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steel1

  1. C STEEL1    SOURCE    PV        17/07/20    21:15:05     9512           
  2. *---------------------------------------------------------------------
  3. *
  4.       SUBROUTINE STEEL1
  5.      .       ( EYOUN, FSY__, FSU__, EPSH_, EPSU_, ROFAC, BFACT,
  6.      .         A1FAC, A2FAC, FACLD, A6FAC, CFACT, AFACT, IFLAG,
  7.      .         STRAI, RFACT, EPSON, SIGMA, TANGE, STRES )
  8. *
  9. *---------------------------------------------------------------------
  10. *
  11. *   STEEL BEHAVIOUR MODEL (MENEGOTTO-PINTO MODEL)
  12. *                         (INCLUDING THE MONOTONIC CURVE)
  13. *                         (AND THE BUCKLING EFFECT)
  14. *---------------------------------------------------------------------
  15. *
  16. *   INPUT :
  17. *   -----
  18. *               EYOUN : YOUNG MODULUS
  19. *               FSY__ : YELDING STRESS
  20. *               FSU__ : ULTIMATE STRESS
  21. *               EPSH_ : HARDENING STRAIN
  22. *               EPSU_ : ULTIMATE STRAIN
  23. *               ROFAC : Ro FACTOR
  24. *               BFACT : b  FACTOR
  25. *               A1FAC : a1 FACTOR
  26. *               A2FAC : a2 FACTOR
  27. *               FACLD : L/D FACTOR (BUCKLING EFFECT)
  28. *               A6FAC : a6 FACTOR FOR THE NEW YOUNG MODULUS
  29. *               CFACT : c FACTOR FOR THE "GAMAs" VALUE
  30. *               AFACT : a FACTOR FOR THE NEW "BFACT"
  31. *               IFLAG : FLAG DEFINING THE STEEL STAGE
  32. *               STRAI : ACTUAL STRAIN VALUE
  33. *               RFACT : R FACTOR
  34. *               EPSON : HISTORY OF REVERSAL STRAIN POINTS
  35. *               SIGMA : HISTORY OF REVERSAL STRESS POINTS
  36. *
  37. *   OUTPUT :
