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NONLIPLS.for
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SUBROUTINE SDVINI(STATEV,COORDS,NSTATV,NCRDS,NOEL,NPT,
1 LAYER,KSPT)
C
INCLUDE 'ABA_PARAM.INC'
C
DIMENSION STATEV(NSTATV),COORDS(NCRDS)
DOUBLE PRECISION DEPTH,RPHI,G(10),RTHETA
REAL RDEG
INTEGER i, j
CHARACTER FilLoc*31, sdvNum*5
C
PARAMETER (ZERO=0.D0,ONE=1.D0,TWO=2.D0,TEN=10.D0,FOUR=4.D0,
1 CONS1=5.235987755983D0,PI=3.14159265359D0,FFD=0.57735026919D0)
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C THIS SUBROUTINE SETS THE INITIAL VALUES OF THE NON-HOMOGENEOUS MATERIAL PARAMETERS
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
C Note: this is a more generic subroutine, and I only activated the lines related to this study.
C
C STATEV ARGUMENTS:
C 1 ---> CARTILAGE DEGENERATION TYPE
C 2 ---> FIBER CONSTANT
C 3 ---> INITIAL SOLID MATERIAL CONSTANT
C 4 ---> GAG CONSTANT
C 5 ---> NORMALIZED DEPTH
C 6 ---> GAG PRESSURE
C 7 - 12 ---> ---
C 13 ---> NEW SOLID MATERIAL CONSTANT
C 14 ---> NEW FIBER CONSTANT
C 15 ---> DET(F)
C 16 - 42 ---> UPDATED FIBRILLAR DIRECTIONAL UNIT VECTORS WITHOUT PRESTRESS EFFECTS
C 43 - 69 ---> INITIAL FIBRILLAR DIRECTIONAL UNIT VECTORS WITH PRESTRESS EFFECTS
C 70 - 75 ---> FIBRILLAR STRESS COMPONENTS
C 76 - 81 ---> NON-FIBRILLAR STRESS COMPONENTS
C 82 - 90 ---> INITIAL DFGRD1
C
C FOR STATEV(1):
C STATEV(1)=1 ==>> HEALTHY CARTILAGE
C STATEV(1)=2 ==>> DEGENERATED CARTILAGE WITHOUT FIBRILARATION
C STATEV(1)=3 ==>> DEGENERATED CARTILAGE WITH FIBRILARATION
C
C
FilLoc='C:\temp\HybridML\DATA.txt'
C
DO i = 2, NSTATV ! INITIALIZTION OF STATE VARIBLES
STATEV(i)=ZERO
ENDDO
C
open(UNIT=28,FILE=FilLoc,STATUS='OLD')
read(28,*) i
IF (i.NE.0) THEN
i = 0
DO WHILE (i.EQ.0)
read(28,*,end=10) elLabel,intPoint,STATEV(4),STATEV(5),
1 STATEV(2),STATEV(3)
C 2 ,STATEV(16),STATEV(17),STATEV(18),STATEV(19),STATEV(20)
C 3 ,STATEV(21),STATEV(22),STATEV(23),STATEV(24),STATEV(25)
C 4 ,STATEV(26),STATEV(27),STATEV(28),STATEV(29),STATEV(30)
C 5 ,STATEV(31),STATEV(32),STATEV(33),STATEV(34),STATEV(35)
C 6 ,STATEV(36),STATEV(37),STATEV(38),STATEV(39),STATEV(40)
C 7 ,STATEV(41),STATEV(42)
IF (elLabel.EQ.NOEL .AND. intPoint.EQ.NPT) THEN
GO TO 10
ENDIF
ENDDO
ELSE
read(28,*,end=10) DEPTH, STATEV(1)
DEPTH=DBLE(COORDS(2)/DEPTH) ! DEPTH NOMALIZATION
STATEV(5)=DEPTH ! NOMALIZED DEPTH
STATEV(2)=DBLE(1.4*(DEPTH**TWO)-1.1*DEPTH+0.59) ! FIBER CONSTANT
IF (STATEV(1).EQ.1) THEN ! SOLID MATERIAL CONSTANT
STATEV(3)=DBLE(0.1+0.2*DEPTH)
ELSE
STATEV(3)=DBLE(0.05+0.2*DEPTH)
ENDIF
C
G(1)=0.005D0
