Merge branch 'tensor-conversion-rename' into development
This commit is contained in:
Martin Diehl
commit
c231c808da
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@ -286,12 +286,11 @@ subroutine CPFEM_general(mode, parallelExecution, ffn, ffn1, temperature_inp, dt
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math_identity2nd, &
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math_mul33x33, &
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math_det33, &
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math_transpose33, &
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math_I3, &
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math_Mandel3333to66, &
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math_Mandel66to3333, &
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math_Mandel33to6, &
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math_Mandel6to33
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math_delta, &
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math_sym3333to66, &
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math_66toSym3333, &
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math_sym33to6, &
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math_6toSym33
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use mesh, only: &
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mesh_FEasCP, &
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mesh_NcpElems, &
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@ -353,8 +352,8 @@ subroutine CPFEM_general(mode, parallelExecution, ffn, ffn1, temperature_inp, dt
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integer(pInt), intent(in) :: mode !< computation mode 1: regular computation plus aging of results
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real(pReal), intent(in) :: temperature_inp !< temperature
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logical, intent(in) :: parallelExecution !< flag indicating parallel computation of requested IPs
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real(pReal), dimension(6), intent(out) :: cauchyStress !< stress vector in Mandel notation
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real(pReal), dimension(6,6), intent(out) :: jacobian !< jacobian in Mandel notation (Consistent tangent dcs/dE)
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real(pReal), dimension(6), intent(out) :: cauchyStress !< stress as 6 vector
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real(pReal), dimension(6,6), intent(out) :: jacobian !< jacobian as 66 tensor (Consistent tangent dcs/dE)
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real(pReal) J_inverse, & ! inverse of Jacobian
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rnd
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@ -534,8 +533,8 @@ subroutine CPFEM_general(mode, parallelExecution, ffn, ffn1, temperature_inp, dt
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if (iand(debug_level(debug_CPFEM), debug_levelBasic) /= 0_pInt) then
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write(6,'(a,1x,i8,1x,i2)') '<< CPFEM >> OUTDATED at elFE ip',elFE,ip
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write(6,'(a,/,3(12x,3(f10.6,1x),/))') '<< CPFEM >> FFN1 old:',&
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math_transpose33(materialpoint_F(1:3,1:3,ip,elCP))
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write(6,'(a,/,3(12x,3(f10.6,1x),/))') '<< CPFEM >> FFN1 now:',math_transpose33(ffn1)
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transpose(materialpoint_F(1:3,1:3,ip,elCP))
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write(6,'(a,/,3(12x,3(f10.6,1x),/))') '<< CPFEM >> FFN1 now:',transpose(ffn1)
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endif
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outdatedFFN1 = .true.
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endif
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@ -593,26 +592,25 @@ subroutine CPFEM_general(mode, parallelExecution, ffn, ffn1, temperature_inp, dt
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endif
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! translate from P to CS
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Kirchhoff = math_mul33x33(materialpoint_P(1:3,1:3,ip,elCP), math_transpose33(materialpoint_F(1:3,1:3,ip,elCP)))
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Kirchhoff = math_mul33x33(materialpoint_P(1:3,1:3,ip,elCP), transpose(materialpoint_F(1:3,1:3,ip,elCP)))
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J_inverse = 1.0_pReal / math_det33(materialpoint_F(1:3,1:3,ip,elCP))
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CPFEM_cs(1:6,ip,elCP) = math_Mandel33to6(J_inverse * Kirchhoff)
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CPFEM_cs(1:6,ip,elCP) = math_sym33to6(J_inverse * Kirchhoff,weighted=.false.)
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! translate from dP/dF to dCS/dE
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H = 0.0_pReal
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do i=1,3; do j=1,3; do k=1,3; do l=1,3; do m=1,3; do n=1,3
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H(i,j,k,l) = H(i,j,k,l) + &
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materialpoint_F(j,m,ip,elCP) * &
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materialpoint_F(l,n,ip,elCP) * &
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materialpoint_dPdF(i,m,k,n,ip,elCP) - &
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math_I3(j,l) * materialpoint_F(i,m,ip,elCP) * materialpoint_P(k,m,ip,elCP) + &
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0.5_pReal * (math_I3(i,k) * Kirchhoff(j,l) + math_I3(j,l) * Kirchhoff(i,k) + &
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math_I3(i,l) * Kirchhoff(j,k) + math_I3(j,k) * Kirchhoff(i,l))
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H(i,j,k,l) = H(i,j,k,l) &
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+ materialpoint_F(j,m,ip,elCP) * materialpoint_F(l,n,ip,elCP) &
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* materialpoint_dPdF(i,m,k,n,ip,elCP) &
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- math_delta(j,l) * materialpoint_F(i,m,ip,elCP) * materialpoint_P(k,m,ip,elCP) &
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+ 0.5_pReal * ( Kirchhoff(j,l)*math_delta(i,k) + Kirchhoff(i,k)*math_delta(j,l) &
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+ Kirchhoff(j,k)*math_delta(i,l) + Kirchhoff(i,l)*math_delta(j,k))
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enddo; enddo; enddo; enddo; enddo; enddo
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forall(i=1:3, j=1:3,k=1:3,l=1:3) &
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H_sym(i,j,k,l) = 0.25_pReal * (H(i,j,k,l) + H(j,i,k,l) + H(i,j,l,k) + H(j,i,l,k))
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CPFEM_dcsde(1:6,1:6,ip,elCP) = math_Mandel3333to66(J_inverse * H_sym)
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CPFEM_dcsde(1:6,1:6,ip,elCP) = math_sym3333to66(J_inverse * H_sym,weighted=.false.)
