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南方科技大学公共卫生及应急管理学院2025级博士研究生招生报考通知

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yiran909

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[交流] 请问哪位能够提供有关hill 48 各向异性屈服准则的详细资料已有3人参与

大家好，我最近在看abaqus documentation 中的各向异性屈服准则的内容，
里边写的很简单就几个公式，也看不懂，
而且查了一些文献，但是那个屈服准则和函数的公式表达也不完全一样，
感觉看不懂，想推导推导，请求哪位能提供详细的关于Hill 48的屈服准则和函数的资料，
不胜感激。

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1楼2013-06-27 15:55:03

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linrn

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Google学术搜索里面一堆文献。
自己动手，丰衣足食。

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2楼2013-06-28 12:55:47

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yiran909

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引用回帖:

2楼: Originally posted by linrn at 2013-06-28 12:55:47
Google学术搜索里面一堆文献。
自己动手，丰衣足食。

哥，关键是我看不懂英文啊，
想找点中文的，像教材集中讲的
不是文献里边哪种，简单提起一下
活着是力学推导，都看不懂啊

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3楼2013-06-28 17:06:36

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linrn

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看不懂英文，最好不学什么屈服方程。

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4楼2013-06-28 22:42:34

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***********************************************************************************
**  UMAT for Abaqus/Standard, large deformation formulation for plane stress    **
**  elements S4R. Implicit integration with continuum Jacobian.                **
***********************************************************************************
C==================================================================================
C                                                                               ==
C *  Copyright:  2007 by Zang Shun lai.  All Rights Reserved.                ==
C *             Date Aug, 24, 2007                                           ==
C *  Address: Xi'an Jiaotong University, Xianning Road, Xi'an Shaanxi,    ==
C *             P.R.China                                                    ==
C *                                                                         ==
C *  E-mail:    shunlai.zang@gmail.com                                     ==
C *                                                                         ==
C==================================================================================
C==================================================================================
C    NOTE:  UMAT FOR ABAQUS
C==================================================================================
C    (1) The statement: include 'aba_param.inc' must be added as below.
C
C    (2) This is current as of version 6.5 of abaqus.
C
C    (3) The current yield function is Hill1948 with three material parameters.
C    The anisotropy of initial yield stress and Lankford values can be described
C    by Hill1948 respectively.
C
C    (4) The current hardening model is isotropic hardening, which can %NOT% model
C    the Bauschinger effect, transient behavior in cyclic loading.
C
C    (5) The default type of variables,whose prefix is i-n��is integer. The name of
C    variables must be cared.
C
C    (6) The engineering shear strain is used in UMAT subroutine interface.
C
C    (7) For different unit system, the TOLER should be adjusted.
C
C==================================================================================
C
*USER SUBROUTINE
   SUBROUTINE UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,RPL,DDSDDT,
   1  DRPLDE,DRPLDT,STRAN,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,
   2  CMNAME,NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,
   3  CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,KSTEP,KINC)