  38. *   ------
  39. *               TANGE : ACTUAL TANGENT MODULUS
  40. *               STRES : ACTUAL STRESS VALUE
  41. *
  42. *       NOTE : POSITIVE STRESSES = TENSION STRESSES
  43. *              NEGATIVE STRESSES = COMPRESSION STRESSES
  44. *
  45. *              POSITIVE STRAIN = TENSION STRAIN
  46. *              NEGATIVE STRAIN = COMPRESSION STRAIN
  47. *
  48. *---------------------------------------------------------------------
  49. *
  50. *       DIFERENT POSSIBLE STAGES OF THE MATERIAL
  51. *
  52. *       ***********************************************************
  53. *       IFLAG = 0  ....  FIRST LOADING ON THE ENVELOPE
  54. *       IFLAG = 1  ....  STEEL IS DISTROIED
  55. *       IFLAG = 2  ....  LOADING OR UNLOD. IN THE POSITIVE DIRECTION
  56. *       IFLAG = 3  ....  LOADING OR UNLOD. IN THE NEGATIVE DIRECTION
  57. *       IFLAG =-4  ....  IDEM "IFLAG = 2" FOR UNLOD. FROM THE MONOTONIC
  58. *       IFLAG =-5  ....  IDEM "IFLAG = 3" FOR UNLOD. FROM THE MONOTONIC
  59. *
  60. *       NOTE: A NEGATIVE VALUE FOR "IFLAG" MEANS THAT THE ENVOLVENT
  61. *             CURVE IS STILL THE MONOTONIC ONE
  62. *
  63. *---------------------------------------------------------------------
  64. C
  65.       IMPLICIT INTEGER(I-N)
  66.        IMPLICIT REAL*8 (A-H,O-Z)
  67. C
  68.        DIMENSION EPSON (5), SIGMA (5)
  69. C
  70. C-------------------------------------------------------------
  71. C       VALUES TO BE KEPT IN EPSON (AND SIGMA) VECTOR(S):
  72. C           EPSON (1) ....  LAST REVERSAL STRAIN
  73. C           EPSON (2) ....  INTERSEPTION POINT OF THE ASYMPTOTES
  74. C           EPSON (3) ....  LAST STRAIN VALUE
  75. C           EPSON (4) ....  MAXIMUM REVERSAL STRAIN IN THE POSIT. DIR.
  76. C           EPSON (5) ....  MAXIMUM REVERSAL STRAIN IN THE NEGAT. DIR.
  77. C-------------------------------------------------------------
  78.        EPSY_ = FSY__/EYOUN
  79. C
  80.        IF (FACLD .GT. 5.0D0) THEN
  81. C-------------------------------------------------------------
  82. C         BUCKLING EFFECT
  83. C-------------------------------------------------------------
  84.           A5FAC = 1.0D0 + (5.0D0-FACLD) / 7.5D0
  85.           FSINF = 4.0D0 * FSY__ / FACLD
  86.           GAMAS = (11.0D0-FACLD) / (EXP(CFACT*FACLD)-1.0D0) / 10.0D0
  87.        ENDIF
  88. C
  89.        IF (IFLAG .EQ. 0) THEN
  90. C-------------------------------------------------------------
  91. C         DEFINITION OF THE FIRST STEP PARAMETERS
  92. C-------------------------------------------------------------
  93.           IF (ABS(STRAI) .LE. 1.0D-10) THEN
  94.              STRES = 0.0D0
  95.              TANGE = EYOUN
  96.              GO TO 2000
  97.           ENDIF
  98. C
  99.           SIGN_ = STRAI/ABS(STRAI)
  100. C
  101.           EPSON(1) = -SIGN_*EPSY_
  102.           SIGMA(1) = -SIGN_*FSY__
  103. C
  104.           EPSON(2) = SIGN_*EPSY_
  105.           SIGMA(2) = SIGN_*FSY__
  106. C
  107.           EPSON(3) = 0.D0
  108.           SIGMA(3) = 0.D0
  109. C
  110.           EPSON(4) = EPSY_
  111.           SIGMA(4) = FSY__
  112. C
  113.           EPSON(5) = -EPSY_
  114.           SIGMA(5) = -FSY__
  115. C
  116.           RFACT = ROFAC
  117. C
  118.           IF (SIGN_ .GT. 0.0D0) THEN
  119.              IFLAG = -2
  120.           ELSE
  121.              IFLAG = -3
  122.           ENDIF
