ABAQUS Gurson 模型子程序代码示例

由于 Gurson 模型需要进行材料本构方程的求解，因此无法完全用 Python 代码来实现。下面是一个简单的 ABAQUS 子程序代码框架，可以用于实现 Gurson 模型的材料行为。

SUBROUTINE GURSON(MAT, STATEV, DDSDDE, SSE, SPD, SCD, RPL, DDSDDT, DRPLDE, DDDSDDE, TIME, DTIME, TEMP, PREDEF, DPRED, CMNAME, NDI, NSHR, NTENS, NSTATV, PROPS, NPROPS, COORDS, DROT, PNEWDT, CELENT, DFGRD0, DFGRD1, NOEL, NPT, KINC)

!**********************************************************************
! Gurson model subroutine for ABAQUS
!
! Inputs:
!   MAT: Material number
!   STATEV: State variables
!   DDSDDE: Elastic-plastic tangent modulus
!   SSE: Elastic strain energy density
!   SPD: Plastic dissipation
!   SCD: Creep dissipation
!   RPL: Plastic strain
!   DDSDDT: Time derivative of the tangent modulus
!   DRPLDE: Derivative of plastic strain with respect to elastic strain
!   DDDSDDE: Time derivative of the elastic-plastic tangent modulus
!   TIME: Current time
!   DTIME: Time step size
!   TEMP: Temperature
!   PREDEF: Predefined field variables
!   DPRED: Derived field variables
!   CMNAME: Material name
!   NDI: Number of direct stress components
!   NSHR: Number of shear stress components
!   NTENS: Total number of stress components
!   NSTATV: Number of state variables
!   PROPS: Material properties
!   NPROPS: Number of material properties
!   COORDS: Element nodal coordinates
!   DROT: Current deformation gradient increment
!   PNEWDT: Suggested new time increment
!   CELENT: Element type
!   DFGRD0: Deformation gradient at beginning of step
!   DFGRD1: Deformation gradient at end of step
!   NOEL: Element number
!   NPT: Integration point number
!   KINC: Increment number
!
! Outputs:
!   DDSDDE: Elastic-plastic tangent modulus
!   SSE: Elastic strain energy density
!   SPD: Plastic dissipation
!   SCD: Creep dissipation
!   RPL: Plastic strain
!   DDSDDT: Time derivative of the tangent modulus
!   DRPLDE: Derivative of plastic strain with respect to elastic strain
!   DDDSDDE: Time derivative of the elastic-plastic tangent modulus
!   PNEWDT: Suggested new time increment
!
!**********************************************************************
! Define material properties
  REAL :: E0, SIGY, N, Q, ALPHA, BETA, ETA
  E0 = PROPS(1)
  SIGY = PROPS(2)
  N = PROPS(3)
  Q = PROPS(4)
  ALPHA = PROPS(5)
  BETA = PROPS(6)
  ETA = PROPS(7)
  
! Define state variables
  REAL :: R, A, ZET, DEL, XIR, F, GAMMA
  R = STATEV(1)
  A = STATEV(2)
  ZET = STATEV(3)
  DEL = STATEV(4)
  XIR = STATEV(5)
  F = STATEV(6)
  GAMMA = STATEV(7)

! Get current stress and strain
  REAL :: STRESS(NTENS), STRAIN(NTENS)
  CALL GETVRM(NOEL, NPT, 'STRESS', STRESS)
  CALL GETVRM(NOEL, NPT, 'STRAIN', STRAIN)

! Compute equivalent stress and strain
  REAL :: SEQ, EQVSTRAIN
  SEQ = SQRT(2.0/3.0*(STRESS(1)**2 + STRESS(2)**2 + STRESS(3)**2 - STRESS(1)*STRESS(2) - STRESS(2)*STRESS(3) - STRESS(3)*STRESS(1)))
  EQVSTRAIN = SQRT(2.0/3.0*(STRAIN(1)**2 + STRAIN(2)**2 + STRAIN(3)**2 - STRAIN(1)*STRAIN(2) - STRAIN(2)*STRAIN(3) - STRAIN(3)*STRAIN(1)))

! Compute porosity
  REAL :: POROSITY
  POROSITY = R**3

! Compute damage evolution equation
  REAL :: DRDT, DADT, ZETDOT, DELDOT, XIRDOT, FDOT, GAMMADOT
  DRDT = ALPHA*SEQ/(E0*EQVSTRAIN + ALPHA*SEQ)
  DADT = BETA*SEQ/(SIGY + BETA*SEQ)
  ZETDOT = ETA*(1.0 - POROSITY)**N*SEQ**Q*(1.0 - R)**2
  DELDOT = ZETDOT*(1.0 - DEL)
  XIRDOT = 1.0 - EXP(-ZET/(A*(1.0 - DEL)))
  FDOT = XIRDOT*(1.0 - F)*ZETDOT/(1.0 - DEL)
  GAMMADOT = 2.0/3.0*FDOT/EQVSTRAIN

! Update state variables
  R = R + DRDT*DTIME
  A = A + DADT*DTIME
  ZET = ZET + ZETDOT*DTIME
  DEL = DEL + DELDOT*DTIME
  XIR = XIR + XIRDOT*DTIME
  F = F + FDOT*DTIME
  GAMMA = GAMMA + GAMMADOT*DTIME

! Update stress and strain
  DO I=1,NTENS
    DDSDDE(I,I) = E0*(1.0 - R)**2
  END DO
  SSE = 0.5*E0*(1.0 - R)**2*EQVSTRAIN**2
  SPD = 0.0
  SCD = 0.0
  RPL = RPL + GAMMA
  DDSDDT = 0.0
  DRPLDE = 1.0 - R
  DDDSDDE = 0.0
  PNEWDT = DTIME

! Update state variables
  STATEV(1) = R
  STATEV(2) = A
  STATEV(3) = ZET
  STATEV(4) = DEL
  STATEV(5) = XIR
  STATEV(6) = F
  STATEV(7) = GAMMA

END SUBROUTINE GURSON

请注意，这只是一个简单的框架，需要根据实际情况进行修改和优化。此外，还需要在 ABAQUS 中设置材料属性和状态变量才能使用此子程序。

希望这个简单的示例能够帮助您理解 Gurson 模型在 ABAQUS 中的应用。