      INCLUDE 'ABA_PARAM.INC'
      CHARACTER*8 CMNAME

      DIMENSION STRESS(NTENS),STATEV(NSTATV),DDSDDE(NTENS,NTENS),
   1  DDSDDT(NTENS),DRPLDE(NTENS),STRAN(NTENS),DSTRAN(NTENS),TIME(2),
   2  PREDEF(1),DPRED(1),PROPS(NPROPS),COORDS(3),DROT(3,3),
   3  DFGRD0(3,3),DFGRD1(3,3)
C
C LOCAL ARRAYS
C ===================================================================
C EELAS  - ELASTIC STRAINS
C EPLAS  - PLASTIC STRAINS
C ===================================================================
C
   PARAMETER(ZERO=0.D0,ONE=1.D0,TWO=2.D0,THREE=3.D0,FOUR=4.D0,
1       FIVE=5.D0,SIX=6.D0,SEVEN=7.D0,EIGHT=8.D0,
   2       ENUMAX=.4999D0,NEWTON=60,TOLER=1.0D-9,
   3       E=2.718281828459045235D0,THRESHOLD=50.D0,KKSTEP=5)
   DIMENSION EELAS(NTENS+1),EPLAS(NTENS+1),
1       RPOTENTIAL(KKSTEP),
2       DEELAS(NTENS),DEPLAS(NTENS),
3       DSIGMA(NTENS),RSIGMA(NTENS),
   4       STRESSOLD(NTENS),EELASOLD(NTENS+1),EPLASOLD(NTENS+1),
5       STRESS_B(NTENS),STRESSNEW(NTENS),
6       PFPSIGMA(NTENS), PAPSIGMA(NTENS,NTENS),
   7       O(NTENS,NTENS),OREVERSE(NTENS,NTENS),ATOREVERSE(NTENS),
8       CEA(NTENS),T1(NTENS),
   9       R(NTENS,NTENS),RA(NTENS),ATR(NTENS),RAATR(NTENS,NTENS),
   1       XIDEN(NTENS,NTENS),STR(NTENS,NTENS),IS(NTENS),JS(NTENS)
C
EMOD = PROPS(1)
   ENU    = MIN(PROPS(2),ENUMAX)
   EG    = EMOD/(TWO*(ONE+ENU))
   ELAM = (EMOD*ENU)/((ONE+ENU)*(ONE-TWO*ENU))
EG2    = TWO*EG
ELAMBAR = (EG2*ELAM)/(ELAM+EG2)
C
C ELASTIC STIFFNESS
C
   DO K1=1,NTENS
DO K2=1,NTENS
   DDSDDE(K1,K2) = ZERO
END DO
END DO

DO K1=1,NDI
      DO K2=1,NDI
      DDSDDE(K2,K1)=ELAMBAR
      END DO
      DDSDDE(K1,K1)=EG2+ELAMBAR
   END DO
   DO K1=NDI+1,NTENS
      DDSDDE(K1,K1)=EG
   END DO
C

C       CALCULATE NEW EFFECTIVE STRESS EFSTRESS
C
      CALL KCALES(STRESSNEW,YR0,YR45,YR90,EFSTRESS)

DELTA_LAMBDA = DELTA_LAMBDA + DDELTA_LAMBDA
DEQPLAS = DELTA_LAMBDA
EQPLAS=EQPLASOLD+DEQPLAS
C
C
C check yield criterion with updated constitutive values
C
SYIELD= SYIEL0 + EQ*(ONE-E**(-EB*EQPLAS))
RHS = EFSTRESS-SYIELD
IF(DABS(RHS) .LT. (TOLER*SYIEL0)) GOTO 11

   END DO !ENDDO FOR DO KEWTON=1,NEWTON
C
C       WRITE WARNING MESSAGE TO THE .MSG FILE
C
C       WRITE(7,2) KEWTON, RHS, EFSTRESS, EQPLAS

11 CONTINUE

   END IF !END FOR IF(ZY .GT. THRESHOLD)
C
C
C    UPDATE STRESS, ELASTIC AND PLASTIC STRAINS AND
C    EQUIVALENT PLASTIC STRAIN
C
   CALL CALDR(STRESSNEW,YR0,YR45,YR90,PFPSIGMA)
   DO K1=1,NTENS
      STRESS(K1)=STRESSNEW(K1)
      DEELAS(K1)=DSTRAN(K1)-DELTA_LAMBDA*PFPSIGMA(K1)
      DEPLAS(K1)=DELTA_LAMBDA*PFPSIGMA(K1)
      END DO
C
C    FORMULATE THE JACOBIAN (MATERIAL TANGENT)
C
C    CALCULATE PFPSIGMA(NTENS)
C
      CALL CALDR(STRESS,YR0,YR45,YR90,PFPSIGMA)
      CALL KCALES(STRESS,YR0,YR45,YR90,EFSTRESS)
C
C    CALCULATE A_iso
C
   H = EB*EQ*(E**(-EB*EQPLAS))
      A_iso = H
C
C    CALCULATE THE PAPSIGMA \FRAC{\PARTIAL A}{\PARTIAL \SIGMA}
C
      CALL CAL2DR(STRESS,YR0,YR45,YR90,PAPSIGMA)
C
C    CALCULATE THE TEMP VARIABLE O
C
   DO K1=1,NTENS
   DO K2=1,NTENS
      O(K1,K2)=ZERO
   END DO
   END DO

