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umatcrystal_cohesive_neper5.f
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umatcrystal_cohesive_neper5.f
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SUBROUTINE UEXTERNALDB(LOP,LRESTART,TIME,DTIME,KSTEP,KINC)
C
INCLUDE 'ABA_PARAM.INC'
CHARACTER*100 FILE,FILE1,FILE2
C
DIMENSION TIME(2)
integer nmax_p
parameter (nmax_p=5E5)
real*8 FP_0(nmax_p),LOCAL_FP0(nmax_p)
real*8 LOCALGAMMAMAX(nmax_p),LOCALGAMMAMIN(nmax_p),
1 LOCALTAUMAX(nmax_p),LOCALTAUMIN(nmax_p),LOCALEPSILONMAX(nmax_p),
2 LOCALEPSILONMIN(nmax_p),LOCALSIGMAMAX(nmax_p),LOCALFIP(nmax_p),
3 Damage_rate(nmax_p),LOCALDAMAGE(nmax_p),
4 FIPMAX,Damage_critical,N_cycle
integer FLAG_CYCLE,FLAG_XIT
COMMON LOCALGAMMAMAX,LOCALGAMMAMIN,
1 LOCALTAUMAX,LOCALTAUMIN,LOCALEPSILONMAX,
2 LOCALEPSILONMIN,LOCALSIGMAMAX,LOCALFIP,
3 Damage_rate,LOCALDAMAGE,
4 N_cycle,FIPMAX,Damage_critical,FLAG_CYCLE,FLAG_XIT
C NINALL = 2000000
C
C user coding to set up the Fortran environment, open files, close files,
C calculate user-defined model-independent history information,
C write history information to external files,
C recover history information during restart analyses, etc.
C do not include calls to utility routine XIT
C 积分点的总数量
real*8 J_fc,m_fc,delta_Df,C_fc
C call MutexInit( 1 )
C call MutexInit( 2 )
C call MutexInit( 3 )
C call MutexInit( 4 )
FP_0 = 0.0
m_fc = 2.0
delta_Df = 0.1
C_fc = 1.5E5
J_fc = 0.3
IF(MOD(KSTEP,2).eq.0)THEN
FLAG_CYCLE = 1
ELSE
FLAG_CYCLE = 0
ENDIF
C call MutexLock( 1 )
IF(LOP.eq.0)THEN
FILE1='E:\temp\UmatCryspl\texture_init_230822_3.dat'
OPEN(91,FILE=FILE1,STATUS='UNKNOWN',ACCESS='APPEND')
FILE2='E:\temp\UmatCryspl\texture_end_230822_3.dat'
OPEN(92,FILE=FILE2,STATUS='UNKNOWN',ACCESS='APPEND')
ENDIF
IF(LOP.eq.6.and.FLAG_CYCLE.eq.1)THEN
LOCALFIP = (LOCALEPSILONMAX-LOCALEPSILONMIN)/2.0*LOCALSIGMAMAX
1 + J_fc*(LOCALGAMMAMAX-LOCALGAMMAMIN)*(LOCALTAUMAX-LOCALTAUMIN)
FIPMAX = MAXVAL(LOCALFIP)
C Damage_rate = (ABS(LOCALFIP - FP_0))**m_fc/C_fc
LOCAL_FP0 = ABS(LOCALFIP - FP_0)
C Damage_rate = LOCAL_FP0*LOCAL_FP0/C_fc
Damage_rate = LOCAL_FP0**m_fc/C_fc
C Damage_rate = LOCAL_FP0C_fc
Damage_critical = MAXVAL(Damage_rate)
d_N_cycle = delta_Df/Damage_critical
LOCALDAMAGE = LOCALDAMAGE + Damage_rate*d_N_cycle
N_cycle = N_cycle + d_N_cycle
END IF
C call MutexUnlock( 1 )
RETURN
END
SUBROUTINE USDFLD(FIELD,STATEV,PNEWDT,DIRECT,T,CELENT,
1 TIME,DTIME,CMNAME,ORNAME,NFIELD,NSTATV,NOEL,NPT,LAYER,
2 KSPT,KSTEP,KINC,NDI,NSHR,COORD,JMAC,JMATYP,MATLAYO,LACCFLA)
C
INCLUDE 'ABA_PARAM.INC'
CHARACTER*100 FILE,FILE1,FILE2
C
CHARACTER*80 CMNAME,ORNAME
CHARACTER*3 FLGRAY(15)
DIMENSION FIELD(NFIELD),STATEV(NSTATV),DIRECT(3,3),
1 T(3,3),TIME(2)
DIMENSION ARRAY(15),JARRAY(15),JMAC(*),JMATYP(*),COORD(*)
integer nmax_p
parameter (nmax_p=5E5)
real*8 LOCALGAMMAMAX(nmax_p),LOCALGAMMAMIN(nmax_p),
1 LOCALTAUMAX(nmax_p),LOCALTAUMIN(nmax_p),LOCALEPSILONMAX(nmax_p),
2 LOCALEPSILONMIN(nmax_p),LOCALSIGMAMAX(nmax_p),LOCALFIP(nmax_p),