G(2)=0.01D0
G(3)=0.025D0
G(4)=0.035D0
G(5)=0.042D0
G(6)=0.048D0
G(7)=0.053D0
G(8)=0.058D0
G(9)=0.06D0
G(10)=0.06D0
STATEV(4)=G(INT(DEPTH*9)+1) ! GAG CONSTANT
C
IF (DEPTH.GT.0.3) THEN
RPHI = PI/2
RTHETA = ZERO
ELSEIF (DEPTH.LE.0.3) THEN
RPHI=DBLE(CONS1*DEPTH)
IF (STATEV(1).EQ.3) THEN
CALL RANDOM_NUMBER (RDEG)
RPHI=RDEG*PI/TWO
ENDIF
ENDIF
C
RTHETA = PI/TWO-RPHI ! JUST FOR 2D
C
STATEV(16)=COS(RPHI) ! PRIMARY NVEC UNIT VECTOR DEGREES (RPHI, RTHETA, ...)
STATEV(17)=COS(RTHETA)
STATEV(18)=ZERO
STATEV(19)=COS(PI-RPHI) ! OTHER PRIMARY NVEC UNIT VECTOR
STATEV(20)=COS(RTHETA)
STATEV(21)=ZERO
STATEV(22)=ONE ! (0,PI/2,PI/2)
STATEV(23)=ZERO
STATEV(24)=ZERO
STATEV(25)=ZERO ! (PI/2,0,PI/2)
STATEV(26)=ONE
STATEV(27)=ZERO
STATEV(28)=ZERO ! (PI/2,PI/2,0)
STATEV(29)=ZERO
STATEV(30)=ONE
STATEV(31)=FFD ! (PI/4,PI/4,PI/4)
STATEV(32)=FFD
STATEV(33)=FFD
STATEV(34)=-FFD ! (-PI/4,PI/4,PI/4)
STATEV(35)=FFD
STATEV(36)=FFD
STATEV(37)=FFD ! (PI/4,-PI/4,PI/4)
STATEV(38)=-FFD
STATEV(39)=FFD
STATEV(40)=FFD ! (PI/4,PI/4,-PI/4)
STATEV(41)=FFD
STATEV(42)=-FFD
C
C
C
C ADDED FOR THIS PARTICULAR STUDY
C
C
C
STATEV(5) = -1.0D0 ! DEPTH
STATEV(4) = 0.01D0 ! GAG CONSTANT
STATEV(2) = 0.39D0 ! TOTAL FIBRILLAR DENSITY
STATEV(3) = 0.15D0 ! SOLID VOLUME FRACTION CONSTANT
C
C
C
C
C
C
ENDIF
10 close(UNIT=28)
C
STATEV(6)=STATEV(4)
STATEV(1)=ONE
STATEV(15)=ONE
DO i = 16,42
STATEV(27+i) = STATEV(i) ! FIBRILLAR DIRECTIONS
ENDDO
STATEV(82) = ONE ! DFGRDC
STATEV(85) = ONE
STATEV(88) = ONE
C
C
C
RETURN
END
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
C
C
SUBROUTINE FLOW(H,SINK,U,KSTEP,KINC,TIME,NOEL,NPT,COORDS,
1 JLTYP,SNAME)
C
INCLUDE 'ABA_PARAM.INC'
DIMENSION TIME(2), COORDS(3)
CHARACTER*80 SNAME
H=1
SINK=0
IF (COORDS(1).LE.12.5) THEN
H=0
ENDIF
RETURN
END
C
C
C
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,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)
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C LOCAL PARAMETERS AND VARIABLES
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
DOUBLE PRECISION TRANF(3,3),DET,IDENT(3,3),INDEX(2,6),ALPHA1,
1 ALPHA2,IGAGD,NVEC0(27),RH,W1,W2,W3,W4,W5,W6,STRG(NTENS,NTENS),
2 EPS,FV1(3),HH,NEWV1(3),NSTR(NTENS),STR,LANDA,DELTAV(NTENS),
3 BVEC(NTENS),C,NS0,E1MP,E2MP,K1MP,CSTR,DFGRD(3,3),EP,STRS(NTENS),
4 STATE(NSTATV),GAG,VV(NTENS),DETC,EPSC
INTEGER i,j,k,l,r,m,n,K1,K2,K3,K4,K5,K6,KKK,FF
PARAMETER (ZERO=0.D0,ONE=1.D0,TWO=2.D0,THREE=3.D0,FOUR=4.D0,
1 SEVEN=7.D0,SIX=6.D0,HALF=5.D-1,TEN=10D0)
C
C
C Note: this is a more generic subroutine, and I only activated the lines related to this study.