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endif terminalIllness
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endif validCalculation
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@ -639,7 +637,7 @@ subroutine CPFEM_general(mode, parallelExecution, ffn, ffn1, temperature_inp, dt
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!*** remember extreme values of stress ...
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cauchyStress33 = math_Mandel6to33(CPFEM_cs(1:6,ip,elCP))
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cauchyStress33 = math_6toSym33(CPFEM_cs(1:6,ip,elCP),weighted=.false.)
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if (maxval(cauchyStress33) > debug_stressMax) then
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debug_stressMaxLocation = [elCP, ip]
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debug_stressMax = maxval(cauchyStress33)
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@ -649,7 +647,7 @@ subroutine CPFEM_general(mode, parallelExecution, ffn, ffn1, temperature_inp, dt
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debug_stressMin = minval(cauchyStress33)
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endif
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!*** ... and Jacobian
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jacobian3333 = math_Mandel66to3333(CPFEM_dcsdE(1:6,1:6,ip,elCP))
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jacobian3333 = math_66toSym3333(CPFEM_dcsdE(1:6,1:6,ip,elCP),weighted=.false.)
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if (maxval(jacobian3333) > debug_jacobianMax) then
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debug_jacobianMaxLocation = [elCP, ip]
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debug_jacobianMax = maxval(jacobian3333)
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@ -102,8 +102,6 @@ subroutine UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,&
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calcMode, &
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terminallyIll, &
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symmetricSolver
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use math, only: &
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invnrmMandel
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use debug, only: &
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debug_info, &
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debug_reset, &
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@ -305,9 +303,9 @@ subroutine UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,&
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! ABAQUS implicit: 11, 22, 33, 12, 13, 23
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! ABAQUS implicit: 11, 22, 33, 12
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forall(i=1:ntens) ddsdde(1:ntens,i) = invnrmMandel(i)*ddsdde_h(1:ntens,i)*invnrmMandel(1:ntens)
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stress(1:ntens) = stress_h(1:ntens)*invnrmMandel(1:ntens)
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if(symmetricSolver) ddsdde(1:ntens,1:ntens) = 0.5_pReal*(ddsdde(1:ntens,1:ntens) + transpose(ddsdde(1:ntens,1:ntens)))
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ddsdde = ddsdde_h(1:ntens,1:ntens)
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stress = stress_h(1:ntens)
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if(symmetricSolver) ddsdde = 0.5_pReal*(ddsdde + transpose(ddsdde))
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if(ntens == 6) then
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stress_h = stress
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stress(5) = stress_h(6)
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@ -127,9 +127,6 @@ subroutine hypela2(d,g,e,de,s,t,dt,ngens,m,nn,kcus,matus,ndi,nshear,disp, &
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calcMode, &
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terminallyIll, &
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symmetricSolver
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use math, only: &
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math_transpose33,&
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invnrmMandel
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use debug, only: &
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debug_level, &
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debug_LEVELBASIC, &
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@ -235,9 +232,9 @@ subroutine hypela2(d,g,e,de,s,t,dt,ngens,m,nn,kcus,matus,ndi,nshear,disp, &
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write(6,'(a,i12)') ' Nodes: ', nnode
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write(6,'(a,i1)') ' Deformation gradient: ', itel
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write(6,'(/,a,/,3(3(f12.7,1x)/))',advance='no') ' Deformation gradient at t=n:', &
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math_transpose33(ffn)
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transpose(ffn)
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write(6,'(/,a,/,3(3(f12.7,1x)/))',advance='no') ' Deformation gradient at t=n+1:', &
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math_transpose33(ffn1)
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transpose(ffn1)
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endif
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!$ defaultNumThreadsInt = omp_get_num_threads() ! remember number of threads set by Marc
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@ -357,8 +354,8 @@ subroutine hypela2(d,g,e,de,s,t,dt,ngens,m,nn,kcus,matus,ndi,nshear,disp, &
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! Marc: 11, 22, 33, 12, 23, 13
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! Marc: 11, 22, 33, 12
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forall(i=1:ngens) d(1:ngens,i) = invnrmMandel(i)*ddsdde(1:ngens,i)*invnrmMandel(1:ngens)
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s(1:ndi+nshear) = stress(1:ndi+nshear)*invnrmMandel(1:ndi+nshear)
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d = ddsdde(1:ngens,1:ngens)
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s = stress(1:ndi+nshear)
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g = 0.0_pReal
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if(symmetricSolver) d = 0.5_pReal*(d+transpose(d))
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405
src/math.f90
405
src/math.f90
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@ -24,33 +24,25 @@ module math
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0.0_pReal,0.0_pReal,1.0_pReal &
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],[3,3]) !< 3x3 Identity
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! ToDo MD: Our naming scheme is a little bit odd: We use essentially the re-ordering according to Nye
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! (convenient because Abaqus and Marc want to have 12 on position 4)
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! but weight the shear components according to Mandel (convenient for matrix multiplications)
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! I suggest to keep Voigt3333to66 (required for reading in elasticity matrices) but rename
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! mapMandel to mapNye, math_MandelXtoY to math_XtoY and math_PlainXtoY to math_XtoY.