3 Damage_rate(nmax_p),LOCALDAMAGE(nmax_p),
4 FIPMAX,Damage_critical,N_cycle
integer FLAG_CYCLE,FLAG_XIT
COMMON LOCALGAMMAMAX,LOCALGAMMAMIN,
1 LOCALTAUMAX,LOCALTAUMIN,LOCALEPSILONMAX,
2 LOCALEPSILONMIN,LOCALSIGMAMAX,LOCALFIP,
3 Damage_rate,LOCALDAMAGE,
4 N_cycle,FIPMAX,Damage_critical,FLAG_CYCLE,FLAG_XIT
C NINALL = 2000000
C user coding to define FIELD and, if necessary, STATEV and PNEWDT
C 设置当前积分点编号
C ELS = 335232
C NOELN = (NOEL-ELS)*3 + NPT
NOELN = NOEL*3 + NPT
IF(NOELN.gt.nmax_p)then
NOELN = MOD(NOELN,nmax_p)
ENDIF
CALL GETVRM(' E',ARRAY,JARRAY,FLGRAY,JRCD,JMAC,JMATYP,MATLAYO,
1 LACCFLA)
E33 = ARRAY(1)
E13 = ARRAY(4)
E23 = ARRAY(5)
CALL GETVRM(' S',ARRAY,JARRAY,FLGRAY,JRCD,JMAC,JMATYP,MATLAYO,
1 LACCFLA)
S33 = ARRAY(1)
S13 = ARRAY(4)
S23 = ARRAY(5)
GAMMA_eq = sqrt(E13**2. + E23**2.)
TAU_eq = sqrt(S13**2. + S23**2.)
EPSILON = E33
SIGMA = S33
C call MutexLock( 1 )
if(KINC.eq.1)then
LOCALGAMMAMAX(NOELN) = GAMMA_eq
LOCALGAMMAMIN(NOELN) = GAMMA_eq
LOCALTAUMAX(NOELN) = TAU_eq
LOCALTAUMIN(NOELN) = TAU_eq
LOCALEPSILONMAX(NOELN) = EPSILON
LOCALEPSILONMIN(NOELN) = EPSILON
LOCALSIGMAMAX(NOELN) = ABS(SIGMA)
else
if(GAMMA_eq>LOCALGAMMAMAX(NOELN))then
LOCALGAMMAMAX(NOELN) = GAMMA_eq
endif
if(GAMMA_eq<LOCALGAMMAMIN(NOELN))then
LOCALGAMMAMIN(NOELN) = GAMMA_eq
endif
if(TAU_eq>LOCALTAUMAX(NOELN))then
LOCALTAUMAX(NOELN) = TAU_eq
endif
if(TAU_eq<LOCALTAUMIN(NOELN))then
LOCALTAUMIN(NOELN) = TAU_eq
endif
if(EPSILON>LOCALEPSILONMAX(NOELN))then
LOCALEPSILONMAX(NOELN) = EPSILON
endif
if(EPSILON<LOCALEPSILONMIN(NOELN))then
LOCALEPSILONMIN(NOELN) = EPSILON
endif
if(ABS(SIGMA)>LOCALSIGMAMAX(NOELN))then
LOCALSIGMAMAX(NOELN) = ABS(SIGMA)
endif
endif
IF(LOCALDAMAGE(NOELN)>0.99.and.KINC.eq.1)THEN
FLAG_XIT=1
ELSE IF(LOCALDAMAGE(NOELN)>0.99.and.KINC.ne.1)THEN
CALL XIT
ELSE
FIELD(1) = LOCALDAMAGE(NOELN)
STATEV(1) = LOCALDAMAGE(NOELN)
C STATEV(1) = GAMMA_eq
STATEV(2) = LOCALFIP(NOELN)
C STATEV(2) = LOCALGAMMAMIN(NOELN)
STATEV(3) = N_cycle
ENDIF
C call MutexUnlock( 1 )
RETURN
END
SUBROUTINE UTRACLOAD(ALPHA,T_USER,KSTEP,KINC,TIME,NOEL,NPT,
1 COORDS,DIRCOS,JLTYP,SNAME)
C
INCLUDE 'ABA_PARAM.INC'
C
DIMENSION T_USER(3), TIME(2), COORDS(3), DIRCOS(3,3)
CHARACTER*80 SNAME
integer nmax_p
parameter (nmax_p=5E5)
real*8 LOCALGAMMAMAX(nmax_p),LOCALGAMMAMIN(nmax_p),
1 LOCALTAUMAX(nmax_p),LOCALTAUMIN(nmax_p),LOCALEPSILONMAX(nmax_p),
2 LOCALEPSILONMIN(nmax_p),LOCALSIGMAMAX(nmax_p),LOCALFIP(nmax_p),
3 Damage_rate(nmax_p),LOCALDAMAGE(nmax_p),
4 FIPMAX,Damage_critical,N_cycle,gamma_qd,judge_Miu
integer FLAG_CYCLE,FLAG_XIT
COMMON LOCALGAMMAMAX,LOCALGAMMAMIN,
1 LOCALTAUMAX,LOCALTAUMIN,LOCALEPSILONMAX,
2 LOCALEPSILONMIN,LOCALSIGMAMAX,LOCALFIP,
3 Damage_rate,LOCALDAMAGE,
4 N_cycle,FIPMAX,Damage_critical,FLAG_CYCLE,FLAG_XIT
real x,z,velocity
real move
C call MutexLock( 1 )
IF(FLAG_CYCLE.eq.1)THEN
velocity = 2.0
ELSE
velocity = 0.0
ENDIF
C call MutexUnlock( 1 )
x = coords(1)
z = coords(3)
move = velocity*time(1)
c user coding to define ALPHA and T_USER
c 受力方向
T_USER(1) = -1.