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C INITIALIZATION
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
DO i = 1, 3
DELTAV(i)=ONE ! KRONKER-DELTA IN VOIGT-NOTATION
DO j = 1, 3
IDENT(j,i) = ZERO ! KRONKER-DELTA 2ND ORDER TENSOR
TRANF(j,i) = ZERO ! TRANSOPSE OF DEFORMATION GRADIENT TENSOR (DFGRD1) IN THE END OF THE INCREMNT
ENDDO
IDENT(i,i) = ONE
ENDDO
DO i = 1,NTENS
STRESS(i)=ZERO ! CAUCHY STRESS TENSOR THAT SHOULD BE UPDATED
STRS(i)=ZERO ! FIBRILLAR STRESS TENSOR
DO j = 1,NTENS
DDSDDE(j,i)=ZERO ! JACOBIAN MATRIX TENSOR THAT SHOULD BE UPDATED.
ENDDO
ENDDO
C
C ALPHA1=STATEV(4) ! DEPTH-DEPENDENT GAG CONSTANT (DEACTIVATED FOR THIS PARTICULAR STUDY)
ALPHA1=PROPS(3) ! DEPTH-DEPENDENT GAG CONSTANT (ONLY FOR THIS PARTICULAR STUDY)
C
IF (JSTEP(1).EQ.1) THEN
ALPHA2=ZERO ! GAG CONSTANT
DETC=ONE
ELSE
ALPHA2=3.22D0
ENDIF
C=3.009D0 ! FIBRILLAR RELATIVE DENSITY CONSTANT
RH=STATEV(2) ! TOTAL FIBRILLAR DENSITY
NS0=STATEV(3) ! DEPTH-DEPENDENT SOLID VOLUME FRACTION CONSTANT
DO i=4,NTENS ! NTENS CONTROLS THE DIMENTIONALITY OF THE CODE
DELTAV(i)=ZERO
ENDDO
INDEX(1,1)=1 ! INDEX ARRAY ARE USED TO CIRCOMVENT ASSIGNING EQUAL COMPONENTS DUE TO SYMMYTRY OF HIYER ORDER TENSORS
INDEX(2,1)=1
INDEX(1,2)=2
INDEX(2,2)=2
INDEX(1,3)=3
INDEX(2,3)=3
INDEX(1,4)=1
INDEX(2,4)=2
INDEX(1,5)=1
INDEX(2,5)=3
INDEX(1,6)=2
INDEX(2,6)=3
C
DO i = 1,27
NVEC0(i) = STATEV(42+i) ! INITIAL FIBRILLAR DIRECTIONS
ENDDO
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C DDSDDE DERIVATION VIA PERTURBATION METHOD (INITIALIZATION)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
KKK=1
EP=10D-8
DO i = 1,3
DO j = 1,3
DFGRD(j,i)=DFGRD1(j,i)
ENDDO
ENDDO
DO K6=1,NSTATV
STATE(K6)=STATEV(K6)
ENDDO
i=1
j=1
80 CONTINUE
DO K1=1,3
DO K2=1,3
DFGRD1(K2,K1)=DFGRD(K2,K1)+(IDENT(K2,i)*DFGRD(j,K1)+IDENT(K2,j)
1 *DFGRD(i,K1))*EP/TWO
ENDDO
ENDDO
90 CONTINUE
DO K6=1,NTENS
STRESS(K6)=ZERO
ENDDO
DO K6=1,NSTATV
STATEV(K6)=STATE(K6)
ENDDO