   DO K1=1,NTENS
   DO K2=1,NTENS
      DO K3=1,NTENS
      O(K1,K2)=O(K1,K2)+DDSDDE(K1,K3)*PAPSIGMA(K3,K2)
      END DO
   END DO
   END DO

       DO K1=1,NTENS
   DO K2=1,NTENS
      O(K1,K2)=XIDEN(K1,K2)+DELTA_LAMBDA*O(K1,K2)
   END DO
   END DO
C
C    CALCULATE OREVERSE \Theta^{-1}
C
   DO K1=1,NTENS
   DO K2=1,NTENS
      OREVERSE(K1,K2) = O(K1,K2)
   END DO
   END DO

      CALL BRINV(OREVERSE,NTENS,L,IS,JS)

   IF (L .EQ. 0) THEN
C       WRITE(7,15) KEWTON
15    FORMAT(//,30X,'***WARNING - THE MATRIX \Theta12356 DID NOT ',
   1                'CONVERGE AFTER ',I3,' ITERATIONS')
   END IF
C
C    CALCULATE R(NTENS,NTENS)=OREVERSE * DDSDDE
C
      DO K1=1,NTENS
   DO K2=1,NTENS
      R(K1,K2) = 0.D0
   END DO
   END DO

   DO K1=1,NTENS
   DO K2=1,NTENS
      DO K3=1,NTENS
      R(K1,K2) = R(K1,K2) + OREVERSE(K1,K3)*DDSDDE(K3,K2)
      END DO
   END DO
   END DO
C
C    CALCULATE RA(NTENS)
C
      DO K1=1,NTENS
      RA(K1)=0.D0
   END DO

      DO K1=1,NTENS
   DO K2=1,NTENS
      RA(K1)=RA(K1)+R(K1,K2)*PFPSIGMA(K2)
   END DO
   END DO
C
C    CALCULAT ATR(NTENS)
C
      DO K1=1,NTENS
      ATR(K1)=0.D0
   END DO

   DO K1=1,NTENS
   DO K2=1,NTENS
      ATR(K1)=ATR(K1)+PFPSIGMA(K2)*R(K2,K1)
   END DO
   END DO
C
C    CALCULAT RAATR(NTENS,NTENS)
C
      DO K1=1,NTENS
   DO K2=1,NTENS
      RAATR(K1,K2)=RA(K1)*ATR(K2)
   END DO
   END DO
C
C    CALCULAT ATRA
C
      ATRA=0.D0
   DO K1=1,NTENS
      ATRA= ATRA + PFPSIGMA(K1)*RA(K1)
   END DO
C
C    COPY TO DDSDDE(NTENS,NTENS)
C
      DO K1=1,NTENS
   DO K2=1,NTENS
      DDSDDE(K1,K2)=ZERO
   END DO
   END DO

   DO K1=1,NTENS
      DO K2=1,NTENS
      DDSDDE(K1,K2)=R(K1,K2)-RAATR(K1,K2)/(ATRA+A_iso)
      END DO
   END DO
END IF !END IF FOR IF(ZY .GT. 0.D0)
*********************************************************************
C STORE ELASTIC AND (EQUIVALENT) PLASTIC STRAINS
C IN STATE VARIABLE ARRAY
*********************************************************************
C
C    SAVE 11 AND 22 COMPONENT
C
DO K1=1,NDI
      STATEV(K1)=EELASOLD(K1)+DEELAS(K1)
      STATEV(K1+(NTENS+1))=EPLASOLD(K1)+DEPLAS(K1)
   END DO
C
C    SAVE 33 COMPONENT
C
   STATEV(3)=EELASOLD(3)-(ENU*(DEELAS(1)+DEELAS(2)))/(ONE-ENU)
STATEV(7)=EPLASOLD(3)-DEPLAS(1)-DEPLAS(2)
C
C    SAVE 12 COMPONENT
C
STATEV(4)=EELASOLD(4)+DEELAS(3)
STATEV(8)=EPLASOLD(4)+DEPLAS(3)
C
C    SAVE EQUIVALENT PLASTIC STRAIN
C
   STATEV(9)=EQPLAS
   RETURN
   END