T_USER(2) = 0.
T_USER(3) = 0.
c 受力大小
Miu_max = 1831.05*0.05
a_ellip = 0.2097
b_ellip = 0.1401
x_c = 0. + move
z_c = 0.5
gamma_qd = 3.1415926/2 - 1.7982
C judge_p_ij = 1-((pis*cos(gamma_qd)+pj*sin(gamma_qd))/b(k,h))^2-((-pis*sin(gamma_qd)+pj*cos(gamma_qd))/a(k,h))^2
judge_Miu = 1-(((x-x_c)*cos(gamma_qd)+(z-z_c)*
1 sin(gamma_qd))/b_ellip)**2
2 -((-(x-x_c)*sin(gamma_qd)+(z-z_c)*cos(gamma_qd))/a_ellip)**2
if(judge_Miu>=0.)then
if(FLAG_CYCLE.eq.1)then
alpha = Miu_max*sqrt(judge_Miu)
else
alpha = time(1)*Miu_max*sqrt(judge_Miu)
endif
C if(x>=12.and.x<=18)then
C if (z <= move+18 .and. z >= move+12)then
C alpha = 10.0
C else
C alpha = 0.0
C end if
else
alpha = 0.0
end if
RETURN
END
SUBROUTINE DLOAD(F,KSTEP,KINC,TIME,NOEL,NPT,LAYER,KSPT,
1 COORDS,JLTYP,SNAME)
C
INCLUDE 'ABA_PARAM.INC'
C
DIMENSION TIME(2), COORDS (3)
CHARACTER*80 SNAME
integer nmax_p
parameter (nmax_p=5E5)
real*8 LOCALGAMMAMAX(nmax_p),LOCALGAMMAMIN(nmax_p),
1 LOCALTAUMAX(nmax_p),LOCALTAUMIN(nmax_p),LOCALEPSILONMAX(nmax_p),
2 LOCALEPSILONMIN(nmax_p),LOCALSIGMAMAX(nmax_p),LOCALFIP(nmax_p),
3 Damage_rate(nmax_p),LOCALDAMAGE(nmax_p),
4 FIPMAX,Damage_critical,N_cycle,gamma_qd,judge_P
integer FLAG_CYCLE,FLAG_XIT
COMMON LOCALGAMMAMAX,LOCALGAMMAMIN,
1 LOCALTAUMAX,LOCALTAUMIN,LOCALEPSILONMAX,
2 LOCALEPSILONMIN,LOCALSIGMAMAX,LOCALFIP,
3 Damage_rate,LOCALDAMAGE,
4 N_cycle,FIPMAX,Damage_critical,FLAG_CYCLE,FLAG_XIT
real x,z,velocity
real move
C call MutexLock( 1 )
IF(FLAG_CYCLE.eq.1)THEN
velocity = 2.0
ELSE
velocity = 0.0
ENDIF
C call MutexUnlock( 1 )
x = coords(1)
z = coords(3)
move = velocity*time(1)
P_max = 1831.05
a_ellip = 0.2097
b_ellip = 0.1401
x_c = 0. + move
z_c = 0.5
gamma_qd = 3.1415926/2 - 1.7982
C judge_p_ij = 1-((pis*cos(gamma_qd)+pj*sin(gamma_qd))/b(k,h))^2-((-pis*sin(gamma_qd)+pj*cos(gamma_qd))/a(k,h))^2
judge_P = 1-(((x-x_c)*cos(gamma_qd)+(z-z_c)*
1 sin(gamma_qd))/b_ellip)**2
2 -((-(x-x_c)*sin(gamma_qd)+(z-z_c)*cos(gamma_qd))/a_ellip)**2
if(judge_P>=0.)then
if(FLAG_CYCLE.eq.1)then
F = P_max*sqrt(judge_P)
else
F = time(1)*P_max*sqrt(judge_P)
endif
C if(x>=12.and.x<=18)then
C if (z <= move+18 .and. z >= move+12)then
C F = 200.0
C else
C F = 0.0
C end if
else
F = 0.0
end if
RETURN
END
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 WRITE (6,*) '
c NOTE: MODIFICATIONS TO *UMAT FOR ABAQUS VERSION 5.3 (14 APR '94)
c
c (1) The list of variables above defining the *UMAT subroutine,
c and the first (standard) block of variables dimensioned below,
c have variable names added compared to earlier ABAQUS versions.
