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umat_general.for
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SUBROUTINE PULL2(PK,SIG,FINV,DET,NDI)
C> PULL-BACK TIMES DET OF A 2ND ORDER TENSOR
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER I1,J1,II1,JJ1,NDI
DOUBLE PRECISION PK(NDI,NDI),FINV(NDI,NDI)
DOUBLE PRECISION SIG(NDI,NDI)
DOUBLE PRECISION AUX,DET
C
DO I1=1,NDI
DO J1=1,NDI
AUX=ZERO
DO II1=1,NDI
DO JJ1=1,NDI
AUX=AUX+DET*FINV(I1,II1)*FINV(J1,JJ1)*SIG(II1,JJ1)
END DO
END DO
PK(I1,J1)=AUX
END DO
END DO
C
RETURN
END SUBROUTINE PULL2
SUBROUTINE PINVARIANTS(A,INV4,NDI,ST,LAMBDA,BARLAMBDA,DET)
C> AND 4TH PSEUDO-INVARIANTS OF A TENSOR
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI,I,J
DOUBLE PRECISION A(NDI,NDI),DET,SCALE1,ST(NDI,NDI),LAMBDA
DOUBLE PRECISION BARLAMBDA,INV4
C
INV4=ZERO
DO I=1,NDI
DO J=1, NDI
INV4=INV4+A(I,J)*ST(I,J)
ENDDO
ENDDO
C STRETCH
SCALE1=DET**(-ONE /THREE)
BARLAMBDA=DSQRT(INV4)
LAMBDA=BARLAMBDA/SCALE1
C
RETURN
END SUBROUTINE PINVARIANTS
SUBROUTINE METVOL(CVOL,C,PV,PPV,DET,NDI)
C> VOLUMETRIC MATERIAL ELASTICITY TENSOR
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI,I1,J1,K1,L1
DOUBLE PRECISION C(NDI,NDI),CINV(NDI,NDI),
1 CVOL(NDI,NDI,NDI,NDI)
DOUBLE PRECISION PV,PPV,DET
C
CALL MATINV3D(C,CINV,NDI)
C
DO I1 = 1, NDI
DO J1 = 1, NDI
DO K1 = 1, NDI
DO L1 = 1, NDI
CVOL(I1,J1,K1,L1)=
1 DET*PPV*CINV(I1,J1)*CINV(K1,L1)
2 -DET*PV*(CINV(I1,K1)*CINV(J1,L1)
3 +CINV(I1,L1)*CINV(J1,K1))
END DO
END DO
END DO
END DO
C
RETURN
END SUBROUTINE METVOL
SUBROUTINE CONTRACTION42(S,LT,RT,NDI)
C> DOUBLE CONTRACTION BETWEEN 4TH ORDER AND 2ND ORDER TENSOR
C> INPUT:
C> LT - RIGHT 4TH ORDER TENSOR
C> RT - LEFT 2ND ODER TENSOR
C> OUTPUT:
C> S - DOUBLE CONTRACTED TENSOR (2ND ORDER)
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER I1,J1,K1,L1,NDI
C
DOUBLE PRECISION RT(NDI,NDI),LT(NDI,NDI,NDI,NDI)
DOUBLE PRECISION S(NDI,NDI)
DOUBLE PRECISION AUX
C
DO I1=1,NDI
DO J1=1,NDI
AUX=ZERO
DO K1=1,NDI
DO L1=1,NDI
AUX=AUX+LT(I1,J1,K1,L1)*RT(K1,L1)
END DO
END DO
S(I1,J1)=AUX
END DO
END DO
RETURN
END SUBROUTINE CONTRACTION42
C>********************************************************************
C> Record of revisions: |
C> Date Programmer Description of change |
C> ==== ========== ===================== |
C> 15/11/2017 Joao Ferreira cont mech general eqs |
C> 01/11/2018 Joao Ferreira comments added |
C>--------------------------------------------------------------------
C> Description:
C> UMAT: IMPLEMENTATION OF THE CONSTITUTIVE EQUATIONS BASED UPON
C> A STRAIN-ENERGY FUNCTION (SEF).
C> THIS CODE, AS IS, EXPECTS A SEF BASED ON THE INVARIANTS OF THE
C> CAUCHY-GREEN TENSORS. A VISCOELASTIC COMPONENT IS ALSO
C> INCLUDED IF NEEDED.
C> YOU CAN CHOOSE TO COMPUTE AT THE MATERIAL FRAME AND THEN
C> PUSHFORWARD OR COPUTE AND THE SPATIAL FRAME DIRECTLY.
C>--------------------------------------------------------------------
C> IF YOU WANT TO ADAPT THE CODE ACCORDING TO YOUR SEF:
C> ISOMAT - DERIVATIVES OF THE SEF IN ORDER TO THE INVARIANTS
C> ADD OTHER CONTRIBUTIONS: STRESS AND TANGENT MATRIX
C>--------------------------------------------------------------------
C STATE VARIABLES: CHECK ROUTINES - INITIALIZE, WRITESDV, READSDV.