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C STRESS CALCULATIONS
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
E1MP=PROPS(1) ! LINEAR MATERIAL CONSTANT OF FIBRILLAR PART
E2MP=PROPS(2) ! NONLINEAR MATERIAL CONSTANT OF FIBRILLAR PART
CALL TRANSPOSE(DFGRD1,TRANF)
CALL VMATMUL(DFGRD1,TRANF,NTENS,BVEC) ! BVEC IS THE LEFT CAUCHY-GREEN OR FINGER DEFORMATION TENSOR
CALL DETERMINANT(DFGRD1,DET) ! CURRENT VOLUME CHANGE FROM THE STRESS-FREE STATE
IF (JSTEP(1).EQ.1) THEN
STATEV(15)=DET ! DET(F) WITH RESPE
ELSE
DETC=DET/STATEV(15) ! CURRENT VOLUME CHANGE FROM THE PRESTRESSED STATE
ENDIF
HH=NS0*(RH*C)/(TWO*C+SEVEN) ! CNTRIBUTION OF OTHER CONSTANTS ON FIBRILAR STRESS
IF (STATEV(1).NE.1) THEN
E2MP=3670/FOUR ! FOR OA
ENDIF
E1MP=E1MP*HH
E2MP=E2MP*HH
C write(6,*) E1MP, E2MP, JSTEP(1)
DO i=0,8
IF (i.EQ.2) THEN ! SECONDARY FIBRIL HAVE LOWER DENSITY BY C CONSTANT.
E1MP=E1MP/C
E2MP=E2MP/C
ENDIF
DO m = 1,3
FV1(m)=ZERO ! FV VETOR IS THE INNER PRODUCT OF DFGRD1 AND NVEC0
DO n = 1,3
FV1(m)=DFGRD1(m,n)*NVEC0(3*i+n)+FV1(m)
ENDDO
ENDDO
LANDA=SQRT(FV1(1)**TWO+FV1(2)**TWO+FV1(3)**TWO) ! LANDA IS THE ELONGATION
EPS=LOG(LANDA) ! EPS IS THE FIBRIL LOGARITMIC STRIN
DO n=1,3
NEWV1(n)=FV1(n)/LANDA ! NEWV1 IS THE CURRENT FIBRIL DIRECTION
STATEV(n+3*i+15)=NEWV1(n) ! DEGREES OF NEW DIRECTIONS
ENDDO
IF (EPS.GT.ZERO) THEN
STR=(E1MP+E2MP*EPS)*EPS*LANDA/DET ! STR IS THE LOCAL FIBRIL STRESS
DO K6=1,NTENS
K3=INDEX(1,K6)
K4=INDEX(2,K6)
VV(K6)=NEWV1(K3)*NEWV1(K4) ! VV IS THE DYADIC PRODUCT OF CURRENT DIRECTION VECTORS THAT IS THE STRUCTRAL VECTOR
STRS(K6)=STR*VV(K6) ! STRS IS THE GLOBAL FIBRIL STRESS
STRESS(K6)=STRESS(K6)+STRS(K6)
ENDDO
ENDIF
ENDDO
DO K1=1,NTENS
STATEV(69+K1)=STRESS(K1) ! STRESS IN THE FIBRILLAR PART
ENDDO
C
GM=0.723D0 ! PG NEO-HOOKEAN CONSTANT
GM=GM*NS0*(ONE-RH) ! CONTRIBUTION OF OTHER CONSTANTS
W5=GM/DET
W6=((LOG(DET)/SIX)*(((THREE*NS0/(DET-NS0))
1 *((DET*LOG(DET)/(DET-NS0))-TWO))-FOUR)+(DET**(TWO/THREE)))*W5
DO K6=1,NTENS
NSTR(K6)=-DELTAV(K6)*W6+BVEC(K6)*W5
