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@ -453,8 +453,8 @@ pure subroutine kinetics(Mp,T,instance,of, &
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associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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do j = 1, prm%sum_N_sl
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tau_pos(j) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,j))
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tau_neg(j) = math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,j))
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tau_pos(j) = math_tensordot(Mp,prm%nonSchmid_pos(1:3,1:3,j))
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tau_neg(j) = math_tensordot(Mp,prm%nonSchmid_neg(1:3,1:3,j))
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enddo
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@ -580,7 +580,7 @@ module subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of)
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do i = 1,6
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P_sb = 0.5_pReal * math_outer(matmul(eigVectors,sb_sComposition(1:3,i)),&
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matmul(eigVectors,sb_mComposition(1:3,i)))
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tau = math_mul33xx33(Mp,P_sb)
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tau = math_tensordot(Mp,P_sb)
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significantShearBandStress: if (abs(tau) > tol_math_check) then
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StressRatio_p = (abs(tau)/prm%sbResistance)**prm%p_sb
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@ -665,7 +665,7 @@ module subroutine plastic_dislotwin_dotState(Mp,T,instance,of)
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rho_dip_distance_min = prm%CEdgeDipMinDistance*prm%b_sl
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slipState: do i = 1, prm%sum_N_sl
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tau = math_mul33xx33(Mp,prm%P_sl(1:3,1:3,i))
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tau = math_tensordot(Mp,prm%P_sl(1:3,1:3,i))
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significantSlipStress: if (dEq0(tau)) then
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dot_rho_dip_formation(i) = 0.0_pReal
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@ -906,7 +906,7 @@ pure subroutine kinetics_slip(Mp,T,instance,of, &
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associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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do i = 1, prm%sum_N_sl
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tau(i) = math_mul33xx33(Mp,prm%P_sl(1:3,1:3,i))
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tau(i) = math_tensordot(Mp,prm%P_sl(1:3,1:3,i))
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enddo
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tau_eff = abs(tau)-dst%tau_pass(:,of)
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@ -977,7 +977,7 @@ pure subroutine kinetics_twin(Mp,T,dot_gamma_sl,instance,of,&
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associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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do i = 1, prm%sum_N_tw
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tau(i) = math_mul33xx33(Mp,prm%P_tw(1:3,1:3,i))
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tau(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
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isFCC: if (prm%fccTwinTransNucleation) then
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s1=prm%fcc_twinNucleationSlipPair(1,i)
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s2=prm%fcc_twinNucleationSlipPair(2,i)
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@ -1045,7 +1045,7 @@ pure subroutine kinetics_trans(Mp,T,dot_gamma_sl,instance,of,&
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associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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do i = 1, prm%sum_N_tr
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tau(i) = math_mul33xx33(Mp,prm%P_tr(1:3,1:3,i))
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tau(i) = math_tensordot(Mp,prm%P_tr(1:3,1:3,i))
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isFCC: if (prm%fccTwinTransNucleation) then
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s1=prm%fcc_twinNucleationSlipPair(1,i)
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s2=prm%fcc_twinNucleationSlipPair(2,i)
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@ -175,7 +175,7 @@ module subroutine plastic_isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of)
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associate(prm => param(instance), stt => state(instance))
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Mp_dev = math_deviatoric33(Mp)
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squarenorm_Mp_dev = math_mul33xx33(Mp_dev,Mp_dev)
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squarenorm_Mp_dev = math_tensordot(Mp_dev,Mp_dev)
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norm_Mp_dev = sqrt(squarenorm_Mp_dev)
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if (norm_Mp_dev > 0.0_pReal) then
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@ -279,9 +279,9 @@ module subroutine plastic_isotropic_dotState(Mp,instance,of)
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associate(prm => param(instance), stt => state(instance), dot => dotState(instance))
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if (prm%dilatation) then
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norm_Mp = sqrt(math_mul33xx33(Mp,Mp))
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norm_Mp = sqrt(math_tensordot(Mp,Mp))
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else