C>--------------------------------------------------------------------
C> UEXTERNALDB: READ FILAMENTS ORIENTATION AND PREFERED DIRECTION
C>--------------------------------------------------------------------
C>---------------------------------------------------------------------
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,NSTATEV,PROPS,NPROPS,COORDS,DROT,PNEWDT,
4 CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,KSTEP,KINC)
C
C----------------------------------------------------------------------
C--------------------------- DECLARATIONS -----------------------------
C----------------------------------------------------------------------
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C ADD COMMON BLOCKS HERE IF NEEDED (and in uexternal)
C COMMON /KBLOCK/KBLOCK
COMMON /KFIB/FIBORI
C
CHARACTER*8 CMNAME
C
INTEGER NDI, NSHR, NTENS, NSTATEV, NPROPS, NOEL, NPT,
1 LAYER, KSPT, KSTEP, KINC
C
DOUBLE PRECISION STRESS(NTENS),STATEV(NSTATEV),
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 FIBORI(NELEM,4)
C
DOUBLE PRECISION SSE, SPD, SCD, RPL, DRPLDT, DTIME, TEMP,
1 DTEMP,PNEWDT,CELENT
C
INTEGER NTERM
C
C FLAGS
C INTEGER FLAG1
C UTILITY TENSORS
DOUBLE PRECISION UNIT2(NDI,NDI),UNIT4(NDI,NDI,NDI,NDI),
1 UNIT4S(NDI,NDI,NDI,NDI),
2 PROJE(NDI,NDI,NDI,NDI),PROJL(NDI,NDI,NDI,NDI)
C KINEMATICS
DOUBLE PRECISION DISTGR(NDI,NDI),C(NDI,NDI),B(NDI,NDI),
1 CBAR(NDI,NDI),BBAR(NDI,NDI),DISTGRINV(NDI,NDI),
2 UBAR(NDI,NDI),VBAR(NDI,NDI),ROT(NDI,NDI),
3 DFGRD1INV(NDI,NDI)
DOUBLE PRECISION DET,CBARI1,CBARI2
C VOLUMETRIC CONTRIBUTION
DOUBLE PRECISION PKVOL(NDI,NDI),SVOL(NDI,NDI),
1 CVOL(NDI,NDI,NDI,NDI),CMVOL(NDI,NDI,NDI,NDI)
DOUBLE PRECISION KBULK,PV,PPV,SSEV
C ISOCHORIC CONTRIBUTION
DOUBLE PRECISION SISO(NDI,NDI),PKISO(NDI,NDI),PK2(NDI,NDI),
1 CISO(NDI,NDI,NDI,NDI),CMISO(NDI,NDI,NDI,NDI),
2 SFIC(NDI,NDI),CFIC(NDI,NDI,NDI,NDI),
3 PKFIC(NDI,NDI),CMFIC(NDI,NDI,NDI,NDI)
C ISOCHORIC ISOTROPIC CONTRIBUTION
DOUBLE PRECISION C10,C01,SSEISO,DISO(5),PKMATFIC(NDI,NDI),
1 SMATFIC(NDI,NDI),SISOMATFIC(NDI,NDI),
2 CMISOMATFIC(NDI,NDI,NDI,NDI),
3 CISOMATFIC(NDI,NDI,NDI,NDI)
C ISOCHORIC ANISOTROPIC CONTRIBUTION
DOUBLE PRECISION K1,K2,KDISP,SSEANISO,
1 DANISO(4),
2 PKMATFICANISO(NDI,NDI),
3 SANISOMATFIC(NDI,NDI),
4 CMANISOMATFIC(NDI,NDI,NDI,NDI),
6 CANISOMATFIC(NDI,NDI,NDI,NDI),
8 LAMBDA,BARLAMBDA,
9 CBARI4
DOUBLE PRECISION VORIF(3),VD(3),M0(3,3),MM(3,3),
1 VORIF2(3),VD2(3),N0(3,3),NN(3,3)
C LIST VARS OF OTHER CONTRIBUTIONS HERE
C
C VISCOUS PROPERTIES (GENERALIZED MAXWEL DASHPOTS)
DOUBLE PRECISION VSCPROPS(6)
INTEGER VV
C JAUMMAN RATE CONTRIBUTION (REQUIRED FOR ABAQUS UMAT)
DOUBLE PRECISION CJR(NDI,NDI,NDI,NDI)
C CAUCHY STRESS AND ELASTICITY TENSOR
DOUBLE PRECISION SIGMA(NDI,NDI),DDSIGDDE(NDI,NDI,NDI,NDI),
1 DDPKDDE(NDI,NDI,NDI,NDI)
C TESTING/DEBUG VARS
DOUBLE PRECISION STEST(NDI,NDI), CTEST(NDI,NDI,NDI,NDI)
C----------------------------------------------------------------------
C-------------------------- INITIALIZATIONS ---------------------------
C----------------------------------------------------------------------
C IDENTITY AND PROJECTION TENSORS
UNIT2=ZERO
UNIT4=ZERO
UNIT4S=ZERO
PROJE=ZERO
PROJL=ZERO
C KINEMATICS
DISTGR=ZERO
C=ZERO
B=ZERO
CBAR=ZERO
BBAR=ZERO
UBAR=ZERO
VBAR=ZERO
ROT=ZERO
DET=ZERO
CBARI1=ZERO
CBARI2=ZERO
C VOLUMETRIC
PKVOL=ZERO
SVOL=ZERO
CVOL=ZERO
KBULK=ZERO
PV=ZERO
PPV=ZERO
SSEV=ZERO
C ISOCHORIC
SISO=ZERO
PKISO=ZERO
PK2=ZERO
CISO=ZERO
CFIC=ZERO
SFIC=ZERO
PKFIC=ZERO
C ISOTROPIC
C10=ZERO
C01=ZERO
SSEISO=ZERO
DISO=ZERO
PKMATFIC=ZERO
SMATFIC=ZERO
SISOMATFIC=ZERO
CMISOMATFIC=ZERO
CISOMATFIC=ZERO
C INITIALIZE OTHER CONT HERE
C
C JAUMANN RATE
CJR=ZERO
C TOTAL CAUCHY STRESS AND ELASTICITY TENSORS
SIGMA=ZERO
DDSIGDDE=ZERO
C
C----------------------------------------------------------------------
C------------------------ IDENTITY TENSORS ----------------------------
C----------------------------------------------------------------------