ENDDO
DO K1=1,NTENS
STATEV(75+K1)=NSTR(K1) ! STRESS IN THE FIBRILLAR PART
ENDDO
C GAG=ALPHA1*(DETC**(-ALPHA2))-ALPHA1
GAG=ALPHA1*(DETC**(-ALPHA2))
STATEV(6)=GAG ! S22 STRESS OF GAG PART
DO K6=1,3
STRESS(K6)=NSTR(K6)-GAG+STRESS(K6)
ENDDO
DO K6=4,NTENS
STRESS(K6)=NSTR(K6)+STRESS(K6)
ENDDO
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C DDSDDE DERIVATION VIA PERTURBATION METHOD (THE SECOND PART)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
IF (KKK.LT.NTENS) THEN
DO K5=1,NTENS
DDSDDE(K5,KKK)=STRESS(K5)*DET
ENDDO
KKK=KKK+1
i=INDEX(1,KKK)
j=INDEX(2,KKK)
GO TO 80
ENDIF
IF (KKK.EQ.NTENS) THEN
DO K5=1,NTENS
DDSDDE(K5,KKK)=STRESS(K5)*DET
ENDDO
DO K1=1,3
DO K2=1,3
DFGRD1(K2,K1)=DFGRD(K2,K1)
ENDDO
ENDDO
KKK=KKK+1
GO TO 90
ENDIF
W2=ONE/EP
W1=W2/DET
DO K6=1,NTENS
DO K5=1,NTENS
DDSDDE(K5,K6)=W1*DDSDDE(K5,K6)-W2*STRESS(K5)
ENDDO
ENDDO
C
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C OTHER STATEV UPDATES
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C
STATEV(13)=NS0/DET ! NEW SOLID MATERIAL CONSTANT
STATEV(14)=RH/DET ! NEW SOLID MATERIAL CONSTANT
C
RETURN
END
C
C TRANSPOSE(A)
C
SUBROUTINE TRANSPOSE(A,AT)
INTEGER i , j
DOUBLE PRECISION A(3,3), AT(3,3)
Do i = 1 , 3
DO j = 1 , 3
AT(j,i) = A(i,j)
ENDDO
ENDDO
RETURN
END
C
C DETERMINANT(A)
C
SUBROUTINE DETERMINANT(A,DET)
DOUBLE PRECISION A(3,3), DET
DET=A(1,1)*A(2,2)*A(3,3)-A(1,1)*A(2,3)*A(3,2)
1 -A(2,1)*A(1,2)*A(3,3)+A(2,1)*A(1,3)*A(3,2)
2 +A(3,1)*A(1,2)*A(2,3)-A(3,1)*A(1,3)*A(2,2)
RETURN
END
C
C INNER PRODUCT OF TWO MATRICES IN VOIGT-NOTATION
C
SUBROUTINE VMATMUL(A,B,N,C)
DOUBLE PRECISION A(3,3), B(3,3), C(N)
INTEGER i , j
C(1)=A(1,1)*B(1,1)+A(1,2)*B(2,1)+A(1,3)*B(3,1)
C(2)=A(2,1)*B(1,2)+A(2,2)*B(2,2)+A(2,3)*B(3,2)
C(3)=A(3,1)*B(1,3)+A(3,2)*B(2,3)+A(3,3)*B(3,3)
C(4)=A(1,1)*B(1,2)+A(1,2)*B(2,2)+A(1,3)*B(3,2)
IF (N.EQ.6) THEN
C(5)=A(1,1)*B(1,3)+A(1,2)*B(2,3)+A(1,3)*B(3,3)
C(6)=A(2,1)*B(1,3)+A(2,2)*B(2,3)+A(2,3)*B(3,3)
ENDIF
RETURN
END