Abaqus 本构模型中径向返回算法的 Fortran 代码示例

以下是一个径向返回算法的 Fortran 代码，用于在 Abaqus 的本构模型中：

SUBROUTINE RADIAL_RETURN(STRESS, STRAINP, STRAINN, YIELD, YOUNG, POISSON, TANGENT)
! This subroutine implements the radial return algorithm for a plasticity model in Abaqus.
! Inputs:
!   STRESS  - the current stress tensor
!   STRAINP - the plastic strain tensor from the previous step
!   STRAINN - the strain tensor from the current step
!   YIELD   - the yield stress of the material
!   YOUNG   - the Young's modulus of the material
!   POISSON - the Poisson's ratio of the material
! Outputs:
!   STRESS  - the updated stress tensor
!   STRAINP - the updated plastic strain tensor
!   TANGENT - the updated tangent stiffness tensor

IMPLICIT NONE

REAL*8, DIMENSION(6) :: STRESS, STRAINP, STRAINN, TANGENT
REAL*8 :: YIELD, YOUNG, POISSON, MU, K, GAMMA, R, Q, DQ
REAL*8, DIMENSION(6,6) :: ELASTIC, PLASTIC, IDENTITY
REAL*8, DIMENSION(6) :: STRAIND, STRESSD, STRAINE, STRESSE, DELTA_STRESS
REAL*8 :: TRACE, NORM_STRESS, TOLERANCE
INTEGER :: I

! Define the elastic and plastic stiffness tensors
MU = YOUNG / (2.0 * (1.0 + POISSON))
K = YOUNG / (3.0 * (1.0 - 2.0 * POISSON))
ELASTIC = MU * (IDENTITY(1:6,1:6) - 2.0 / 3.0 * IDENTITY(7,7)) + K * IDENTITY(7,7)
PLASTIC = MU * IDENTITY(1:6,1:6)

! Calculate the deviatoric and volumetric parts of the strain tensor
STRAIND(1:6) = STRAINN(1:6) - STRAINP(1:6)
TRACE = STRAINN(1) + STRAINN(2) + STRAINN(3)
STRAINE(1:6) = 1.0 / 3.0 * TRACE * IDENTITY(7,7)

! Calculate the deviatoric and volumetric parts of the stress tensor
STRESSD(1:6) = MATMUL(ELASTIC(1:6,1:6), STRAIND(1:6))
STRESSE(1:6) = K * TRACE * IDENTITY(7,7)

! Calculate the norm of the deviatoric stress tensor
NORM_STRESS = SQRT(2.0 / 3.0 * (STRESSD(1)**2 + STRESSD(2)**2 + STRESSD(3)**2 + 2.0 * (STRESSD(4)**2 + STRESSD(5)**2 + STRESSD(6)**2)))

! Check if the yield condition is satisfied
IF (NORM_STRESS > YIELD) THEN

  ! Calculate the radial return step
  R = YIELD / NORM_STRESS
  DELTA_STRESS(1:6) = R * STRESSD(1:6)
  GAMMA = 1.0 - R

  ! Calculate the plastic strain increment
  STRAINP(1:6) = STRAINP(1:6) + GAMMA * STRAIND(1:6)

  ! Calculate the plastic tangent stiffness tensor
  Q = MU / (3.0 * K + 2.0 * MU)
  DQ = 2.0 * MU / (3.0 * K + 2.0 * MU)**2
TANGENT(1:6,1:6) = ELASTIC(1:6,1:6) - DQ * MATMUL(DELTA_STRESS(1:6), TRANSPOSE(DELTA_STRESS(1:6))) + Q * (MATMUL(DELTA_STRESS(1:6), TRANSPOSE(DELTA_STRESS(1:6))) - 2.0 / 3.0 * (DELTA_STRESS(1)*IDENTITY(1,1) + DELTA_STRESS(2)*IDENTITY(2,2) + DELTA_STRESS(3)*IDENTITY(3,3) + 2.0 * (DELTA_STRESS(4)*IDENTITY(4,4) + DELTA_STRESS(5)*IDENTITY(5,5) + DELTA_STRESS(6)*IDENTITY(6,6))))

  ! Update the stress tensor
  STRESS(1:6) = STRESS(1:6) + DELTA_STRESS(1:6)

ELSE

  ! Update the elastic tangent stiffness tensor
  TANGENT(1:6,1:6) = ELASTIC(1:6,1:6)

END IF

! Set the tolerance for the norm of the deviatoric stress tensor
TOLERANCE = YIELD / 100.0

! Apply the volumetric strain to the stress and tangent stiffness tensors
STRESS(1:6) = STRESS(1:6) + STRESSE(1:6)
TANGENT(1:6,1:6) = TANGENT(1:6,1:6) + K * IDENTITY(1:6,1:6)

END SUBROUTINE

该代码实现了径向返回算法，用于更新应力、塑性应变和切线刚度矩阵。该算法适用于 Abaqus 的塑性模型，并在每次增量步中执行。

代码说明:

输入参数：
- STRESS: 当前应力张量
- STRAINP: 上一步的塑性应变张量
- STRAINN: 当前步的应变张量
- YIELD: 材料的屈服强度
- YOUNG: 材料的杨氏模量
- POISSON: 材料的泊松比
输出参数：
- STRESS: 更新后的应力张量
- STRAINP: 更新后的塑性应变张量
- TANGENT: 更新后的切线刚度张量

代码步骤：

定义弹性和塑性刚度张量
计算应变张量的偏应力和体积部分
计算应力张量的偏应力和体积部分
计算偏应力张量的范数
检查是否满足屈服条件
如果满足屈服条件，则计算径向返回步骤，并更新塑性应变、切线刚度张量和应力张量
如果不满足屈服条件，则更新弹性切线刚度张量
将体积应变应用于应力和切线刚度张量

该代码示例可作为在 Abaqus 本构模型中实现径向返回算法的基础，用户可以根据自己的需求进行修改和扩展。