CALL ONEM(UNIT2,UNIT4,UNIT4S,NDI)
C----------------------------------------------------------------------
C------------------- MATERIAL CONSTANTS AND DATA ----------------------
C----------------------------------------------------------------------
C VOLUMETRIC
KBULK = PROPS(1)
C ISOCHORIC ISOTROPIC NEO HOOKE
C10 = PROPS(2)
C01 = PROPS(3)
C ISOCHORIC ANISOTROPIC GHO
K1 = PROPS(4)
K2 = PROPS(5)
KDISP = PROPS(6)
C VISCOUS EFFECTS: MAXWELL ELEMENTS (MAX:3)
C VV = INT(PROPS(7))
C VSCPROPS = PROPS(8:13)
C NUMERICAL COMPUTATIONS
NTERM = 60
C
C STATE VARIABLES
C
IF ((TIME(1).EQ.ZERO).AND.(KSTEP.EQ.1)) THEN
CALL INITIALIZE(STATEV)
ENDIF
C READ STATEV
CALL SDVREAD(STATEV)
C
C----------------------------------------------------------------------
C---------------------------- KINEMATICS ------------------------------
C----------------------------------------------------------------------
C DISTORTION GRADIENT
CALL FSLIP(DFGRD1,DISTGR,DET,NDI)
C INVERSE OF DISTORTION GRADIENT
CALL MATINV3D(DFGRD1,DFGRD1INV,NDI)
C INVERSE OF DISTORTION GRADIENT
CALL MATINV3D(DISTGR,DISTGRINV,NDI)
C CAUCHY-GREEN DEFORMATION TENSORS
CALL DEFORMATION(DFGRD1,C,B,NDI)
CALL DEFORMATION(DISTGR,CBAR,BBAR,NDI)
C FIBER UNIT VECTOR AND STRUCTURAL TENSOR
CALL FIBDIR(FIBORI,M0,MM,NELEM,NOEL,NDI,VORIF,VD,DISTGR,DFGRD1)
C INVARIANTS OF DEVIATORIC DEFORMATION TENSORS
CALL INVARIANTS(CBAR,CBARI1,CBARI2,NDI)
C
CALL PINVARIANTS(CBAR,CBARI4,NDI,M0,LAMBDA,BARLAMBDA,DET)
C
C STRETCH TENSORS
CALL STRETCH(CBAR,BBAR,UBAR,VBAR,NDI)
C ROTATION TENSORS
CALL ROTATION(DISTGR,ROT,UBAR,NDI)
C DEVIATORIC PROJECTION TENSORS
CALL PROJEUL(UNIT2,UNIT4S,PROJE,NDI)
C
CALL PROJLAG(C,UNIT4,PROJL,NDI)
C----------------------------------------------------------------------
C--------------------- CONSTITUTIVE RELATIONS ------------------------
C----------------------------------------------------------------------
C
C---- VOLUMETRIC ------------------------------------------------------
C STRAIN-ENERGY AND DERIVATIVES (CHANGE HERE ACCORDING TO YOUR MODEL)
CALL VOL(SSEV,PV,PPV,KBULK,DET)
CALL ISOMAT(SSEISO,DISO,C10,C01,CBARI1,CBARI2)
CALL ANISOMAT(SSEANISO,DANISO,DISO,K1,K2,KDISP,CBARI4,CBARI1)
C
C---- ISOCHORIC ISOTROPIC ---------------------------------------------
C PK2 'FICTICIOUS' STRESS TENSOR
CALL PK2ISOMATFIC(PKMATFIC,DISO,CBAR,CBARI1,UNIT2,NDI)
C CAUCHY 'FICTICIOUS' STRESS TENSOR
CALL SIGISOMATFIC(SISOMATFIC,PKMATFIC,DISTGR,DET,NDI)
C 'FICTICIOUS' MATERIAL ELASTICITY TENSOR
CALL CMATISOMATFIC(CMISOMATFIC,CBAR,CBARI1,CBARI2,
1 DISO,UNIT2,UNIT4,DET,NDI)
C 'FICTICIOUS' SPATIAL ELASTICITY TENSOR
CALL CSISOMATFIC(CISOMATFIC,CMISOMATFIC,DISTGR,DET,NDI)
C
C---- FIBERS (ONE FAMILY) -------------------------------------------
C
CALL PK2ANISOMATFIC(PKMATFICANISO,DANISO,CBAR,CBARI4,M0,NDI)
CALL PUSH2(SANISOMATFIC,PKMATFICANISO,DISTGR,DET,NDI)
C
CALL CMATANISOMATFIC(CMANISOMATFIC,M0,DANISO,UNIT2,DET,NDI)
CALL PUSH4(CANISOMATFIC,CMANISOMATFIC,DISTGR,DET,NDI)
C----------------------------------------------------------------------
C SUM OF ALL ELASTIC CONTRIBUTIONS
C----------------------------------------------------------------------
C STRAIN-ENERGY
SSE=SSEV+SSEISO+SSEANISO
C PK2 'FICTICIOUS' STRESS
PKFIC=PKMATFIC+PKMATFICANISO
C CAUCHY 'FICTICIOUS' STRESS
SFIC=SISOMATFIC+SANISOMATFIC
C MATERIAL 'FICTICIOUS' ELASTICITY TENSOR
CMFIC=CMISOMATFIC+CMANISOMATFIC
C SPATIAL 'FICTICIOUS' ELASTICITY TENSOR
CFIC=CISOMATFIC+CANISOMATFIC
C
C----------------------------------------------------------------------
C-------------------------- STRESS MEASURES ---------------------------
C----------------------------------------------------------------------
C
C---- VOLUMETRIC ------------------------------------------------------
C PK2 STRESS
CALL PK2VOL(PKVOL,PV,C,NDI)
C CAUCHY STRESS
CALL SIGVOL(SVOL,PV,UNIT2,NDI)
C
C---- ISOCHORIC -------------------------------------------------------
C PK2 STRESS
CALL PK2ISO(PKISO,PKFIC,PROJL,DET,NDI)
C CAUCHY STRESS