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! It is then clear that math_33to9 just reorders and math_33to6 does the "DAMASK conversion"
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! without leaving the impression that it follows any established convention
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real(pReal), dimension(6), parameter, private :: &
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nrmMandel = [&
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1.0_pReal, 1.0_pReal, 1.0_pReal, &
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sqrt(2.0_pReal), sqrt(2.0_pReal), sqrt(2.0_pReal) ] !< weighting for Mandel notation (forward)
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real(pReal), dimension(6), parameter , private :: &
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invnrmMandel = [&
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1.0_pReal, 1.0_pReal, 1.0_pReal, &
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1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal) ] !< weighting for Mandel notation (backward)
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integer(pInt), dimension (2,6), parameter, private :: &
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mapMandel = reshape([&
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mapNye = reshape([&
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1_pInt,1_pInt, &
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2_pInt,2_pInt, &
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3_pInt,3_pInt, &
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1_pInt,2_pInt, &
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2_pInt,3_pInt, &
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1_pInt,3_pInt &
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],[2,6]) !< arrangement in Mandel notation. Differs from https://en.wikipedia.org/wiki/Voigt_notation#Mandel_notation
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real(pReal), dimension(6), parameter, private :: &
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nrmMandel = [&
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1.0_pReal, 1.0_pReal, 1.0_pReal, &
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sqrt(2.0_pReal), sqrt(2.0_pReal), sqrt(2.0_pReal) ] !< weighting for Mandel notation (forward)
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real(pReal), dimension(6), parameter , public :: &
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invnrmMandel = [&
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1.0_pReal, 1.0_pReal, 1.0_pReal, &
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1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal), 1.0_pReal/sqrt(2.0_pReal) ] !< weighting for Mandel notation (backward)
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],[2,6]) !< arrangement in Nye notation.
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integer(pInt), dimension (2,6), parameter, private :: &
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mapVoigt = reshape([&
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@ -62,10 +54,6 @@ module math
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1_pInt,2_pInt &
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],[2,6]) !< arrangement in Voigt notation
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real(pReal), dimension(6), parameter, private :: &
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nrmVoigt = 1.0_pReal, & !< weighting for Voigt notation (forward)
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invnrmVoigt = 1.0_pReal !< weighting for Voigt notation (backward)
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integer(pInt), dimension (2,9), parameter, private :: &
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mapPlain = reshape([&
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1_pInt,1_pInt, &
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@ -79,6 +67,56 @@ module math
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3_pInt,3_pInt &
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],[2,9]) !< arrangement in Plain notation
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!--------------------------------------------------------------------------------------------------
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! Provide deprecated names for compatibility
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! ToDo MD: Our naming scheme was a little bit odd: We use essentially the re-ordering according to Nye
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! (convenient because Abaqus and Marc want to have 12 on position 4)
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! but weight the shear components according to Mandel (convenient for matrix multiplications)
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interface math_Plain33to9
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module procedure math_33to9
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end interface math_Plain33to9
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interface math_Plain9to33
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module procedure math_9to33
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end interface math_Plain9to33
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interface math_Mandel33to6
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module procedure math_sym33to6
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end interface math_Mandel33to6
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interface math_Mandel6to33
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module procedure math_6toSym33
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end interface math_Mandel6to33
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interface math_Plain3333to99
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module procedure math_3333to99
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end interface math_Plain3333to99
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interface math_Plain99to3333
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module procedure math_99to3333
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end interface math_Plain99to3333
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interface math_Mandel3333to66
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module procedure math_sym3333to66
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end interface math_Mandel3333to66
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interface math_Mandel66to3333
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module procedure math_66toSym3333
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end interface math_Mandel66to3333
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public :: &
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math_Plain33to9, &
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math_Plain9to33, &
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math_Mandel33to6, &
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math_Mandel6to33, &
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math_Plain3333to99, &
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math_Plain99to3333, &
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math_Mandel3333to66, &
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math_Mandel66to3333
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!---------------------------------------------------------------------------------------------------
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public :: &
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math_init, &
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math_qsort, &
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@ -116,16 +154,14 @@ module math
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math_equivStress33, &