c
c (2) The statement: include 'aba_param.inc' must be added as below.
c
c (3) As of version 5.3, ABAQUS files use double precision only.
c The file aba_param.inc has a line "implicit real*8" and, since
c it is included in the main subroutine, it will define the variables
c there as double precision. But other subroutines still need the
c definition "implicit real*8" since there may be variables that are
c not passed to them through the list or common block.
c
c (4) This is current as of version 5.6 of ABAQUS.
c
c (5) Note added by J. W. Kysar (4 November 1997). This UMAT has been
c modified to keep track of the cumulative shear strain in each
c individual slip system. This information is needed to correct an
c error in the implementation of the Bassani and Wu hardening law.
c Any line of code which has been added or modified is preceded
c immediately by a line beginning CFIXA and succeeded by a line
c beginning CFIXB. Any comment line added or modified will begin
c with CFIX.
c
c The hardening law by Bassani and Wu was implemented incorrectly.
c This law is a function of both hyperbolic secant squared and hyperbolic
c tangent. However, the arguments of sech and tanh are related to the *total*
c slip on individual slip systems. Formerly, the UMAT implemented this
c hardening law by using the *current* slip on each slip system. Therein
c lay the problem. The UMAT did not restrict the current slip to be a
c positive value. So when a slip with a negative sign was encountered, the
c term containing tanh led to a negative hardening rate (since tanh is an
c odd function).
c The UMAT has been fixed by adding state variables to keep track of the
c *total* slip on each slip system by integrating up the absolute value
c of slip rates for each individual slip system. These "solution dependent
c variables" are available for postprocessing. The only required change
c in the input file is that the DEPVAR command must be changed.
c
C----- Use single precision on Cray by
C (1) deleting the statement "IMPLICIT*8 (A-H,O-Z)";
C (2) changing "REAL*8 FUNCTION" to "FUNCTION";
C (3) changing double precision functions DSIGN to SIGN.
C
C----- Subroutines:
C
C ROTATION -- forming rotation matrix, i.e. the direction
C cosines of cubic crystal [100], [010] and [001]
C directions in global system at the initial
C state
C
C SLIPSYS -- calculating number of slip systems, unit
C vectors in slip directions and unit normals to
C slip planes in a cubic crystal at the initial
C state
C
C GSLPINIT -- calculating initial value of current strengths
C at initial state
C
C STRAINRATE -- based on current values of resolved shear
C stresses and current strength, calculating
C shear strain-rates in slip systems
C
C LATENTHARDEN -- forming self- and latent-hardening matrix
C
C ITERATION -- generating arrays for the Newton-Rhapson
C iteration
C
C LUDCMP -- LU decomposition
C
C LUBKSB -- linear equation solver based on LU
C decomposition method (must call LUDCMP first)
C----- Function subprogram:
C F -- shear strain-rates in slip systems
C----- Variables:
C
C STRESS -- stresses (INPUT & OUTPUT)
C Cauchy stresses for finite deformation
C STATEV -- solution dependent state variables (INPUT & OUTPUT)
C DDSDDE -- Jacobian matrix (OUTPUT)
C----- Variables passed in for information:
C
C STRAN -- strains
C logarithmic strain for finite deformation
C (actually, integral of the symmetric part of velocity
C gradient with respect to time)
C DSTRAN -- increments of strains
C CMNAME -- name given in the *MATERIAL option
C NDI -- number of direct stress components
C NSHR -- number of engineering shear stress components
C NTENS -- NDI+NSHR
C NSTATV -- number of solution dependent state variables (as
C defined in the *DEPVAR option)
C PROPS -- material constants entered in the *USER MATERIAL
C option
C NPROPS -- number of material constants
C
C----- This subroutine provides the plastic constitutive relation of
C single crystals for finite element code ABAQUS. The plastic slip
C of single crystal obeys the Schmid law. The program gives the
C choice of small deformation theory and theory of finite rotation
C and finite strain.
C The strain increment is composed of elastic part and plastic
C part. The elastic strain increment corresponds to lattice
C stretching, the plastic part is the sum over all slip systems of
C plastic slip. The shear strain increment for each slip system is
C assumed a function of the ratio of corresponding resolved shear
C stress over current strength, and of the time step. The resolved
C shear stress is the double product of stress tensor with the slip
C deformation tensor (Schmid factor), and the increment of current
C strength is related to shear strain increments over all slip
C systems through self- and latent-hardening functions.