CALL SIGISO(SISO,SFIC,PROJE,NDI)
C
C---- VOLUMETRIC + ISOCHORIC ------------------------------------------
C PK2 STRESS
PK2 = PKVOL + PKISO
C CAUCHY STRESS
SIGMA = SVOL + SISO
C
C----------------------------------------------------------------------
C-------------------- MATERIAL ELASTICITY TENSOR ----------------------
C----------------------------------------------------------------------
C
C---- VOLUMETRIC ------------------------------------------------------
C
CALL METVOL(CMVOL,C,PV,PPV,DET,NDI)
C
C---- ISOCHORIC -------------------------------------------------------
C
CALL METISO(CMISO,CMFIC,PROJL,PKISO,PKFIC,C,UNIT2,DET,NDI)
C
C----------------------------------------------------------------------
C
DDPKDDE= CMVOL + CMISO
C
C----------------------------------------------------------------------
C--------------------- SPATIAL ELASTICITY TENSOR ----------------------
C----------------------------------------------------------------------
C
C---- VOLUMETRIC ------------------------------------------------------
C
CALL SETVOL(CVOL,PV,PPV,UNIT2,UNIT4S,NDI)
C
C---- ISOCHORIC -------------------------------------------------------
C
CALL SETISO(CISO,CFIC,PROJE,SISO,SFIC,UNIT2,NDI)
C
C-----JAUMMAN RATE ----------------------------------------------------
C
CALL SETJR(CJR,SIGMA,UNIT2,NDI)
C
C----------------------------------------------------------------------
C
C ELASTICITY TENSOR
DDSIGDDE=CVOL+CISO+CJR
C
C----------------------------------------------------------------------
C------------------------- INDEX ALLOCATION ---------------------------
C----------------------------------------------------------------------
C VOIGT NOTATION - FULLY SIMMETRY IMPOSED
CALL INDEXX(STRESS,DDSDDE,SIGMA,DDSIGDDE,NTENS,NDI)
C
C----------------------------------------------------------------------
C--------------------------- STATE VARIABLES --------------------------
C----------------------------------------------------------------------
C DO K1 = 1, NTENS
C STATEV(1:27) = VISCOUS TENSORS
CALL SDVWRITE(DET,LAMBDA,STATEV)
C END DO
C----------------------------------------------------------------------
RETURN
END
C----------------------------------------------------------------------
C--------------------------- END OF UMAT ------------------------------
C----------------------------------------------------------------------
C
SUBROUTINE PROJEUL(A,AA,PE,NDI)
C> EULERIAN PROJECTION TENSOR
C INPUTS:
C IDENTITY TENSORS - A, AA
C OUTPUTS:
C 4TH ORDER SYMMETRIC EULERIAN PROJECTION TENSOR - PE
C
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER I,J,K,L,NDI
C
DOUBLE PRECISION A(NDI,NDI),AA(NDI,NDI,NDI,NDI),
1 PE(NDI,NDI,NDI,NDI)
C
DO I=1,NDI
DO J=1,NDI
DO K=1,NDI
DO L=1,NDI
PE(I,J,K,L)=AA(I,J,K,L)-(ONE/THREE)*(A(I,J)*A(K,L))
END DO
END DO
END DO
END DO
C
RETURN
END SUBROUTINE PROJEUL
SUBROUTINE SIGVOL(SVOL,PV,UNIT2,NDI)
C> VOLUMETRIC CAUCHY STRESS
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI,I1,J1
DOUBLE PRECISION UNIT2(NDI,NDI),SVOL(NDI,NDI)
DOUBLE PRECISION PV
C
DO I1=1,NDI
DO J1=1,NDI
SVOL(I1,J1)=PV*UNIT2(I1,J1)
END DO
END DO
C
RETURN
END SUBROUTINE SIGVOL
SUBROUTINE ISOMAT(SSEISO,DISO,C10,C01,CBARI1,CBARI2)
C> ISOTROPIC MATRIX : ISOCHORIC SEF AND DERIVATIVES
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
DOUBLE PRECISION SSEISO,DISO(5)
DOUBLE PRECISION C10,C01,CBARI1,CBARI2
C
SSEISO=C10*(CBARI1-THREE)+C01*(CBARI2-THREE)
C
!FIRST DERIVATIVE OF SSEISO IN ORDER TO I1
DISO(1)=C10
!FIRST DERIVATIVE OF SSEISO IN ORDER TO I2
DISO(2)=C01
!SECOND DERIVATIVE OF SSEISO IN ORDER TO I1
DISO(3)=ZERO
!SECOND DERIVATIVE OF SSEISO IN ORDER TO I2
DISO(4)=ZERO
!SECOND DERIVATIVE OF SSEISO IN ORDER TO I1 AND I2
DISO(5)=ZERO
C
RETURN
END SUBROUTINE ISOMAT
SUBROUTINE SDVREAD(STATEV)
C> VISCOUS DISSIPATION: READ STATE VARS
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
DOUBLE PRECISION STATEV(NSDV)
C read your sdvs here. they should be allocated.