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norm_Mp = sqrt(math_mul33xx33(math_deviatoric33(Mp),math_deviatoric33(Mp)))
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norm_Mp = sqrt(math_tensordot(math_deviatoric33(Mp),math_deviatoric33(Mp)))
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endif
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dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp /(prm%M*stt%xi(of))) **prm%n
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@ -421,8 +421,8 @@ pure subroutine kinetics(Mp,instance,of, &
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nonSchmidActive = size(prm%nonSchmidCoeff) > 0
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do i = 1, prm%sum_N_sl
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tau_pos(i) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i)) - stt%crss_back(i,of)
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tau_neg(i) = merge(math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,i)) - stt%crss_back(i,of), &
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tau_pos(i) = math_tensordot(Mp,prm%nonSchmid_pos(1:3,1:3,i)) - stt%crss_back(i,of)
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tau_neg(i) = merge(math_tensordot(Mp,prm%nonSchmid_neg(1:3,1:3,i)) - stt%crss_back(i,of), &
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0.0_pReal, nonSchmidActive)
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enddo
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@ -864,15 +864,15 @@ module subroutine plastic_nonlocal_LpAndItsTangent(Lp,dLp_dMp, &
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rhoSgl = rho(:,sgl)
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do s = 1,ns
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tau(s) = math_mul33xx33(Mp, prm%Schmid(1:3,1:3,s))
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tau(s) = math_tensordot(Mp, prm%Schmid(1:3,1:3,s))
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tauNS(s,1) = tau(s)
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tauNS(s,2) = tau(s)
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if (tau(s) > 0.0_pReal) then
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tauNS(s,3) = math_mul33xx33(Mp, +prm%nonSchmid_pos(1:3,1:3,s))
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tauNS(s,4) = math_mul33xx33(Mp, -prm%nonSchmid_neg(1:3,1:3,s))
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tauNS(s,3) = math_tensordot(Mp, +prm%nonSchmid_pos(1:3,1:3,s))
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tauNS(s,4) = math_tensordot(Mp, -prm%nonSchmid_neg(1:3,1:3,s))
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else
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tauNS(s,3) = math_mul33xx33(Mp, +prm%nonSchmid_neg(1:3,1:3,s))
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tauNS(s,4) = math_mul33xx33(Mp, -prm%nonSchmid_pos(1:3,1:3,s))
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tauNS(s,3) = math_tensordot(Mp, +prm%nonSchmid_neg(1:3,1:3,s))
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tauNS(s,4) = math_tensordot(Mp, -prm%nonSchmid_pos(1:3,1:3,s))
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endif
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enddo
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tauNS = tauNS + spread(dst%tau_back(:,of),2,4)
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@ -987,7 +987,7 @@ module subroutine plastic_nonlocal_deltaState(Mp,instance,of,ip,el)
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!*** calculate limits for stable dipole height
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do s = 1,prm%totalNslip
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tau(s) = math_mul33xx33(Mp, prm%Schmid(1:3,1:3,s)) +dst%tau_back(s,of)
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tau(s) = math_tensordot(Mp, prm%Schmid(1:3,1:3,s)) +dst%tau_back(s,of)
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if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
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enddo
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@ -1148,7 +1148,7 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
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!****************************************************************************
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!*** limits for stable dipole height
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do s = 1,ns
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tau(s) = math_mul33xx33(Mp, prm%Schmid(1:3,1:3,s)) + dst%tau_back(s,of)
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tau(s) = math_tensordot(Mp, prm%Schmid(1:3,1:3,s)) + dst%tau_back(s,of)
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if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
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enddo
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@ -437,8 +437,8 @@ pure subroutine kinetics_slip(Mp,instance,of, &
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associate(prm => param(instance), stt => state(instance))
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do i = 1, prm%sum_N_sl
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tau_slip_pos(i) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))
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tau_slip_neg(i) = merge(math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,i)), &
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tau_slip_pos(i) = math_tensordot(Mp,prm%nonSchmid_pos(1:3,1:3,i))
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tau_slip_neg(i) = merge(math_tensordot(Mp,prm%nonSchmid_neg(1:3,1:3,i)), &
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0.0_pReal, prm%nonSchmidActive)
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enddo
