黄永刚单晶塑性有限元umat子程序

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 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)

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