C after the viscous terms (only if you use viscosity check hvread)
! POS1=9*VV
! DO I1=1,NCH
! POS2=POS1+I1
! FRAC(I1)=STATEV(POS2)
! ENDDO
C
C
RETURN
C
END SUBROUTINE SDVREAD
SUBROUTINE ANISOMAT(SSEANISO,DANISO,DISO,K1,K2,KDISP,I4,I1)
C> ANISOTROPIC PART : ISOCHORIC SEF AND DERIVATIVES
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
DOUBLE PRECISION SSEISO,DANISO(4),DISO(5)
DOUBLE PRECISION K1,K2,KDISP,I4,I1
DOUBLE PRECISION DUDI1,D2UD2I1,SSEANISO
DOUBLE PRECISION E1,EE2,EE3,DUDI4,D2UD2I4,D2DUDI1DI4,D2DUDI2DI4
C
DUDI1=DISO(1)
D2UD2I1=DISO(3)
C
E1=I4*(ONE-THREE*KDISP)+I1*KDISP-ONE
C
SSEANISO=(K1/K2)*(DEXP(K1*E1*E1)-ONE)
IF(E1.GT.ZERO) THEN
C
EE2=DEXP(K2*E1*E1)
EE3=(ONE+TWO*K2*E1*E1)
C
DUDI1=DUDI1+K1*KDISP*E1*EE2
D2UD2I1=D2UD2I1+K1*KDISP*KDISP*EE3*EE2
C
DUDI4=K1*(ONE-THREE*KDISP)*E1*EE2
C
D2UD2I4=K1*((ONE-THREE*KDISP)**TWO)*EE3*EE2
D2DUDI1DI4=K1*(ONE-THREE*KDISP)*KDISP*EE3*EE2
D2DUDI2DI4=ZERO
C
ELSE
DUDI4=ZERO
D2UD2I4=ZERO
D2DUDI1DI4=ZERO
D2DUDI2DI4=ZERO
D2UD2I1=ZERO
C
END IF
!FIRST DERIVATIVE OF SSEANISO IN ORDER TO I1
DANISO(1)=DUDI4
!FIRST DERIVATIVE OF SSEANISO IN ORDER TO I2
DANISO(2)=D2UD2I4
!2ND DERIVATIVE OF SSEANISO IN ORDER TO I1
DANISO(3)=D2DUDI1DI4
!2ND DERIVATIVE OF SSEANISO IN ORDER TO I2
DANISO(4)=D2DUDI2DI4
C
DISO(1)=DUDI1
DISO(3)=D2UD2I1
C
RETURN
END SUBROUTINE ANISOMAT
SUBROUTINE PK2VOL(PKVOL,PV,C,NDI)
C> VOLUMETRIC PK2 STRESS
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI,I1,J1
DOUBLE PRECISION PKVOL(NDI,NDI),C(NDI,NDI),CINV(NDI,NDI)
DOUBLE PRECISION PV
C
CALL MATINV3D(C,CINV,NDI)
C
DO I1=1,NDI
DO J1=1,NDI
PKVOL(I1,J1)=PV*CINV(I1,J1)
END DO
END DO
C
RETURN
END SUBROUTINE PK2VOL
SUBROUTINE PULL4(MAT,SPATIAL,FINV,DET,NDI)
C> PULL-BACK TIMES DET OF 4TH ORDER TENSOR
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER I1,J1,K1,L1,II1,JJ1,KK1,LL1,NDI
DOUBLE PRECISION MAT(NDI,NDI,NDI,NDI),FINV(NDI,NDI)
DOUBLE PRECISION SPATIAL(NDI,NDI,NDI,NDI)
DOUBLE PRECISION AUX,DET
C
DO I1=1,NDI
DO J1=1,NDI
DO K1=1,NDI
DO L1=1,NDI
AUX=ZERO
DO II1=1,NDI
DO JJ1=1,NDI
DO KK1=1,NDI
DO LL1=1,NDI
AUX=AUX+DET*
+ FINV(I1,II1)*FINV(J1,JJ1)*
+ FINV(K1,KK1)*FINV(L1,LL1)*SPATIAL(II1,JJ1,KK1,LL1)
END DO
END DO
END DO
END DO
MAT(I1,J1,K1,L1)=AUX
END DO
END DO
END DO
END DO
C
RETURN
END SUBROUTINE PULL4
SUBROUTINE SETJR(CJR,SIGMA,UNIT2,NDI)
C> JAUMAN RATE CONTRIBUTION FOR THE SPATIAL ELASTICITY TENSOR
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI,I1,J1,K1,L1
DOUBLE PRECISION UNIT2(NDI,NDI),
1 CJR(NDI,NDI,NDI,NDI),SIGMA(NDI,NDI)
C
DO I1 = 1, NDI
DO J1 = 1, NDI
DO K1 = 1, NDI
DO L1 = 1, NDI
CJR(I1,J1,K1,L1)=
1 (ONE/TWO)*(UNIT2(I1,K1)*SIGMA(J1,L1)
2 +SIGMA(I1,K1)*UNIT2(J1,L1)+UNIT2(I1,L1)*SIGMA(J1,K1)