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math_trace33, &
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math_det33, &
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math_Plain33to9, &
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math_Plain9to33, &
|
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math_Mandel33to6, &
|
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math_Mandel6to33, &
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math_Plain3333to99, &
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math_Plain99to3333, &
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math_Mandel66toPlain66, &
|
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math_Plain66toMandel66, &
|
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math_Mandel3333to66, &
|
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math_Mandel66to3333, &
|
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math_33to9, &
|
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math_9to33, &
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math_sym33to6, &
|
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math_6toSym33, &
|
||||
math_3333to99, &
|
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math_99to3333, &
|
||||
math_sym3333to66, &
|
||||
math_66toSym3333, &
|
||||
math_Voigt66to3333, &
|
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math_qRand, &
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math_qMul, &
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||||
|
|
@ -423,7 +459,7 @@ pure function math_identity2nd(dimen)
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real(pReal), dimension(dimen,dimen) :: math_identity2nd
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math_identity2nd = 0.0_pReal
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forall (i=1_pInt:dimen) math_identity2nd(i,i) = 1.0_pReal
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forall(i=1_pInt:dimen) math_identity2nd(i,i) = 1.0_pReal
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end function math_identity2nd
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||||
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|
@ -437,9 +473,11 @@ pure function math_identity4th(dimen)
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integer(pInt), intent(in) :: dimen !< tensor dimension
|
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integer(pInt) :: i,j,k,l
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real(pReal), dimension(dimen,dimen,dimen,dimen) :: math_identity4th
|
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real(pReal), dimension(dimen,dimen) :: identity2nd
|
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forall (i=1_pInt:dimen,j=1_pInt:dimen,k=1_pInt:dimen,l=1_pInt:dimen) math_identity4th(i,j,k,l) = &
|
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0.5_pReal*(math_I3(i,k)*math_I3(j,l)+math_I3(i,l)*math_I3(j,k))
|
||||
identity2nd = math_identity2nd(dimen)
|
||||
forall(i=1_pInt:dimen,j=1_pInt:dimen,k=1_pInt:dimen,l=1_pInt:dimen) &
|
||||
math_identity4th(i,j,k,l) = 0.5_pReal*(identity2nd(i,k)*identity2nd(j,l)+identity2nd(i,l)*identity2nd(j,k))
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||||
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||||
end function math_identity4th
|
||||
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||||
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|
@ -508,7 +546,7 @@ pure function math_tensorproduct(A,B)
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|||
real(pReal), dimension(size(A,1),size(B,1)) :: math_tensorproduct
|
||||
integer(pInt) :: i,j
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||||
|
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forall (i=1_pInt:size(A,1),j=1_pInt:size(B,1)) math_tensorproduct(i,j) = A(i)*B(j)
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forall(i=1_pInt:size(A,1),j=1_pInt:size(B,1)) math_tensorproduct(i,j) = A(i)*B(j)
|
||||
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||||
end function math_tensorproduct
|
||||
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||||
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|
@ -523,7 +561,7 @@ pure function math_tensorproduct33(A,B)
|
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real(pReal), dimension(3), intent(in) :: A,B
|
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integer(pInt) :: i,j
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||||
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||||
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt) math_tensorproduct33(i,j) = A(i)*B(j)
|
||||
forall(i=1_pInt:3_pInt,j=1_pInt:3_pInt) math_tensorproduct33(i,j) = A(i)*B(j)
|
||||
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||||
end function math_tensorproduct33
|
||||
|
||||
|
|
@ -564,7 +602,7 @@ real(pReal) pure function math_mul33xx33(A,B)
|
|||
integer(pInt) :: i,j
|
||||
real(pReal), dimension(3,3) :: C
|
||||
|
||||
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt) C(i,j) = A(i,j) * B(i,j)
|
||||
forall(i=1_pInt:3_pInt,j=1_pInt:3_pInt) C(i,j) = A(i,j) * B(i,j)
|
||||
math_mul33xx33 = sum(C)
|
||||
|
||||
end function math_mul33xx33
|
||||
|
|
@ -581,8 +619,7 @@ pure function math_mul3333xx33(A,B)
|
|||
real(pReal), dimension(3,3), intent(in) :: B
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall(i = 1_pInt:3_pInt,j = 1_pInt:3_pInt) &
|
||||
math_mul3333xx33(i,j) = sum(A(i,j,1:3,1:3)*B(1:3,1:3))
|
||||
forall(i = 1_pInt:3_pInt,j = 1_pInt:3_pInt) math_mul3333xx33(i,j) = sum(A(i,j,1:3,1:3)*B(1:3,1:3))
|
||||
|
||||
end function math_mul3333xx33
|
||||
|
||||
|
|
@ -614,8 +651,7 @@ pure function math_mul33x33(A,B)
|
|||
real(pReal), dimension(3,3), intent(in) :: A,B
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt) &
|
||||
math_mul33x33(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j)
|
||||
forall(i=1_pInt:3_pInt,j=1_pInt:3_pInt) math_mul33x33(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j)
|
||||
|
||||
end function math_mul33x33
|
||||
|
||||
|
|
@ -630,9 +666,9 @@ pure function math_mul66x66(A,B)
|
|||
real(pReal), dimension(6,6), intent(in) :: A,B
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:6_pInt,j=1_pInt:6_pInt) math_mul66x66(i,j) = &
|
||||
A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) + &
|
||||
A(i,4)*B(4,j) + A(i,5)*B(5,j) + A(i,6)*B(6,j)
|
||||
forall(i=1_pInt:6_pInt,j=1_pInt:6_pInt) &
|
||||
math_mul66x66(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) &
|
||||
+ A(i,4)*B(4,j) + A(i,5)*B(5,j) + A(i,6)*B(6,j)
|
||||
|
||||
end function math_mul66x66
|
||||
|
||||
|
|
@ -647,10 +683,10 @@ pure function math_mul99x99(A,B)
|
|||
real(pReal), dimension(9,9), intent(in) :: A,B
|
||||
integer(pInt) i,j
|
||||
|
||||
forall (i=1_pInt:9_pInt,j=1_pInt:9_pInt) math_mul99x99(i,j) = &
|
||||
A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) + &
|
||||
A(i,4)*B(4,j) + A(i,5)*B(5,j) + A(i,6)*B(6,j) + &
|
||||
A(i,7)*B(7,j) + A(i,8)*B(8,j) + A(i,9)*B(9,j)
|
||||
forall(i=1_pInt:9_pInt,j=1_pInt:9_pInt) &
|
||||
math_mul99x99(i,j) = A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) &
|
||||
+ A(i,4)*B(4,j) + A(i,5)*B(5,j) + A(i,6)*B(6,j) &
|
||||
+ A(i,7)*B(7,j) + A(i,8)*B(8,j) + A(i,9)*B(9,j)
|
||||
|
||||
end function math_mul99x99
|
||||
|
||||
|
|
@ -698,9 +734,8 @@ pure function math_mul66x6(A,B)
|
|||
real(pReal), dimension(6), intent(in) :: B
|
||||
integer(pInt) :: i
|
||||
|
||||
forall (i=1_pInt:6_pInt) math_mul66x6(i) = &
|
||||
A(i,1)*B(1) + A(i,2)*B(2) + A(i,3)*B(3) + &
|
||||
A(i,4)*B(4) + A(i,5)*B(5) + A(i,6)*B(6)
|
||||
forall (i=1_pInt:6_pInt) math_mul66x6(i) = A(i,1)*B(1) + A(i,2)*B(2) + A(i,3)*B(3) &
|
||||
+ A(i,4)*B(4) + A(i,5)*B(5) + A(i,6)*B(6)
|
||||
|
||||
end function math_mul66x6
|
||||
|
||||
|
|
@ -747,8 +782,8 @@ end function math_transpose33
|
|||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief Cramer inversion of 33 matrix (function)
|
||||
! direct Cramer inversion of matrix A.
