/PROP/TYPE8 (SPR_GENE)

Block Format Keyword This spring property works with six independent modes of deformation. This spring accounts for nonlinear stiffness, damping and different unloading.

Deformation, force and energy based failure criteria are available. The general spring property is often used to model a joint connection between two parts.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/PROP/TYPE8/prop_ID/unit_ID or /PROP/SPR_GENE/prop_ID/unit_ID
prop_title
Mass I Skew_ID sens_ID Isflag Ifail Ifail2 Iequil
Translation in X
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
K1 C1 A1 B1 D1
fct_ID11 H1 fct_ID21 fct_ID31 fct_ID41   δ min 1 δ max 2
F1 E1 Ascale1 Hscale1    
Translation in Y
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
K2 C2 A2 B2 D2
fct_ID12 H2 fct_ID22 fct_ID32 fct_ID42   δ min 2 δ max 2
F2 E2 Ascale2 Hscale2    
Translation in Z
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
K3 C3 A3 B3 D3
fct_ID13 H3 fct_ID23 fct_ID33 fct_ID43   δ min 3 δ max 3
F3 E3 Ascale3 Hscale3    
Rotation in X
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
K4 C4 A4 B4 D4
fct_ID14 H4 fct_ID24 fct_ID34 fct_ID44   θ min 4 θ max 4
F4 E4 Ascale4 Hscale4    
Rotation in Y
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
K5 C5 A5 B5 D5
fct_ID15 H5 fct_ID25 fct_ID35 fct_ID45   θ min 5 θ max 5
F5 E5 Ascale5 Hscale5    
Rotation in Z
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
K6 C6 A6 B6 D6
fct_ID16 H6 fct_ID26 fct_ID36 fct_ID46   θ min 6 θ max 6
F6 E6 Ascale6 Hscale6    
Filtering forces
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Fsmooth Fcut              

Definitions

Field Contents SI Unit Example
prop_ID Property identifier

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier

(Integer, maximum 10 digits)

 
prop_title Property title

(Character, maximum 100 characters)

 
Mass Mass

(Real)

[ kg ]
I Inertia

(Real)

[ m 2 kg ]
Skew_ID Skew system identifier. If not defined, then global coordinate system is used.

(Integer)

 
sens_ID Sensor identifier

(Integer)

 
Isflag Sensor flag. 12
=0
Spring element activated
=1
Spring element deactivated.
=2
Spring element activated or deactivated.

(Integer)

 
Ifail Failure criteria.
= 0
Uni-directional criteria.
= 1
Multi-directional criteria.

(Integer)

 
Ifail2 Failure model flag. 4
= 0 (Default)
Displacement criteria (rotation criteria).
= 1
Force criteria (moment criteria).
= 3
Internal energy criteria.

(Integer)

 
Iequil Equilibrium flag. 2
= 0
No equilibrium.
= 1
Force and moment equilibrium.

(Integer)

 
K1 Transitional stiffness (for linear spring) or unloading stiffness (for elasto-plastic spring). 6

(Real)

[ N m ]
C1 Transitional damping for translation in X.

(Real)

[ N s m ]
A1 Coefficient in strain rate effect in direction X (homogeneous to a force).

Default = 1.0 (Real)

[ N ]
B1 Logarithmic coefficient in strain rate effect in direction X (homogeneous to a force).

(Real)

[ N ]
D1 Scale coefficients for translational velocity in X.

Default = 1.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
fct_ID11 Function identifier defining f δ transition in X.
= 0
Linear spring

If H1 = 4: Function identifier defining upper yield curve

(Integer)

 
H1 Transitional hardening flag.
=0
Nonlinear elastic spring.
=1
Nonlinear elastic plastic spring.
=2
Nonlinear elasto-plastic spring with decoupled hardening in tension and compression.
=4
Nonlinear elastic plastic spring "kinematic" hardening.
=5
Nonlinear elasto-plastic spring with nonlinear unloading.
=6
Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading.
=7
Nonlinear spring with elastic hysteresis.

(Integer)

 
fct_ID21 Function identifier defining g ( δ ˙ ) transition in X.

(Integer)

 
fct_ID31 Function used only for unloading for translation in X.

If H1 = 4: Function identifier defining lower yield curve (transitional).

If H1 = 5: Function identifier defining residual displacement vs maximum displacement.

If H1= 6: Function identifier defining nonlinear unloading.

If H1= 7: Function identifier unloading curve for force vs displacement (relative displacement).

(Integer)

 
fct_ID41 Function identifier defining g ( δ ˙ ) for translation in X.

(Integer)

 
δ min 1 Negative failure displacement, transitional.

Default = -1030 (Real)

[ m ]
δ max 1 Positive failure displacement, transitional.

Default = 1030 (Real)

[ m ]
F1 Scale factor for δ , transitional for translation in X.

(Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
E1 Coefficient for strain rate effect in direction X (homogeneous to a force).

(Real)

[ N ]
Ascale1 Abscissa scale factor for δ (fct_ID11 and fct_ID13).

Default = 1 (Real)

[ m ]
Hscale1 Coefficient for fct_ID41 used for translation in X (homogeneous to a force).

Default = 1 (Real)

[ N ]
K2 Transitional stiffness (for linear spring) or unloading stiffness (for elasto-plastic spring) for translation in Y.

(Real)

[ N m ]
C2 Transitional damping for translation in Y.

(Real)

[ Ns m ]
A2 Coefficient for strain rate effect in direction Y (homogeneous to a force).