  123.           GO TO 100
  124.        ENDIF
  125. C
  126.        IF (IFLAG .EQ. -4) THEN
  127. C-------------------------------------------------------------
  128. C         DISCHARGE UNDER THE LIMITS OF THE MONOTONIC CURVE
  129. C-------------------------------------------------------------
  130.           IF ((EPSON(4)-STRAI) .GT. (EPSY_/3.0D0)) THEN
  131.              IFLAG = 3
  132.           ELSE
  133.              STRES = EYOUN * (STRAI-EPSON(4)) + SIGMA(4)
  134.              TANGE = EYOUN
  135. C
  136.              ACOEF = -1.0D0 * (FSU__-FSY__) / ((EPSU_-EPSH_)**2)
  137.              BCOEF = -2.0D0 * ACOEF * EPSU_
  138.              CCOEF = FSU__ - ACOEF * (EPSU_**2) - BCOEF * EPSU_
  139.              STRE1 = ACOEF * STRAI**2 +
  140.      .               BCOEF * STRAI +
  141.      .               CCOEF
  142. C
  143.              IF (STRES .LT. STRE1) GOTO 2000
  144.              IFLAG = -2
  145.           ENDIF
  146.        ELSEIF (IFLAG .EQ. -5) THEN
  147.           IF ((STRAI-EPSON(5)) .GT. (EPSY_/3.0D0)) THEN
  148.              IFLAG = 2
  149.           ELSE
  150.              STRES = EYOUN * (STRAI-EPSON(5)) + SIGMA(5)
  151.              TANGE = EYOUN
  152. C
  153.              ACOEF = -1.0D0 * (FSU__-FSY__) / ((EPSU_-EPSH_)**2)
  154.              BCOEF = -2.0D0 * ACOEF * EPSU_
  155.              CCOEF = FSU__ - ACOEF * (EPSU_**2) - BCOEF * EPSU_
  156.              STRE1 = -1.0D0 * ACOEF * STRAI**2 +
  157.      .                      BCOEF * STRAI -
  158.      .                      CCOEF
  159. C
  160.              IF (STRES .GT. STRE1) GOTO 2000
  161.              IFLAG = -3
  162.           ENDIF
  163.        ENDIF
  164. C-------------------------------------------------------------
  165.        IF (ABS(STRAI) .GT. EPSU_) IFLAG = 1
  166. C
  167.        IF (IFLAG .EQ. 1) THEN
  168. C-------------------------------------------------------------
  169. C         THE STEEL IS DISTROIED
  170. C-------------------------------------------------------------
  171. CPP       WRITE (*,*) ' THE STEEL IS DISTROIED !!!'
  172.           STRES = 0.0D0
  173.           TANGE = 0.0D0
  174.           GO TO 2000
  175.        ENDIF
  176. C-------------------------------------------------------------
  177.        IF (IABS(IFLAG) .EQ. 2) THEN
  178.           IF (STRAI .GT. EPSON(3)) THEN
  179. C-------------------------------------------------------------
  180. C            MOVEMENT IN THE SAME DIRECTION
  181. C-------------------------------------------------------------
  182.              GO TO 100
  183.           ENDIF
  184. C-------------------------------------------------------------
  185. C         MOVEMENT IN THE OPPOSITE DIRECTION
  186. C-------------------------------------------------------------
  187.           SIGN_= 1.0D0
  188. C
  189.           IFLAG = IABS(IFLAG) / IFLAG * 3
  190.           IF (IFLAG .LT. 0) THEN
  191.              IF (ABS(EPSON(3)) .GT. EPSY_) THEN
  192. C-------------------------------------------------------------
  193. C               CORRECTION OF REVERSAL STRAIN AND STRESS VALUES
  194. C-------------------------------------------------------------
  195.                 EPSOO = EPSON(3)
  196.                 EPSON(3) = EPSY_ - SIGMA(3) /
  197.      .                     (EYOUN*(1.0D0-BFACT)) +
  198.      .                     EPSOO / (1.0D0-BFACT)