|
||||
! returns all zeroes if not possible, i.e. if det close to zero
|
||||
!> @details Direct Cramer inversion of matrix A. Returns all zeroes if not possible, i.e.
|
||||
! if determinant is close to zero
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_inv33(A)
|
||||
use prec, only: &
|
||||
|
|
@ -784,9 +819,9 @@ end function math_inv33
|
|||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief Cramer inversion of 33 matrix (subroutine)
|
||||
! direct Cramer inversion of matrix A.
|
||||
! also returns determinant
|
||||
! returns error if not possible, i.e. if det close to zero
|
||||
!> @details Direct Cramer inversion of matrix A. Also returns determinant
|
||||
! Returns an error if not possible, i.e. if determinant is close to zero
|
||||
! ToDo: Output arguments should be first
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure subroutine math_invert33(A, InvA, DetA, error)
|
||||
use prec, only: &
|
||||
|
|
@ -843,20 +878,38 @@ function math_invSym3333(A)
|
|||
dgetrf, &
|
||||
dgetri
|
||||
|
||||
temp66_real = math_Mandel3333to66(A)
|
||||
temp66_real = math_sym3333to66(A)
|
||||
call dgetrf(6,6,temp66_real,6,ipiv6,ierr)
|
||||
call dgetri(6,temp66_real,6,ipiv6,work6,6,ierr)
|
||||
if (ierr == 0_pInt) then
|
||||
math_invSym3333 = math_Mandel66to3333(temp66_real)
|
||||
math_invSym3333 = math_66toSym3333(temp66_real)
|
||||
else
|
||||
call IO_error(400_pInt, ext_msg = 'math_invSym3333')
|
||||
endif
|
||||
|
||||
end function math_invSym3333
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief invert quadratic matrix of arbitrary dimension
|
||||
! ToDo: replaces math_invert
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
subroutine math_invert2(InvA, error, A)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(:,:), intent(in) :: A
|
||||
|
||||
real(pReal), dimension(size(A,1),size(A,1)), intent(out) :: invA
|
||||
logical, intent(out) :: error
|
||||
|
||||
call math_invert(size(A,1), A, InvA, error)
|
||||
|
||||
end subroutine math_invert2
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief invert matrix of arbitrary dimension
|
||||
! ToDo: Wrong order of arguments and superfluous myDim argument.
|
||||
! Use math_invert2 instead
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
subroutine math_invert(myDim,A, InvA, error)
|
||||
|
||||
|
|
@ -961,15 +1014,14 @@ pure function math_equivStrain33(m)
|
|||
real(pReal), dimension(3,3), intent(in) :: m
|
||||
real(pReal), dimension(3) :: e,s
|
||||
real(pReal) :: math_equivStrain33
|
||||
real(pReal), parameter :: TWOTHIRD = 2.0_pReal/3.0_pReal
|
||||
|
||||
e = [2.0_pReal*m(1,1)-m(2,2)-m(3,3), &
|
||||
2.0_pReal*m(2,2)-m(3,3)-m(1,1), &
|
||||
2.0_pReal*m(3,3)-m(1,1)-m(2,2)]/3.0_pReal
|
||||
s = [m(1,2),m(2,3),m(1,3)]*2.0_pReal
|
||||
|
||||
math_equivStrain33 = TWOTHIRD*(1.50_pReal*(sum(e**2.0_pReal)) + &
|
||||
0.75_pReal*(sum(s**2.0_pReal)))**(0.5_pReal)
|
||||
math_equivStrain33 = 2.0_pReal/3.0_pReal &
|
||||
* (1.50_pReal*(sum(e**2.0_pReal))+ 0.75_pReal*(sum(s**2.0_pReal)))**(0.5_pReal)
|
||||
|
||||
end function math_equivStrain33
|
||||
|
||||
|
|
@ -1041,172 +1093,188 @@ end function math_detSym33
|
|||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert 33 matrix into vector 9
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Plain33to9(m33)
|
||||
pure function math_33to9(m33)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(9) :: math_Plain33to9
|
||||
real(pReal), dimension(9) :: math_33to9
|
||||
real(pReal), dimension(3,3), intent(in) :: m33
|
||||
|
||||
integer(pInt) :: i
|
||||
|
||||
forall (i=1_pInt:9_pInt) math_Plain33to9(i) = m33(mapPlain(1,i),mapPlain(2,i))
|
||||
forall(i=1_pInt:9_pInt) math_33to9(i) = m33(mapPlain(1,i),mapPlain(2,i))
|
||||
|
||||
end function math_Plain33to9
|
||||
end function math_33to9
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert Plain 9 back to 33 matrix
|
||||
!> @brief convert 9 vector into 33 matrix
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Plain9to33(v9)
|
||||
pure function math_9to33(v9)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3,3) :: math_Plain9to33
|
||||
real(pReal), dimension(3,3) :: math_9to33
|
||||
real(pReal), dimension(9), intent(in) :: v9
|
||||
|
||||
integer(pInt) :: i
|
||||
|
||||
forall (i=1_pInt:9_pInt) math_Plain9to33(mapPlain(1,i),mapPlain(2,i)) = v9(i)
|
||||
forall(i=1_pInt:9_pInt) math_9to33(mapPlain(1,i),mapPlain(2,i)) = v9(i)
|
||||
|
||||
end function math_Plain9to33
|
||||
end function math_9to33
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert symmetric 33 matrix into Mandel vector 6
|
||||
!> @brief convert symmetric 33 matrix into 6 vector
|
||||
!> @details Weighted conversion (default) rearranges according to Nye and weights shear
|
||||
! components according to Mandel. Advisable for matrix operations.
