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C DDSIGGC   SOURCE    CB215821  16/04/21    21:16:18     8920      SUBROUTINE ddsiggc(sigma,d2gc,ag,P2,pi2,i1,i6,fc,fb,lcp) c     This subroutine calculates the second derivative of the plastic potential in compressioncc     Plastic potential: gc = SQRT(3 J2) + ag I1  with  J2 : 2nd invariant of the deviatoric stressc                                                   and   I1 : 1st invariant of the stress       IMPLICIT REAL*8 (A-B,D-H,O-Z)      implicit integer (I-K,M,N)      implicit logical (L)      implicit character*10 (C)       dimension vloc(6),vloc1(1),pi2(6),vloc2(1,6)      dimension d2gc(6,6),p2(i6,i6),sigma(6),vloc6(6,6)       r1 = 1.      r2 = 2.       do jloc=1,6        do iloc=1,6          d2gc(iloc,jloc) = 0.d0        enddo      enddo      call mulAB(P2,sigma,vloc,6,6,6,1)      call mulATB(sigma,vloc,vloc1,6,1,6,1)      rloc = 0.5d0 * vloc1(1)      if (rloc.le.0.d0) then        psi2 = 0.d0      else        psi2 = SQRT(rloc)      endif      call mulATB(sigma,P2,vloc2,6,1,6,6)      call mulAB(vloc,vloc2,vloc6,6,1,1,6)      test = ag*(sigma(1)+sigma(2)+sigma(3))      psi2lim=max(1.E-7*test,1.d-3)      if (ABS(psi2).le.psi2lim) then        continuec       d2gc = 0      else        do jloc=1,6          do iloc=1,6            d2gc(iloc,jloc)=(P2(iloc,jloc)/(2.0d0*psi2))     .                     - (vloc6(iloc,jloc)/(4.0d0*psi2*psi2*psi2))          enddo        enddo      endif       RETURN      END

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