  199.                 SIGMA(3) = EYOUN * (EPSON(3)-EPSOO) + SIGMA(3)
  200. C
  201.                 IF ((EPSON(3)-STRAI) .GT. (EPSY_/3.0D0)) THEN
  202.                    IFLAG = 3
  203.                 ELSE
  204.                    IFLAG = -4
  205.                    STRES = EYOUN * (STRAI-EPSON(3)) + SIGMA(3)
  206.                    TANGE = EYOUN
  207.                 ENDIF
  208.              ENDIF
  209.           ENDIF
  210.           IF (EPSON(3) .GT. EPSON(4)) THEN
  211.              EPSON(4) = EPSON(3)
  212.              SIGMA(4) = SIGMA(3)
  213.           ENDIF
  214.        ELSEIF (IABS(IFLAG) .EQ. 3) THEN
  215.           IF (STRAI .LT. EPSON(3)) THEN
  216. C-------------------------------------------------------------
  217. C            MOVEMENT IN THE SAME DIRECTION
  218. C-------------------------------------------------------------
  219.              IF (FACLD .GT. 5.0D0 .AND.
  220.      .           STRAI .LT. (-0.95D0*EPSY_)) IFLAG = 3
  221.              GO TO 100
  222.           ENDIF
  223. C-------------------------------------------------------------
  224. C         MOVEMENT IN THE OPPOSITE DIRECTION
  225. C-------------------------------------------------------------
  226.           SIGN_= -1.0D0
  227. C
  228.           IFLAG = IABS(IFLAG) / IFLAG * 2
  229.           IF (IFLAG .LT. 0) THEN
  230.              IF (ABS(EPSON(3)) .GT. EPSY_) THEN
  231. C-------------------------------------------------------------
  232. C               CORRECTION OF REVERSAL STRAIN AND STRESS VALUES
  233. C-------------------------------------------------------------
  234.                 EPSOO = EPSON(3)
  235.                 EPSON(3) = EPSY_ + SIGMA(3) /
  236.      .                     (EYOUN*(1.0D0-BFACT)) -
  237.      .                     EPSOO / (1.0D0-BFACT)
  238.                 EPSON(3) = -1.D0 * EPSON(3)
  239.                 SIGMA(3) = EYOUN * (EPSON(3)-EPSOO) + SIGMA(3)
  240. C
  241.                 IF ((STRAI-EPSON(3)) .GT. (EPSY_/3.0D0)) THEN
  242.                    IFLAG = 2
  243.                 ELSE
  244.                    IFLAG = -5
  245.                    STRES = EYOUN * (STRAI-EPSON(3)) + SIGMA(3)
  246.                    TANGE = EYOUN
  247.                 ENDIF
  248.              ENDIF
  249.           ENDIF
  250.           IF (EPSON(3) .lT. EPSON(5)) THEN
  251.              EPSON(5) = EPSON(3)
  252.              SIGMA(5) = SIGMA(3)
  253.           ENDIF
  254.        ENDIF
  255. C
  256. C
  257. C      ######################################
  258. C
  259. C      ......   CHANGE OF PARAMETERS   ......
  260. C
  261. C      ######################################
  262. C
  263. C
  264.   200  EPSON(1) = EPSON(3)
  265.        SIGMA(1) = SIGMA(3)
  266. C
  267.        R1FAC = ROFAC
  268.        YOUNG = EYOUN
  269.        BFACN = BFACT
  270. C
  271.        STRSH = 0.0D0
  272.        EPSSH = 0.0D0
  273.        IF (FACLD .GT. 5.0D0) THEN
  274.           IF (IABS(IFLAG) .EQ. 2) THEN
  275.              DO ITEST = 1,5
  276.                 EPSON(2) = (-SIGN_*BFACN*EPSY_-EPSON(1)+
  277.      .                     (SIGMA(1)+SIGN_*FSY__)/YOUNG)/(BFACN-1.0D0)
  278.                 EPSIS = ABS(EPSON(IABS(IFLAG)+2)-EPSON(2))
  279.              YOUNG = EYOUN * (A5FAC+(1.0D0-A5FAC)*EXP(-A6FAC*EPSIS**2))
  280.                 BFACN = BFACT * EYOUN / YOUNG
  281.              ENDDO
  282.           ELSEIF (IABS(IFLAG) .EQ. 3) THEN
  283.              EPSIM = EPSON(4) - EPSON(5) - 2.0D0*FSY__/EYOUN
  284. C
  285.              BFACN = AFACT * (5.0D0-FACLD)
  286.              BFACN = BFACN * EXP(BFACN*EPSIM*EYOUN/(FSY__-FSINF))
  287. C
  288.              STRSH = GAMAS * EYOUN * (BFACT-BFACN) / (1.0D0-BFACN)
  289.              EPSSH = STRSH / EYOUN
  290. C
  291.              BFACN = BFACT
  292.           ENDIF
  293.        ENDIF
  294.        EPSON(2) = (-SIGN_*BFACN*(EPSY_+EPSSH)-EPSON(1)+
  295.      .            (SIGMA(1)+SIGN_*(FSY__+STRSH))/YOUNG)/(BFACN-1.0D0)
  296.        SIGMA(2) = YOUNG*(EPSON(2)-EPSON(1))+SIGMA(1)
  297.        IF (IFLAG .LT. -3) GOTO 2000
  298. C
  299.        EPSIL = ABS((EPSON(IABS(IFLAG)+2)-EPSON(2))/
  300.      .                                  (EPSON(2)-EPSON(1)))