**
*********************************************************************
**          UTILITY SUBROUTINES                               *
*********************************************************************
** CALCULATE YOUNG'S MODULUS, THE CHANGE OF YOUNG'S MODULUS WITH
** EQUIVALENT PLASTIC STRAIN IS CONSIDERED
*********************************************************************
*USER SUBROUTINE
   SUBROUTINE XYMOD(EQPLAS,EMOD1,ESTATMOD,EEPLAS,EMOD)
C
   INCLUDE 'ABA_PARAM.INC'
C
   IF (EQPLAS .LE. 0.04) THEN
      EMOD=EMOD1-((EMOD1-ESTATMOD)*EQPLAS)/EEPLAS
ELSE
   EMOD=ESTATMOD
ENDIF
RETURN
END
**
*********************************************************************
** INVERSE MATRIX                                              *
*********************************************************************
*USER SUBROUTINE
   SUBROUTINE BRINV(A,N,L,IS,JS)
DIMENSION A(N,N),IS(N),JS(N)
DOUBLE PRECISION A,T,D
L=1
DO 100 K=1,N
   D=0.0
   DO 10 I=K,N
   DO 10 J=K,N
      IF (ABS(A(I,J)).GT.D) THEN
      D=ABS(A(I,J))
      IS(K)=I
      JS(K)=J
      END IF
10    CONTINUE
   IF (D+1.0.EQ.1.0) THEN
      L=0
C       WRITE(*,20)
      RETURN
   END IF
20    FORMAT(1X,'ERR**NOT INV')
   DO 30 J=1,N
      T=A(K,J)
      A(K,J)=A(IS(K),J)
      A(IS(K),J)=T
30    CONTINUE
   DO 40 I=1,N
      T=A(I,K)
      A(I,K)=A(I,JS(K))
      A(I,JS(K))=T
40    CONTINUE
   A(K,K)=1/A(K,K)
   DO 50 J=1,N
      IF (J.NE.K) THEN
      A(K,J)=A(K,J)*A(K,K)
      END IF
50    CONTINUE
   DO 70 I=1,N
      IF (I.NE.K) THEN
      DO 60 J=1,N
         IF (J.NE.K) THEN
            A(I,J)=A(I,J)-A(I,K)*A(K,J)
         END IF
60       CONTINUE
      END IF
70    CONTINUE
   DO 80 I=1,N
      IF (I.NE.K) THEN
      A(I,K)=-A(I,K)*A(K,K)
      END IF
80    CONTINUE
100 CONTINUE
DO 130 K=N,1,-1
   DO 110 J=1,N
      T=A(K,J)
      A(K,J)=A(JS(K),J)
      A(JS(K),J)=T
110    CONTINUE
   DO 120 I=1,N
      T=A(I,K)
      A(I,K)=A(I,IS(K))
      A(I,IS(K))=T
120    CONTINUE
130 CONTINUE
RETURN
END
**
*********************************************************************
** CALCULATE EFFECTIVE STRESS FOR HILL48                         *
*********************************************************************
*USER SUBROUTINE
   SUBROUTINE KCALES(SIGMA,XR0,XR45,XR90,EES)

INCLUDE 'ABA_PARAM.INC'
PARAMETER (M=3)
DIMENSION SIGMA(M),P(M,M),PSIGMA(M)

BETA12=XR0/(1.D0+XR0)
BETA66=(XR0+XR90)*(1.D0+2.D0*XR45)/(XR90*(1.D0+XR0))
BETA23=XR0/(XR90*(1.D0+XR0))
BETA22=BETA12+BETA23