3 +SIGMA(I1,L1)*UNIT2(J1,K1))
END DO
END DO
END DO
END DO
C
RETURN
END SUBROUTINE SETJR
SUBROUTINE CONTRACTION44(S,LT,RT,NDI)
C> DOUBLE CONTRACTION BETWEEN 4TH ORDER TENSORS
C> INPUT:
C> LT - RIGHT 4TH ORDER TENSOR
C> RT - LEFT 4TH ORDER TENSOR
C> OUTPUT:
C> S - DOUBLE CONTRACTED TENSOR (4TH ORDER)
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER I1,J1,K1,L1,M1,N1,NDI
C
DOUBLE PRECISION LT(NDI,NDI,NDI,NDI),RT(NDI,NDI,NDI,NDI)
DOUBLE PRECISION S(NDI,NDI,NDI,NDI)
DOUBLE PRECISION AUX
C
DO I1=1,NDI
DO J1=1,NDI
DO K1=1,NDI
DO L1=1,NDI
AUX=ZERO
DO M1=1,NDI
DO N1=1,NDI
AUX=AUX+LT(I1,J1,M1,N1)*RT(M1,N1,K1,L1)
END DO
END DO
S(I1,J1,K1,L1)=AUX
END DO
END DO
END DO
END DO
C
RETURN
END SUBROUTINE CONTRACTION44
SUBROUTINE INITIALIZE(STATEV)
C
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
C COMMON /KCOMMON/KBLOCK
C
C DOUBLE PRECISION TIME(2),KSTEP
INTEGER I1,POS,POS1,POS2,POS3
DOUBLE PRECISION STATEV(NSDV)
C DETERMINANT
STATEV(1)=ONE
C
RETURN
C
END SUBROUTINE INITIALIZE
SUBROUTINE SETVOL(CVOL,PV,PPV,UNIT2,UNIT4S,NDI)
C> VOLUMETRIC SPATIAL ELASTICITY TENSOR
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI,I1,J1,K1,L1
DOUBLE PRECISION UNIT2(NDI,NDI),UNIT4S(NDI,NDI,NDI,NDI),
1 CVOL(NDI,NDI,NDI,NDI)
DOUBLE PRECISION PV,PPV
C
DO I1 = 1, NDI
DO J1 = 1, NDI
DO K1 = 1, NDI
DO L1 = 1, NDI
CVOL(I1,J1,K1,L1)=
1 PPV*UNIT2(I1,J1)*UNIT2(K1,L1)
2 -TWO*PV*UNIT4S(I1,J1,K1,L1)
END DO
END DO
END DO
END DO
C
RETURN
END SUBROUTINE SETVOL
SUBROUTINE PK2ISOMATFIC(FIC,DISO,CBAR,CBARI1,UNIT2,NDI)
C> ISOTROPIC MATRIX: 2PK 'FICTICIOUS' STRESS TENSOR
C INPUT:
C DISO - STRAIN-ENERGY DERIVATIVES
C CBAR - DEVIATORIC LEFT CAUCHY-GREEN TENSOR
C CBARI1,CBARI2 - CBAR INVARIANTS
C UNIT2 - 2ND ORDER IDENTITY TENSOR
C OUTPUT:
C FIC - 2ND PIOLA KIRCHOOF 'FICTICIOUS' STRESS TENSOR
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER I1,J1,NDI
DOUBLE PRECISION FIC(NDI,NDI),DISO(5),CBAR(NDI,NDI),UNIT2(NDI,NDI)
DOUBLE PRECISION DUDI1,DUDI2,CBARI1
DOUBLE PRECISION AUX1,AUX2
C
DUDI1=DISO(1)
DUDI2=DISO(2)
C
AUX1=TWO*(DUDI1+CBARI1*DUDI2)
AUX2=-TWO*DUDI2
C
DO I1=1,NDI
DO J1=1,NDI
FIC(I1,J1)=AUX1*UNIT2(I1,J1)+AUX2*CBAR(I1,J1)
END DO
END DO
C
RETURN
END SUBROUTINE PK2ISOMATFIC
SUBROUTINE UEXTERNALDB(LOP,LRESTART,TIME,DTIME,KSTEP,KINC)
C> READ MESH DATA
INCLUDE 'ABA_PARAM.INC'
INCLUDE 'PARAM_UMAT.INC'
C
C UEXTERNAL just called once; work in parallel computing
C ADD COMMON BLOCKS HERE IF NEEDED (and in UMAT)
C COMMON /KBLOCK/KBLOCK
COMMON /KFIB/FIBORI
C
REAL*8 DTIME
DIMENSION TIME(2)
CHARACTER(256) FILENAME
CHARACTER(256) JOBDIR
INTEGER LENJOBDIR
REAL*8 FIBORI(NELEM,4)
C LOP=0 --> START OF THE ANALYSIS
