matrix)"
! DO I = 1, NTENS
! DO J = 1, NTENS
! PRINT *, DDSDDE(I, J)
! END DO
! END DO
C
RETURN
END