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@ -503,7 +503,7 @@ pure subroutine kinetics_twin(Mp,instance,of,&
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associate(prm => param(instance), stt => state(instance))
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do i = 1, prm%sum_N_tw
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tau_twin(i) = math_mul33xx33(Mp,prm%P_tw(1:3,1:3,i))
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tau_twin(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
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enddo
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where(tau_twin > 0.0_pReal)
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@ -127,7 +127,7 @@ subroutine kinematics_cleavage_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, i
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do i = 1,prm%totalNcleavage
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traction_crit = prm%critLoad(i)* damage(homog)%p(damageOffset)**2.0_pReal
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traction_d = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,1,i))
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traction_d = math_tensordot(S,prm%cleavage_systems(1:3,1:3,1,i))
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if (abs(traction_d) > traction_crit + tol_math_check) then
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udotd = sign(1.0_pReal,traction_d)* prm%sdot0 * ((abs(traction_d) - traction_crit)/traction_crit)**prm%n
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Ld = Ld + udotd*prm%cleavage_systems(1:3,1:3,1,i)
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@ -137,7 +137,7 @@ subroutine kinematics_cleavage_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, i
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+ dudotd_dt*prm%cleavage_systems(k,l,1,i) * prm%cleavage_systems(m,n,1,i)
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endif
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traction_t = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,2,i))
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traction_t = math_tensordot(S,prm%cleavage_systems(1:3,1:3,2,i))
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if (abs(traction_t) > traction_crit + tol_math_check) then
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udott = sign(1.0_pReal,traction_t)* prm%sdot0 * ((abs(traction_t) - traction_crit)/traction_crit)**prm%n
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Ld = Ld + udott*prm%cleavage_systems(1:3,1:3,2,i)
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@ -147,7 +147,7 @@ subroutine kinematics_cleavage_opening_LiAndItsTangent(Ld, dLd_dTstar, S, ipc, i
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+ dudott_dt*prm%cleavage_systems(k,l,2,i) * prm%cleavage_systems(m,n,2,i)
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endif
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traction_n = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,3,i))
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traction_n = math_tensordot(S,prm%cleavage_systems(1:3,1:3,3,i))
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if (abs(traction_n) > traction_crit + tol_math_check) then
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udotn = sign(1.0_pReal,traction_n)* prm%sdot0 * ((abs(traction_n) - traction_crit)/traction_crit)**prm%n
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Ld = Ld + udotn*prm%cleavage_systems(1:3,1:3,3,i)
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@ -73,18 +73,10 @@ module math
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3,3 &
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],[2,9]) !< arrangement in Plain notation
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interface math_eye
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module procedure math_identity2nd
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end interface math_eye
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!--------------------------
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! only for compatibility reasons
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interface math_mul33xx33
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module procedure math_tensordot
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end interface math_mul33xx33
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!--------------------------
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!---------------------------------------------------------------------------------------------------
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private :: &
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@ -155,9 +155,9 @@ subroutine source_damage_anisoBrittle_dotState(S, ipc, ip, el)
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sourceState(phase)%p(sourceOffset)%dotState(1,constituent) = 0.0_pReal
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do i = 1, prm%totalNcleavage
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traction_d = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,1,i))
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traction_t = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,2,i))
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traction_n = math_mul33xx33(S,prm%cleavage_systems(1:3,1:3,3,i))
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traction_d = math_tensordot(S,prm%cleavage_systems(1:3,1:3,1,i))
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traction_t = math_tensordot(S,prm%cleavage_systems(1:3,1:3,2,i))
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traction_n = math_tensordot(S,prm%cleavage_systems(1:3,1:3,3,i))
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traction_crit = prm%critLoad(i)*damage(homog)%p(damageOffset)**2.0_pReal
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