IF(LOP.EQ.0.OR.LOP.EQ.4) THEN
C
CALL GETOUTDIR(JOBDIR,LENJOBDIR)
C DIR1 DEFNIED IN PARAM_UMAT.INC
FILENAME=JOBDIR(:LENJOBDIR)//'/'//DIR1
C
OPEN(15,FILE=FILENAME)
DO I=1,NELEM
READ(15,*) (FIBORI(I,J),J=1,4)
END DO
CLOSE(15)
!C
END IF
C
RETURN
C
END SUBROUTINE UEXTERNALDB
SUBROUTINE GETOUTDIR(OUTDIR, LENOUTDIR)
C> GET CURRENT WORKING DIRECTORY
INCLUDE 'aba_param.inc'
C
CHARACTER*256 OUTDIR
INTEGER LENOUTDIR
C
CALL GETCWD(OUTDIR)
c OUTDIR=OUTDIR(1:SCAN(OUTDIR,'\',BACK=.TRUE.)-1)
LENOUTDIR=LEN_TRIM(OUTDIR)
C
RETURN
END SUBROUTINE GETOUTDIR
SUBROUTINE SIGISOMATFIC(SFIC,PKFIC,F,DET,NDI)
C> ISOTROPIC MATRIX: ISOCHORIC CAUCHY STRESS
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI
DOUBLE PRECISION SFIC(NDI,NDI),F(NDI,NDI),
1 PKFIC(NDI,NDI)
DOUBLE PRECISION DET
C
CALL PUSH2(SFIC,PKFIC,F,DET,NDI)
C
RETURN
END SUBROUTINE SIGISOMATFIC
SUBROUTINE PK2ANISOMATFIC(AFIC,DANISO,CBAR,INV4,ST0,NDI)
C> ANISOTROPIC MATRIX: 2PK 'FICTICIOUS' STRESS TENSOR
C INPUT:
C DANISO - ANISOTROPIC STRAIN-ENERGY DERIVATIVES
C CBAR - DEVIATORIC LEFT CAUCHY-GREEN TENSOR
C INV1,INV4 -CBAR INVARIANTS
C UNIT2 - 2ND ORDER IDENTITY TENSOR
C OUTPUT:
C AFIC - 2ND PIOLA KIRCHOOF 'FICTICIOUS' STRESS TENSOR
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI
DOUBLE PRECISION AFIC(NDI,NDI),DANISO(3),CBAR(3,3)
DOUBLE PRECISION DUDI4,DI4DC(3,3),INV4
DOUBLE PRECISION ST0(3,3)
C
C
C-----------------------------------------------------------------------------
!FIRST DERIVATIVE OF SSEANISO IN ORDER TO I4
DUDI4=DANISO(1)
C
DI4DC=ST0
C
AFIC=TWO*(DUDI4*DI4DC)
C
RETURN
END SUBROUTINE PK2ANISOMATFIC
SUBROUTINE CONTRACTION22(AUX,LT,RT,NDI)
C> DOUBLE CONTRACTION BETWEEN 2ND ORDER AND 2ND ORDER TENSOR
C> INPUT:
C> LT - RIGHT 2ND ORDER TENSOR
C> RT - LEFT 4TH ODER TENSOR
C> OUTPUT:
C> AUX - DOUBLE CONTRACTED TENSOR (SCALAR)
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER I1,J1,K1,L1,NDI
C
DOUBLE PRECISION LT(NDI,NDI),RT(NDI,NDI)
DOUBLE PRECISION AUX
C
AUX=ZERO
DO I1=1,NDI
DO J1=1,NDI
AUX=AUX+LT(I1,J1)*RT(J1,I1)
END DO
END DO
RETURN
END SUBROUTINE CONTRACTION22
SUBROUTINE STRETCH(C,B,U,V,NDI)
C> STRETCH TENSORS
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER NDI
DOUBLE PRECISION C(NDI,NDI),B(NDI,NDI),U(NDI,NDI),V(NDI,NDI)
DOUBLE PRECISION EIGVAL(NDI),OMEGA(NDI),EIGVEC(NDI,NDI)
C
CALL SPECTRAL(C,OMEGA,EIGVEC)
C
EIGVAL(1) = DSQRT(OMEGA(1))
EIGVAL(2) = DSQRT(OMEGA(2))
EIGVAL(3) = DSQRT(OMEGA(3))
C
U(1,1) = EIGVAL(1)
U(2,2) = EIGVAL(2)
U(3,3) = EIGVAL(3)
C
U = MATMUL(MATMUL(EIGVEC,U),TRANSPOSE(EIGVEC))
C
CALL SPECTRAL(B,OMEGA,EIGVEC)
C
EIGVAL(1) = DSQRT(OMEGA(1))
EIGVAL(2) = DSQRT(OMEGA(2))
EIGVAL(3) = DSQRT(OMEGA(3))