|
||||
! Unweighted conversion only changes order according to Nye
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Mandel33to6(m33)
|
||||
pure function math_sym33to6(m33,weighted)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(6) :: math_Mandel33to6
|
||||
real(pReal), dimension(6) :: math_sym33to6
|
||||
real(pReal), dimension(3,3), intent(in) :: m33
|
||||
logical, optional, intent(in) :: weighted
|
||||
|
||||
real(pReal), dimension(6) :: w
|
||||
integer(pInt) :: i
|
||||
|
||||
forall (i=1_pInt:6_pInt) math_Mandel33to6(i) = nrmMandel(i)*m33(mapMandel(1,i),mapMandel(2,i))
|
||||
if(present(weighted)) then
|
||||
w = merge(nrmMandel,1.0_pReal,weighted)
|
||||
else
|
||||
w = nrmMandel
|
||||
endif
|
||||
|
||||
end function math_Mandel33to6
|
||||
forall(i=1_pInt:6_pInt) math_sym33to6(i) = w(i)*m33(mapNye(1,i),mapNye(2,i))
|
||||
|
||||
end function math_sym33to6
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert Mandel 6 back to symmetric 33 matrix
|
||||
!> @brief convert 6 vector into symmetric 33 matrix
|
||||
!> @details Weighted conversion (default) rearranges according to Nye and weights shear
|
||||
! components according to Mandel. Advisable for matrix operations.
|
||||
! Unweighted conversion only changes order according to Nye
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Mandel6to33(v6)
|
||||
pure function math_6toSym33(v6,weighted)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3,3) :: math_6toSym33
|
||||
real(pReal), dimension(6), intent(in) :: v6
|
||||
real(pReal), dimension(3,3) :: math_Mandel6to33
|
||||
logical, optional, intent(in) :: weighted
|
||||
|
||||
real(pReal), dimension(6) :: w
|
||||
integer(pInt) :: i
|
||||
|
||||
forall (i=1_pInt:6_pInt)
|
||||
math_Mandel6to33(mapMandel(1,i),mapMandel(2,i)) = invnrmMandel(i)*v6(i)
|
||||
math_Mandel6to33(mapMandel(2,i),mapMandel(1,i)) = invnrmMandel(i)*v6(i)
|
||||
end forall
|
||||
if(present(weighted)) then
|
||||
w = merge(invnrmMandel,1.0_pReal,weighted)
|
||||
else
|
||||
w = invnrmMandel
|
||||
endif
|
||||
|
||||
end function math_Mandel6to33
|
||||
do i=1_pInt,6_pInt
|
||||
math_6toSym33(mapNye(1,i),mapNye(2,i)) = w(i)*v6(i)
|
||||
math_6toSym33(mapNye(2,i),mapNye(1,i)) = w(i)*v6(i)
|
||||
enddo
|
||||
|
||||
end function math_6toSym33
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert 3333 tensor into plain matrix 99
|
||||
!> @brief convert 3333 matrix into 99 matrix
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Plain3333to99(m3333)
|
||||
pure function math_3333to99(m3333)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(9,9) :: math_3333to99
|
||||
real(pReal), dimension(3,3,3,3), intent(in) :: m3333
|
||||
real(pReal), dimension(9,9) :: math_Plain3333to99
|
||||
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:9_pInt,j=1_pInt:9_pInt) math_Plain3333to99(i,j) = &
|
||||
m3333(mapPlain(1,i),mapPlain(2,i),mapPlain(1,j),mapPlain(2,j))
|
||||
forall(i=1_pInt:9_pInt,j=1_pInt:9_pInt) &
|
||||
math_3333to99(i,j) = m3333(mapPlain(1,i),mapPlain(2,i),mapPlain(1,j),mapPlain(2,j))
|
||||
|
||||
end function math_3333to99
|
||||
|
||||
end function math_Plain3333to99
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief plain matrix 99 into 3333 tensor
|
||||
!> @brief convert 99 matrix into 3333 matrix
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Plain99to3333(m99)
|
||||
pure function math_99to3333(m99)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3,3,3,3) :: math_99to3333
|
||||
real(pReal), dimension(9,9), intent(in) :: m99
|
||||
real(pReal), dimension(3,3,3,3) :: math_Plain99to3333
|
||||
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:9_pInt,j=1_pInt:9_pInt) math_Plain99to3333(mapPlain(1,i),mapPlain(2,i),&
|
||||
mapPlain(1,j),mapPlain(2,j)) = m99(i,j)
|
||||
forall(i=1_pInt:9_pInt,j=1_pInt:9_pInt) &
|
||||
math_99to3333(mapPlain(1,i),mapPlain(2,i),mapPlain(1,j),mapPlain(2,j)) = m99(i,j)
|
||||
|
||||
end function math_Plain99to3333
|
||||
end function math_99to3333
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert Mandel matrix 66 into Plain matrix 66
|
||||
!> @brief convert symmetric 3333 matrix into 66 matrix
|
||||
!> @details Weighted conversion (default) rearranges according to Nye and weights shear
|
||||
! components according to Mandel. Advisable for matrix operations.