C----- The implicit integration method proposed by Peirce, Shih and
C Needleman (1984) is used here. The subroutine provides an option
C of iteration to solve stresses and solution dependent state
C variables within each increment.
C----- The present program is for a single CUBIC crystal. However,
C this code can be generalized for other crystals (e.g. HCP,
C Tetragonal, Orthotropic, etc.). Only subroutines ROTATION and
C SLIPSYS need to be modified to include the effect of crystal
C aspect ratio.
C
C----- Important notice:
C
C (1) The number of state variables NSTATV must be larger than (or
CFIX equal to) TEN (10) times the total number of slip systems in
C all sets, NSLPTL, plus FIVE (5)
CFIX NSTATV >= 10 * NSLPTL + 5
C Denote s as a slip direction and m as normal to a slip plane.
C Here (s,-m), (-s,m) and (-s,-m) are NOT considered
C independent of (s,m). The number of slip systems in each set
C could be either 6, 12, 24 or 48 for a cubic crystal, e.g. 12
C for {110}<111>.
C
C Users who need more parameters to characterize the
C constitutive law of single crystal, e.g. the framework
C proposed by Zarka, should make NSTATV larger than (or equal
C to) the number of those parameters NPARMT plus nine times
C the total number of slip systems, NSLPTL, plus five
CFIX NSTATV >= NPARMT + 10 * NSLPTL + 5
C
C (2) The tangent stiffness matrix in general is not symmetric if
C latent hardening is considered. Users must declare "UNSYMM"
C in the input file, at the *USER MATERIAL card.
C
PARAMETER (ND=150)
C----- The parameter ND determines the dimensions of the arrays in
C this subroutine. The current choice 150 is a upper bound for a
C cubic crystal with up to three sets of slip systems activated.
C Users may reduce the parameter ND to any number as long as larger
C than or equal to the total number of slip systems in all sets.
C For example, if {110}<111> is the only set of slip system
C potentially activated, ND could be taken as twelve (12).
c
include 'aba_param.inc'
integer nmax_p
parameter (nmax_p=5E5)
real*8 LOCALGAMMAMAX(nmax_p),LOCALGAMMAMIN(nmax_p),
1 LOCALTAUMAX(nmax_p),LOCALTAUMIN(nmax_p),LOCALEPSILONMAX(nmax_p),
2 LOCALEPSILONMIN(nmax_p),LOCALSIGMAMAX(nmax_p),LOCALFIP(nmax_p),
3 Damage_rate(nmax_p),LOCALDAMAGE(nmax_p),
4 FIPMAX,Damage_critical,N_cycle,gamma_qd,judge_P
integer FLAG_CYCLE,FLAG_XIT
COMMON LOCALGAMMAMAX,LOCALGAMMAMIN,
1 LOCALTAUMAX,LOCALTAUMIN,LOCALEPSILONMAX,
2 LOCALEPSILONMIN,LOCALSIGMAMAX,LOCALFIP,
3 Damage_rate,LOCALDAMAGE,
4 N_cycle,FIPMAX,Damage_critical,FLAG_CYCLE,FLAG_XIT
c
CHARACTER*100 CMNAME,FILE,FILE1,FILE2
EXTERNAL F
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)
DIMENSION ISPDIR(3), ISPNOR(3), NSLIP(3),
2 SLPDIR(3,ND), SLPNOR(3,ND), SLPDEF(6,ND),
3 SLPSPN(3,ND), DSPDIR(3,ND), DSPNOR(3,ND),
4 DLOCAL(6,6), D(6,6), ROTD(6,6), ROTATE(3,3),
5 FSLIP(ND), DFDXSP(ND), DDEMSD(6,ND),
6 H(ND,ND), DDGDDE(ND,6),
7 DSTRES(6), DELATS(6), DSPIN(3), DVGRAD(3,3),
8 DGAMMA(ND), DTAUSP(ND), DGSLIP(ND),
9 WORKST(ND,ND), INDX(ND), TERM(3,3), TRM0(3,3), ITRM(3)
DIMENSION FSLIP1(ND), STRES1(6), GAMMA1(ND), TAUSP1(ND),
2 GSLP1(ND), SPNOR1(3,ND), SPDIR1(3,ND), DDSDE1(6,6),
3 DSOLD(6), DGAMOD(ND), DTAUOD(ND), DGSPOD(ND),
4 DSPNRO(3,ND), DSPDRO(3,ND),
5 DHDGDG(ND,ND)
C----- NSLIP -- number of slip systems in each set
C----- SLPDIR -- slip directions (unit vectors in the initial state)
C----- SLPNOR -- normals to slip planes (unit normals in the initial
C state)
C----- SLPDEF -- slip deformation tensors (Schmid factors)
C SLPDEF(1,i) -- SLPDIR(1,i)*SLPNOR(1,i)
C SLPDEF(2,i) -- SLPDIR(2,i)*SLPNOR(2,i)
C SLPDEF(3,i) -- SLPDIR(3,i)*SLPNOR(3,i)
C SLPDEF(4,i) -- SLPDIR(1,i)*SLPNOR(2,i)+