  301.        RFACT = R1FAC-A1FAC*EPSIL/(A2FAC+EPSIL)
  302. C
  303. C
  304. C      ############################################
  305. C
  306. C      ......   STRESS AND TANGENT MODULUS   ......
  307. C
  308. C      ############################################
  309. C
  310. C
  311.   100  IF (IFLAG .LT.  0) GOTO 3000
  312.        BFACN = BFACT
  313.        YOUNG = EYOUN
  314.        IF (FACLD .GT. 5.0D0) THEN
  315.           IF (IFLAG .EQ. 2) THEN
  316.              EPSIS = ABS(EPSON(IFLAG+2)-EPSON(2))
  317.              YOUNG = EYOUN * (A5FAC+(1.0D0-A5FAC)*EXP(-A6FAC*EPSIS**2))
  318.              BFACN = BFACT * EYOUN / YOUNG
  319.           ELSEIF (IFLAG .EQ. 3) THEN
  320.              EPSIM = EPSON(4) - EPSON(5) - 2.0D0 * FSY__/EYOUN
  321. C
  322.              BFACN = AFACT * (5.0D0-FACLD)
  323.              BFACN = BFACN * EXP(BFACN*EPSIM*EYOUN/(FSY__-FSINF))
  324.           ENDIF
  325.        ENDIF
  326.        EPSAS = (STRAI-EPSON(1))/(EPSON(2)-EPSON(1))
  327. C
  328.        STRES = SIGMA(1)+(SIGMA(2)-SIGMA(1))*(BFACN+(1.0D0-BFACN)/
  329.      .         ((1.0D0+EPSAS**RFACT)**(1.0D0/RFACT)))*EPSAS
  330.        TANGE = YOUNG*(BFACN+(1.0D0-BFACN)/
  331.      .               (1.0D0+EPSAS**RFACT)**(1.0D0/RFACT+1.0D0))
  332. C-------------------------------------------------------------
  333. C      MONOTONIC CURVE
  334. C-------------------------------------------------------------
  335.  3000  IF (IFLAG .LT. 0) THEN
  336.           IF (ABS(STRAI) .LT. EPSY_) THEN
  337.              STRES = EYOUN * STRAI
  338.              TANGE = EYOUN
  339.           ELSE IF (ABS(STRAI) .LT. EPSH_) THEN
  340.              STRES = STRAI / ABS(STRAI) * FSY__
  341.              TANGE = 0.0D0
  342.           ELSE IF (ABS(STRAI) .LT. EPSU_) THEN
  343. C-------------------------------------------------------------
  344. C            EQUATION OF DEGREE "EXPOE"
  345. C-------------------------------------------------------------
  346.              EXPOE = 4.0D0
  347. C
  348.              STRES = FSU__ - (FSU__-FSY__) *
  349.      .               (((EPSU_-ABS(STRAI)) / (EPSU_-EPSH_))**EXPOE)
  350.              STRES = STRAI / (ABS(STRAI)) * STRES
  351.              TANGE = EXPOE * (FSU__-FSY__) *
  352.      .               ((EPSU_-ABS(STRAI))**(EXPOE-1D0)) /
  353.      .               ((EPSU_-EPSH_)**EXPOE)
  354.              TANGE = 2.0D0 * ACOEF * (ABS(STRAI)) + BCOEF
  355.           ELSE
  356.              STRES = 0.0D0
  357.              TANGE = 0.0D0
  358.           ENDIF
  359.        ENDIF
  360. C
  361.  2000  EPSON(3) = STRAI
  362.        SIGMA(3) = STRES
  363. C
  364.        RETURN
  365.        END
  366.  
  367.  
  368.  
  369.  
  370.  

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