|
||||
! Unweighted conversion only changes order according to Nye
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Mandel66toPlain66(m66)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(6,6), intent(in) :: m66
|
||||
real(pReal), dimension(6,6) :: math_Mandel66toPlain66
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:6_pInt,j=1_pInt:6_pInt) &
|
||||
math_Mandel66toPlain66(i,j) = invnrmMandel(i) * invnrmMandel(j) * m66(i,j)
|
||||
|
||||
end function math_Mandel66toPlain66
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert Plain matrix 66 into Mandel matrix 66
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Plain66toMandel66(m66)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(6,6), intent(in) :: m66
|
||||
real(pReal), dimension(6,6) :: math_Plain66toMandel66
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:6_pInt,j=1_pInt:6_pInt) &
|
||||
math_Plain66toMandel66(i,j) = nrmMandel(i) * nrmMandel(j) * m66(i,j)
|
||||
|
||||
end function math_Plain66toMandel66
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert symmetric 3333 tensor into Mandel matrix 66
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Mandel3333to66(m3333)
|
||||
pure function math_sym3333to66(m3333,weighted)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(6,6) :: math_sym3333to66
|
||||
real(pReal), dimension(3,3,3,3), intent(in) :: m3333
|
||||
real(pReal), dimension(6,6) :: math_Mandel3333to66
|
||||
logical, optional, intent(in) :: weighted
|
||||
|
||||
real(pReal), dimension(6) :: w
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:6_pInt,j=1_pInt:6_pInt) math_Mandel3333to66(i,j) = &
|
||||
nrmMandel(i)*nrmMandel(j)*m3333(mapMandel(1,i),mapMandel(2,i),mapMandel(1,j),mapMandel(2,j))
|
||||
if(present(weighted)) then
|
||||
w = merge(nrmMandel,1.0_pReal,weighted)
|
||||
else
|
||||
w = nrmMandel
|
||||
endif
|
||||
|
||||
end function math_Mandel3333to66
|
||||
forall(i=1_pInt:6_pInt,j=1_pInt:6_pInt) &
|
||||
math_sym3333to66(i,j) = w(i)*w(j)*m3333(mapNye(1,i),mapNye(2,i),mapNye(1,j),mapNye(2,j))
|
||||
|
||||
end function math_sym3333to66
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert Mandel matrix 66 back to symmetric 3333 tensor
|
||||
!> @brief convert 66 matrix into symmetric 3333 matrix
|
||||
!> @details Weighted conversion (default) rearranges according to Nye and weights shear
|
||||
! components according to Mandel. Advisable for matrix operations.
|
||||
! Unweighted conversion only changes order according to Nye
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Mandel66to3333(m66)
|
||||
pure function math_66toSym3333(m66,weighted)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3,3,3,3) :: math_Mandel66to3333
|
||||
real(pReal), dimension(3,3,3,3) :: math_66toSym3333
|
||||
real(pReal), dimension(6,6), intent(in) :: m66
|
||||
logical, optional, intent(in) :: weighted
|
||||
|
||||
real(pReal), dimension(6) :: w
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:6_pInt,j=1_pInt:6_pInt)
|
||||
math_Mandel66to3333(mapMandel(1,i),mapMandel(2,i),mapMandel(1,j),mapMandel(2,j)) = &
|
||||
invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
|
||||
math_Mandel66to3333(mapMandel(2,i),mapMandel(1,i),mapMandel(1,j),mapMandel(2,j)) = &
|
||||
invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
|
||||
math_Mandel66to3333(mapMandel(1,i),mapMandel(2,i),mapMandel(2,j),mapMandel(1,j)) = &
|
||||
invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
|
||||
math_Mandel66to3333(mapMandel(2,i),mapMandel(1,i),mapMandel(2,j),mapMandel(1,j)) = &
|
||||
invnrmMandel(i)*invnrmMandel(j)*m66(i,j)
|
||||
end forall
|
||||
if(present(weighted)) then
|
||||
w = merge(invnrmMandel,1.0_pReal,weighted)
|
||||
else
|
||||
w = invnrmMandel
|
||||
endif
|
||||
|
||||
end function math_Mandel66to3333
|
||||
do i=1_pInt,6_pInt; do j=1_pInt, 6_pInt
|
||||
math_66toSym3333(mapNye(1,i),mapNye(2,i),mapNye(1,j),mapNye(2,j)) = w(i)*w(j)*m66(i,j)
|
||||
math_66toSym3333(mapNye(2,i),mapNye(1,i),mapNye(1,j),mapNye(2,j)) = w(i)*w(j)*m66(i,j)
|
||||
math_66toSym3333(mapNye(1,i),mapNye(2,i),mapNye(2,j),mapNye(1,j)) = w(i)*w(j)*m66(i,j)
|
||||
math_66toSym3333(mapNye(2,i),mapNye(1,i),mapNye(2,j),mapNye(1,j)) = w(i)*w(j)*m66(i,j)
|
||||
enddo; enddo
|
||||
|
||||
end function math_66toSym3333