C SLPDIR(2,i)*SLPNOR(1,i)
C SLPDEF(5,i) -- SLPDIR(1,i)*SLPNOR(3,i)+
C SLPDIR(3,i)*SLPNOR(1,i)
C SLPDEF(6,i) -- SLPDIR(2,i)*SLPNOR(3,i)+
C SLPDIR(3,i)*SLPNOR(2,i)
C where index i corresponds to the ith slip system
C----- SLPSPN -- slip spin tensors (only needed for finite rotation)
C SLPSPN(1,i) -- [SLPDIR(1,i)*SLPNOR(2,i)-
C SLPDIR(2,i)*SLPNOR(1,i)]/2
C SLPSPN(2,i) -- [SLPDIR(3,i)*SLPNOR(1,i)-
C SLPDIR(1,i)*SLPNOR(3,i)]/2
C SLPSPN(3,i) -- [SLPDIR(2,i)*SLPNOR(3,i)-
C SLPDIR(3,i)*SLPNOR(2,i)]/2
C where index i corresponds to the ith slip system
C----- DSPDIR -- increments of slip directions
C----- DSPNOR -- increments of normals to slip planes
C
C----- DLOCAL -- elastic matrix in local cubic crystal system
C----- D -- elastic matrix in global system
C----- ROTD -- rotation matrix transforming DLOCAL to D
C
C----- ROTATE -- rotation matrix, direction cosines of [100], [010]
C and [001] of cubic crystal in global system
C
C----- FSLIP -- shear strain-rates in slip systems
C----- DFDXSP -- derivatives of FSLIP w.r.t x=TAUSLP/GSLIP, where
C TAUSLP is the resolved shear stress and GSLIP is the
C current strength
C
C----- DDEMSD -- double dot product of the elastic moduli tensor with
C the slip deformation tensor plus, only for finite
C rotation, the dot product of slip spin tensor with
C the stress
C
C----- H -- self- and latent-hardening matrix
C H(i,i) -- self hardening modulus of the ith slip
C system (no sum over i)
C H(i,j) -- latent hardening molulus of the ith slip
C system due to a slip in the jth slip system
C (i not equal j)
C
C----- DDGDDE -- derivatice of the shear strain increments in slip
C systems w.r.t. the increment of strains
C
C----- DSTRES -- Jaumann increments of stresses, i.e. corotational
C stress-increments formed on axes spinning with the
C material
C----- DELATS -- strain-increments associated with lattice stretching
C DELATS(1) - DELATS(3) -- normal strain increments
C DELATS(4) - DELATS(6) -- engineering shear strain
C increments
C----- DSPIN -- spin-increments associated with the material element
C DSPIN(1) -- component 12 of the spin tensor
C DSPIN(2) -- component 31 of the spin tensor
C DSPIN(3) -- component 23 of the spin tensor
C
C----- DVGRAD -- increments of deformation gradient in the current
C state, i.e. velocity gradient times the increment of
C time
C
C----- DGAMMA -- increment of shear strains in slip systems
C----- DTAUSP -- increment of resolved shear stresses in slip systems
C----- DGSLIP -- increment of current strengths in slip systems
C
C
C----- Arrays for iteration:
C
C FSLIP1, STRES1, GAMMA1, TAUSP1, GSLP1 , SPNOR1, SPDIR1,
C DDSDE1, DSOLD , DGAMOD, DTAUOD, DGSPOD, DSPNRO, DSPDRO,
C DHDGDG
C
C
C----- Solution dependent state variable STATEV:
C Denote the number of total slip systems by NSLPTL, which
C will be calculated in this code.
C
C Array STATEV:
C 1 - NSLPTL : current strength in slip systems
C NSLPTL+1 - 2*NSLPTL : shear strain in slip systems
C 2*NSLPTL+1 - 3*NSLPTL : resolved shear stress in slip systems
C
C 3*NSLPTL+1 - 6*NSLPTL : current components of normals to slip
C slip planes
C 6*NSLPTL+1 - 9*NSLPTL : current components of slip directions
C
CFIX 9*NSLPTL+1 - 10*NSLPTL : total cumulative shear strain on each
CFIX slip system (sum of the absolute
CFIX values of shear strains in each slip
CFIX system individually)
CFIX
CFIX 10*NSLPTL+1 : total cumulative shear strain on all
C slip systems (sum of the absolute
C values of shear strains in all slip
C systems)
C
CFIX 10*NSLPTL+2 - NSTATV-4 : additional parameters users may need
C to characterize the constitutive law
C of a single crystal (if there are
C any).