   DO K1=1,M
DO K2=1,M
   P(K1,K2) = 0.D0
   PSIGMA(K1) = 0.D0
END DO
END DO

P(1,1)=2.D0*1.D0
P(1,2)=-2.D0*BETA12
P(2,1)=-2.D0*BETA12
P(2,2)=2.D0*BETA22
P(3,3)=2.D0*BETA66

DO K1=1,M
DO K2=1,M
      PSIGMA(K1)=PSIGMA(K1)+P(K1,K2)*SIGMA(K2)
   END DO
END DO

EES=0.D0
DO K1=1,M
   EES = EES + SIGMA(K1)*PSIGMA(K1)
END DO
EES = DSQRT(EES/2.D0)
   RETURN
   END
**
*********************************************************************
** CALCULATE FIRST ORDER DERIVATIVE FOR HILL48                   *
*********************************************************************
*USER SUBROUTINE
   SUBROUTINE CALDR(SIGMA,XR0,XR45,XR90,PFPS)
C
   INCLUDE 'ABA_PARAM.INC'
   PARAMETER(M=3)
   DIMENSION SIGMA(M),PFPS(M),P(M,M),PSIGMA(M)

BETA12=XR0/(1.D0+XR0)
BETA66=(XR0+XR90)*(1.D0+2.D0*XR45)/(XR90*(1.D0+XR0))
BETA23=XR0/(XR90*(1.D0+XR0))
BETA22=BETA12+BETA23

   DO K1=1,M
DO K2=1,M
   P(K1,K2) = 0.D0
   PSIGMA(K1) = 0.D0
END DO
END DO

P(1,1)=2.D0*1.D0
P(1,2)=-2.D0*BETA12
P(2,1)=-2.D0*BETA12
P(2,2)=2.D0*BETA22
P(3,3)=2.D0*BETA66

DO K1=1,M
DO K2=1,M
      PSIGMA(K1)=PSIGMA(K1)+P(K1,K2)*SIGMA(K2)
   END DO
END DO

EES=0.D0
DO K1=1,M
   EES = EES + SIGMA(K1)*PSIGMA(K1)
END DO

EES = DSQRT(EES/2.D0)

DO K1=1,M
   PFPS(K1)=PSIGMA(K1)/(2.D0*EES)
END DO

   RETURN
   END
**
*********************************************************************
** CALCULATE SECOND DERIVATIVE FOR HILL48                      *
*********************************************************************
*USER SUBROUTINE
   SUBROUTINE CAL2DR(SIGMA,XR0,XR45,XR90,PAPS)
C
   INCLUDE 'ABA_PARAM.INC'
   PARAMETER(M=3)
   DIMENSION SIGMA(M),PAPS(M,M),P(M,M),PSIGMA(M),PFPS(M)

BETA12=XR0/(1.D0+XR0)
BETA66=(XR0+XR90)*(1.D0+2.D0*XR45)/(XR90*(1.D0+XR0))
BETA23=XR0/(XR90*(1.D0+XR0))
BETA22=BETA12+BETA23

   DO K1=1,M
DO K2=1,M
   P(K1,K2) = 0.D0
   PSIGMA(K1) = 0.D0
END DO
END DO

P(1,1)=2.D0*1.D0
P(1,2)=-2.D0*BETA12
P(2,1)=-2.D0*BETA12
P(2,2)=2.D0*BETA22
P(3,3)=2.D0*BETA66

DO K1=1,M
DO K2=1,M
      PSIGMA(K1)=PSIGMA(K1)+P(K1,K2)*SIGMA(K2)
   END DO
END DO

EES=0.D0
DO K1=1,M
   EES = EES + SIGMA(K1)*PSIGMA(K1)
END DO

EES = DSQRT(EES/2.D0)

DO K1=1,M
   PFPS(K1)=PSIGMA(K1)/(2.D0*EES)
END DO

DO K1=1,M
DO K2=1,M
   PAPS(K1,K2)=P(K1,K2)/(2.D0*EES)-PFPS(K1)*PFPS(K2)/EES
END DO
END DO

   RETURN
   END

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5楼2019-04-14 17:42:36

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自为胜利而来

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5楼: Originally posted by 吕泽华 at 2019-04-14 17:42:36
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** UMAT for Abaqus/Standard, large deformation formulation for plane stress **
** elements S4R. Implicit ...

非常感谢，学习。

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道系青年

6楼2022-05-18 17:19:08

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