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief convert Voigt matrix 66 back to symmetric 3333 tensor
|
||||
!> @brief convert 66 Voigt matrix into symmetric 3333 matrix
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
pure function math_Voigt66to3333(m66)
|
||||
|
||||
|
|
@ -1215,16 +1283,12 @@ pure function math_Voigt66to3333(m66)
|
|||
real(pReal), dimension(6,6), intent(in) :: m66
|
||||
integer(pInt) :: i,j
|
||||
|
||||
forall (i=1_pInt:6_pInt,j=1_pInt:6_pInt)
|
||||
math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(1,j),mapVoigt(2,j)) = &
|
||||
invnrmVoigt(i)*invnrmVoigt(j)*m66(i,j)
|
||||
math_Voigt66to3333(mapVoigt(2,i),mapVoigt(1,i),mapVoigt(1,j),mapVoigt(2,j)) = &
|
||||
invnrmVoigt(i)*invnrmVoigt(j)*m66(i,j)
|
||||
math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(2,j),mapVoigt(1,j)) = &
|
||||
invnrmVoigt(i)*invnrmVoigt(j)*m66(i,j)
|
||||
math_Voigt66to3333(mapVoigt(2,i),mapVoigt(1,i),mapVoigt(2,j),mapVoigt(1,j)) = &
|
||||
invnrmVoigt(i)*invnrmVoigt(j)*m66(i,j)
|
||||
end forall
|
||||
do i=1_pInt,6_pInt; do j=1_pInt, 6_pInt
|
||||
math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(1,j),mapVoigt(2,j)) = m66(i,j)
|
||||
math_Voigt66to3333(mapVoigt(2,i),mapVoigt(1,i),mapVoigt(1,j),mapVoigt(2,j)) = m66(i,j)
|
||||
math_Voigt66to3333(mapVoigt(1,i),mapVoigt(2,i),mapVoigt(2,j),mapVoigt(1,j)) = m66(i,j)
|
||||
math_Voigt66to3333(mapVoigt(2,i),mapVoigt(1,i),mapVoigt(2,j),mapVoigt(1,j)) = m66(i,j)
|
||||
enddo; enddo
|
||||
|
||||
end function math_Voigt66to3333
|
||||
|
||||
|
|
@ -1632,8 +1696,7 @@ pure function math_qToR(q)
|
|||
real(pReal), dimension(3,3) :: math_qToR, T,S
|
||||
integer(pInt) :: i, j
|
||||
|
||||
forall (i = 1_pInt:3_pInt, j = 1_pInt:3_pInt) &
|
||||
T(i,j) = q(i+1_pInt) * q(j+1_pInt)
|
||||
forall(i = 1_pInt:3_pInt, j = 1_pInt:3_pInt) T(i,j) = q(i+1_pInt) * q(j+1_pInt)
|
||||
|
||||
S = reshape( [0.0_pReal, -q(4), q(3), &
|
||||
q(4), 0.0_pReal, -q(2), &
|
||||
|
|
@ -2038,7 +2101,7 @@ end function math_eigenvectorBasisSym
|
|||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief eigenvector basis of symmetric 33 matrix m
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
function math_eigenvectorBasisSym33(m)
|
||||
pure function math_eigenvectorBasisSym33(m)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3,3) :: math_eigenvectorBasisSym33
|
||||
|
|
@ -2103,7 +2166,7 @@ end function math_eigenvectorBasisSym33
|
|||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief logarithm eigenvector basis of symmetric 33 matrix m
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
function math_eigenvectorBasisSym33_log(m)
|
||||
pure function math_eigenvectorBasisSym33_log(m)
|
||||
|
||||
implicit none
|
||||
real(pReal), dimension(3,3) :: math_eigenvectorBasisSym33_log
|
||||
|
|
@ -2164,6 +2227,7 @@ function math_eigenvectorBasisSym33_log(m)
|
|||
|
||||
end function math_eigenvectorBasisSym33_log
|
||||
|
||||
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
!> @brief rotational part from polar decomposition of 33 tensor m
|
||||
!--------------------------------------------------------------------------------------------------
|
||||
|
|
@ -2608,13 +2672,12 @@ pure function math_rotate_forward3333(tensor,rot_tensor)
|
|||
real(pReal), dimension(3,3,3,3), intent(in) :: tensor
|
||||
integer(pInt) :: i,j,k,l,m,n,o,p
|
||||
|
||||
math_rotate_forward3333= 0.0_pReal
|
||||
|
||||
do i = 1_pInt,3_pInt; do j = 1_pInt,3_pInt; do k = 1_pInt,3_pInt; do l = 1_pInt,3_pInt
|
||||
do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt; do o = 1_pInt,3_pInt; do p = 1_pInt,3_pInt
|
||||
math_rotate_forward3333(i,j,k,l) = math_rotate_forward3333(i,j,k,l) &
|
||||
+ rot_tensor(i,m) * rot_tensor(j,n) &
|
||||
* rot_tensor(k,o) * rot_tensor(l,p) * tensor(m,n,o,p)
|
||||
math_rotate_forward3333 = 0.0_pReal
|
||||
do i = 1_pInt,3_pInt;do j = 1_pInt,3_pInt;do k = 1_pInt,3_pInt;do l = 1_pInt,3_pInt
|
||||
do m = 1_pInt,3_pInt;do n = 1_pInt,3_pInt;do o = 1_pInt,3_pInt;do p = 1_pInt,3_pInt
|
||||
math_rotate_forward3333(i,j,k,l) &
|
||||
= math_rotate_forward3333(i,j,k,l) &
|
||||
+ rot_tensor(i,m) * rot_tensor(j,n) * rot_tensor(k,o) * rot_tensor(l,p) * tensor(m,n,o,p)
|
||||
enddo; enddo; enddo; enddo; enddo; enddo; enddo; enddo
|
||||
|
||||
end function math_rotate_forward3333
|
||||
|
|
|
|||
Loading…
Reference in New Issue