C
C NSTATV-3 : number of slip systems in the 1st set
C NSTATV-2 : number of slip systems in the 2nd set
C NSTATV-1 : number of slip systems in the 3rd set
C NSTATV : total number of slip systems in all
C sets
C
C
C----- Material constants PROPS:
C
C PROPS(1) - PROPS(21) -- elastic constants for a general elastic
C anisotropic material
C
C isotropic : PROPS(i)=0 for i>2
C PROPS(1) -- Young's modulus
C PROPS(2) -- Poisson's ratio
C
C cubic : PROPS(i)=0 for i>3
C PROPS(1) -- c11
C PROPS(2) -- c12
C PROPS(3) -- c44
C
C orthotropic : PORPS(i)=0 for i>9
C PROPS(1) - PROPS(9) are D1111, D1122, D2222,
C D1133, D2233, D3333, D1212, D1313, D2323,
C respectively, which has the same definition
C as ABAQUS for orthotropic materials
C (see *ELASTIC card)
C
C anisotropic : PROPS(1) - PROPS(21) are D1111, D1122,
C D2222, D1133, D2233, D3333, D1112, D2212,
C D3312, D1212, D1113, D2213, D3313, D1213,
C D1313, D1123, D2223, D3323, D1223, D1323,
C D2323, respectively, which has the same
C definition as ABAQUS for anisotropic
C materials (see *ELASTIC card)
C
C
C PROPS(25) - PROPS(56) -- parameters characterizing all slip
C systems to be activated in a cubic
C crystal
C
C PROPS(25) -- number of sets of slip systems (maximum 3),
C e.g. (110)[1-11] and (101)[11-1] are in the
C same set of slip systems, (110)[1-11] and
C (121)[1-11] belong to different sets of slip
C systems
C (It must be a real number, e.g. 3., not 3 !)
C
C PROPS(33) - PROPS(35) -- normal to a typical slip plane in
C the first set of slip systems,
C e.g. (1 1 0)
C (They must be real numbers, e.g.
C 1. 1. 0., not 1 1 0 !)
C PROPS(36) - PROPS(38) -- a typical slip direction in the
C first set of slip systems, e.g.
C [1 1 1]
C (They must be real numbers, e.g.
C 1. 1. 1., not 1 1 1 !)
C
C PROPS(41) - PROPS(43) -- normal to a typical slip plane in
C the second set of slip systems
C (real numbers)
C PROPS(44) - PROPS(46) -- a typical slip direction in the
C second set of slip systems
C (real numbers)
C
C PROPS(49) - PROPS(51) -- normal to a typical slip plane in
C the third set of slip systems
C (real numbers)
C PROPS(52) - PROPS(54) -- a typical slip direction in the
C third set of slip systems
C (real numbers)
C
C
C PROPS(57) - PROPS(72) -- parameters characterizing the initial
C orientation of a single crystal in
C global system
C The directions in global system and directions in local
C cubic crystal system of two nonparallel vectors are needed
C to determine the crystal orientation.
C
C PROPS(57) - PROPS(59) -- [p1 p2 p3], direction of first
C vector in local cubic crystal
C system, e.g. [1 1 0]
C (They must be real numbers, e.g.
C 1. 1. 0., not 1 1 0 !)
C PROPS(60) - PROPS(62) -- [P1 P2 P3], direction of first
C vector in global system, e.g.
C [2. 1. 0.]