C write(*,*) eigvec(1,1),eigvec(2,1),eigvec(3,1)
C
V(1,1) = EIGVAL(1)
V(2,2) = EIGVAL(2)
V(3,3) = EIGVAL(3)
C
V = MATMUL(MATMUL(EIGVEC,V),TRANSPOSE(EIGVEC))
RETURN
END SUBROUTINE STRETCH
SUBROUTINE MATINV3D(A,A_INV,NDI)
C> INVERSE OF A 3X3 MATRIX
C RETURN THE INVERSE OF A(3,3) - A_INV
IMPLICIT NONE
C
INTEGER NDI
C
DOUBLE PRECISION A(NDI,NDI),A_INV(NDI,NDI),DET_A,DET_A_INV
C
DET_A = A(1,1)*(A(2,2)*A(3,3) - A(3,2)*A(2,3)) -
+ A(2,1)*(A(1,2)*A(3,3) - A(3,2)*A(1,3)) +
+ A(3,1)*(A(1,2)*A(2,3) - A(2,2)*A(1,3))
IF (DET_A .LE. 0.D0) THEN
WRITE(*,*) 'WARNING: SUBROUTINE MATINV3D:'
WRITE(*,*) 'WARNING: DET OF MAT=',DET_A
RETURN
END IF
C
DET_A_INV = 1.D0/DET_A
C
A_INV(1,1) = DET_A_INV*(A(2,2)*A(3,3)-A(3,2)*A(2,3))
A_INV(1,2) = DET_A_INV*(A(3,2)*A(1,3)-A(1,2)*A(3,3))
A_INV(1,3) = DET_A_INV*(A(1,2)*A(2,3)-A(2,2)*A(1,3))
A_INV(2,1) = DET_A_INV*(A(3,1)*A(2,3)-A(2,1)*A(3,3))
A_INV(2,2) = DET_A_INV*(A(1,1)*A(3,3)-A(3,1)*A(1,3))
A_INV(2,3) = DET_A_INV*(A(2,1)*A(1,3)-A(1,1)*A(2,3))
A_INV(3,1) = DET_A_INV*(A(2,1)*A(3,2)-A(3,1)*A(2,2))
A_INV(3,2) = DET_A_INV*(A(3,1)*A(1,2)-A(1,1)*A(3,2))
A_INV(3,3) = DET_A_INV*(A(1,1)*A(2,2)-A(2,1)*A(1,2))
C
RETURN
END SUBROUTINE MATINV3D
SUBROUTINE SPECTRAL(A,D,V)
C> EIGENVALUES AND EIGENVECTOR OF A 3X3 MATRIX
C THIS SUBROUTINE CALCULATES THE EIGENVALUES AND EIGENVECTORS OF
C A SYMMETRIC 3X3 MATRIX A.
C
C THE OUTPUT CONSISTS OF A VECTOR D CONTAINING THE THREE
C EIGENVALUES IN ASCENDING ORDER, AND A MATRIX V WHOSE
C COLUMNS CONTAIN THE CORRESPONDING EIGENVECTORS.
C
IMPLICIT NONE
C
INTEGER NP,NROT
PARAMETER(NP=3)
C
DOUBLE PRECISION D(3),V(3,3),A(3,3),E(3,3)
C
E = A
C
CALL JACOBI(E,3,NP,D,V,NROT)
CALL EIGSRT(D,V,3,NP)
C
RETURN
END SUBROUTINE SPECTRAL
C***********************************************************************
SUBROUTINE JACOBI(A,N,NP,D,V,NROT)
C
C COMPUTES ALL EIGENVALUES AND EIGENVECTORS OF A REAL SYMMETRIC
C MATRIX A, WHICH IS OF SIZE N BY N, STORED IN A PHYSICAL
C NP BY NP ARRAY. ON OUTPUT, ELEMENTS OF A ABOVE THE DIAGONAL
C ARE DESTROYED, BUT THE DIAGONAL AND SUB-DIAGONAL ARE UNCHANGED
C AND GIVE FULL INFORMATION ABOUT THE ORIGINAL SYMMETRIC MATRIX.
C VECTOR D RETURNS THE EIGENVALUES OF A IN ITS FIRST N ELEMENTS.
C V IS A MATRIX WITH THE SAME LOGICAL AND PHYSICAL DIMENSIONS AS
C A WHOSE COLUMNS CONTAIN, UPON OUTPUT, THE NORMALIZED
C EIGENVECTORS OF A. NROT RETURNS THE NUMBER OF JACOBI ROTATION
C WHICH WERE REQUIRED.
C
C THIS SUBROUTINE IS TAKEN FROM 'NUMERICAL RECIPES.'
C
IMPLICIT NONE
INCLUDE 'PARAM_UMAT.INC'
C
INTEGER IP,IQ,N,NMAX,NP,NROT,I,J
PARAMETER (NMAX=100)
C
DOUBLE PRECISION A(NP,NP),D(NP),V(NP,NP),B(NMAX),Z(NMAX),
+ SM,TRESH,G,T,H,THETA,S,C,TAU