C (It does not have to be a unit
C vector)
C
C PROPS(65) - PROPS(67) -- direction of second vector in
C local cubic crystal system (real
C numbers)
C PROPS(68) - PROPS(70) -- direction of second vector in
C global system
C
C
C PROPS(73) - PROPS(96) -- parameters characterizing the visco-
C plastic constitutive law (shear
C strain-rate vs. resolved shear
C stress), e.g. a power-law relation
C
C PROPS(73) - PROPS(80) -- parameters for the first set of
C slip systems
C PROPS(81) - PROPS(88) -- parameters for the second set of
C slip systems
C PROPS(89) - PROPS(96) -- parameters for the third set of
C slip systems
C
C
C PROPS(97) - PROPS(144)-- parameters characterizing the self-
C and latent-hardening laws of slip
C systems
C
C PROPS(97) - PROPS(104)-- self-hardening parameters for the
C first set of slip systems
C PROPS(105)- PROPS(112)-- latent-hardening parameters for
C the first set of slip systems and
C interaction with other sets of
C slip systems
C
C PROPS(113)- PROPS(120)-- self-hardening parameters for the
C second set of slip systems
C PROPS(121)- PROPS(128)-- latent-hardening parameters for
C the second set of slip systems
C and interaction with other sets
C of slip systems
C
C PROPS(129)- PROPS(136)-- self-hardening parameters for the
C third set of slip systems
C PROPS(137)- PROPS(144)-- latent-hardening parameters for
C the third set of slip systems and
C interaction with other sets of
C slip systems
C
C
C PROPS(145)- PROPS(152)-- parameters characterizing forward time
C integration scheme and finite
C deformation
C
C PROPS(145) -- parameter theta controlling the implicit
C integration, which is between 0 and 1
C 0. : explicit integration
C 0.5 : recommended value
C 1. : fully implicit integration
C
C PROPS(146) -- parameter NLGEOM controlling whether the
C effect of finite rotation and finite strain
C of crystal is considered,
C 0. : small deformation theory
C otherwise : theory of finite rotation and
C finite strain
C
C
C PROPS(153)- PROPS(160)-- parameters characterizing iteration
C method
C
C PROPS(153) -- parameter ITRATN controlling whether the
C iteration method is used,
C 0. : no iteration
C otherwise : iteration
C
C PROPS(154) -- maximum number of iteration ITRMAX
C
C PROPS(155) -- absolute error of shear strains in slip
C systems GAMERR
C
C----- Elastic matrix in local cubic crystal system: DLOCAL
PI=3.141592653589793238D0
C FILE1='E:\temp\UmatCryspl\temp.dat'
C OPEN(91,FILE=FILE1,STATUS='UNKNOWN',ACCESS='APPEND')
DO J=1,6
DO I=1,6
DLOCAL(I,J)=0.
END DO
END DO
CHECK=0.
DO J=10,21
CHECK=CHECK+ABS(PROPS(J))
END DO
IF (CHECK.EQ.0.) THEN
DO J=4,9
CHECK=CHECK+ABS(PROPS(J))
END DO
IF (CHECK.EQ.0.) THEN
IF (PROPS(3).EQ.0.) THEN
C----- Isotropic material
GSHEAR=PROPS(1)/2./(1.+PROPS(2))
E11=2.*GSHEAR*(1.-PROPS(2))/(1.-2.*PROPS(2))
E12=2.*GSHEAR*PROPS(2)/(1.-2.*PROPS(2))
DO J=1,3
DLOCAL(J,J)=E11
DO I=1,3
IF (I.NE.J) DLOCAL(I,J)=E12
END DO
DLOCAL(J+3,J+3)=GSHEAR
END DO
ELSE
C----- Cubic material
DO J=1,3
DLOCAL(J,J)=PROPS(1)
DO I=1,3
IF (I.NE.J) DLOCAL(I,J)=PROPS(2)
END DO
DLOCAL(J+3,J+3)=PROPS(3)
END DO
END IF
ELSE
C----- Orthotropic metarial
DLOCAL(1,1)=PROPS(1)
DLOCAL(1,2)=PROPS(2)
DLOCAL(2,1)=PROPS(2)
DLOCAL(2,2)=PROPS(3)
DLOCAL(1,3)=PROPS(4)
DLOCAL(3,1)=PROPS(4)
DLOCAL(2,3)=PROPS(5)
DLOCAL(3,2)=PROPS(5)
DLOCAL(3,3)=PROPS(6)
DLOCAL(4,4)=PROPS(7)
DLOCAL(5,5)=PROPS(8)
DLOCAL(6,6)=PROPS(9)
END IF
ELSE
C----- General anisotropic material
ID=0
DO J=1,6
DO I=1,J
ID=ID+1
DLOCAL(I,J)=PROPS(ID)
DLOCAL(J,I)=DLOCAL(I,J)
END DO
END DO
END IF
C----- Rotation matrix: ROTATE, i.e. direction cosines of [100], [010]
C and [001] of a cubic crystal in global system
C
CALL ROTATION (PROPS(57), ROTATE)
C----- Rotation matrix: ROTD to transform local elastic matrix DLOCAL
C to global elastic matrix D
C
DO J=1,3
J1=1+J/3
J2=2+J/2
DO I=1,3
I1=1+I/3
I2=2+I/2
ROTD(I,J)=ROTATE(I,J)**2
ROTD(I,J+3)=2.*ROTATE(I,J1)*ROTATE(I,J2)
ROTD(I+3,J)=ROTATE(I1,J)*ROTATE(I2,J)
ROTD(I+3,J+3)=ROTATE(I1,J1)*ROTATE(I2,J2)+
2 ROTATE(I1,J2)*ROTATE(I2,J1)
END DO
END DO
C----- Elastic matrix in global system: D
C {D} = {ROTD} * {DLOCAL} * {ROTD}transpose
C
DO J=1,6
DO I=1,6
D(I,J)=0.
END DO
END DO
DO J=1,6
DO I=1,J
DO K=1,6
DO L=1,6
D(I,J)=D(I,J)+DLOCAL(K,L)*ROTD(I,K)*ROTD(J,L)
END DO
END DO
D(J,I)=D(I,J)
END DO
END DO