Default = 1.0 (Real)

[ N ]
B2 Logarithmic coefficient for strain rate effect in direction Y (homogeneous to a force).

(Real)

[ N ]
D2 Scale coefficients for translation velocity in Y.

Default = 1.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
fct_ID12 Function identifier defining f( δ ) transition in Y.
= 0
Linear spring.

If H2 = 4: Function identifier defining upper yield curve

(Integer)

 
H2 Transitional hardening flag.
=0
Nonlinear elastic spring.
=1
Nonlinear elastic plastic spring.
=2
Nonlinear elasto-plastic spring with decoupled hardening in tension and compression.
=4
Nonlinear elastic plastic spring "kinematic" hardening.
=5
Nonlinear elasto-plastic spring with nonlinear unloading.
=6
Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading.
=7
Nonlinear spring with elastic hysteresis.

(Integer)

 
fct_ID22 Function identifier defining g ( δ ˙ ) transition in Y.

(Integer)

 
fct_ID32 Function used only for unloading for translation in Y.

If H2 = 4: Function identifier defining lower yield curve (transitional)

If H2 = 5: Function identifier defining residual displacement vs maximum displacement

If H2= 6: Function identifier defining nonlinear unloading.

If H2= 7: Function identifier unloading curve for force vs displacement (relative displacement)

(Integer)

 
fct_ID42 Function identifier defining h ( δ ˙ ) for translation in Y.

(Integer)

 
δ min 2 Negative failure displacement, transitional.

Default = -1030 (Real)

[ m ]
δ max 2 Positive failure displacement, transitional

Default = 1030 (Real)

[ m ]
F2 Scale factor for δ , transitional in translation in Y.

(Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
E2 Coefficient for strain rate effect in direction Y (homogeneous to a force).

(Real)

[ N ]
Ascale2 Abscissa scale factor for δ (fct_ID12 and fct_ID32) for translation in Y.

Default = 1 (Real)

[ m ]
Hscale2 Coefficient for fct_ID42 for translation in Y (homogeneous to a force).

Default = 1 (Real)

[ N ]
K3 Transitional stiffness (for linear spring) or unloading stiffness (for elasto-plastic spring) for translation in Z.

(Real)

[ N m ]
C3 Transitional damping

(Real)

[ Ns m ]
A3 Coefficient for strain rate effect in direction Z (homogeneous to a force).

Default = 1.0 (Real)

[ N ]
B3 Logarithmic coefficient for strain rate effect in direction Z (homogeneous to a force).

(Real)

[ N ]
D3 Scale coefficient for translation velocity in direction Z.

Default = 1.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
fct_ID13 Function identifier defining f( δ ) transitional in Z.
= 0
Linear spring

If H3 = 4: Function identifier defining upper yield curve

(Integer)

 
H3 Transitional hardening flag.
=0
Nonlinear elastic spring.
=1
Nonlinear elastic plastic spring.
=2
Nonlinear elasto-plastic spring with decoupled hardening in tension and compression.
=4
Nonlinear elastic plastic spring "kinematic" hardening.
=5
Nonlinear elasto-plastic spring with nonlinear unloading.
=6
Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading.
=7
Nonlinear spring with elastic hysteresis.

(Integer)

 
fct_ID23 Function identifier defining g( δ ) transition in Z.

(Integer)

 
fct_ID33 Function used only for unloading for translation in Z.

If H3 = 4: Function identifier defining lower yield curve (transitional)

If H3 = 5: Function identifier defining residual displacement vs maximum displacement

If H3 = 6: Function identifier defining nonlinear unloading curve

If H3= 7: Function identifier unloading curve for force vs displacement (relative displacement)

(Integer)

 
fct_ID43 Function identifier defining h ( δ ˙ ) for translation in Z.

(Integer)

 
δ min 3 Negative failure displacement, transitional.

Default = -1030 (Real)

[ m ]
δ max 3 Positive failure displacement, transitional.

Default = 1030 (Real)

[ m ]
F3 Scale factor for δ , transitional for translation in Z.

(Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
E3 Coefficient for strain rate effect in direction Z (homogeneous to a force).

(Real)

[ N ]
Ascale3 Abscissa scale factor for δ (fct_ID13 and fct_ID33).

Default = 1 (Real)

[ m ]
Hscale3 Coefficient for fct_ID43 for translation in Z (homogeneous to a force).

Default = 1 (Real)

[ N ]
K4 Rotational stiffness (for linear spring) or unloading stiffness (for elasto-plastic spring) for torsion in X.

(Real)

[ N m r a d ]
C4 Rotational damping for torsion in X.

(Real)

[ Nms rad ]
A4 Coefficient for strain rate effect torsion in X (homogeneous to a moment).

Default = 1.0 (Real)

[ Nm ]
B4 Logarithmic coefficient for strain rate effect in torsion X (homogeneous to a moment).

(Real)

[ Nm ]
D4 Scale coefficients for torsion velocity in X.

Default = 1.0 (Real)

[ rad s ]
fct_ID14 Function identifier defining f( θ ), rotational for torsion in X.
= 0
Linear spring

If H4 = 4: Function identifier defining upper yield curve

(Integer)

 
H4 Rotational hardening flag.
=0
Nonlinear elastic spring.
=1
Nonlinear elastic plastic spring.
=2
Nonlinear elasto-plastic spring with decoupled hardening in tension and compression.
=4
Nonlinear elastic plastic spring "kinematic" hardening.
=5
Nonlinear elasto-plastic spring with nonlinear unloading.
=6
Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading.
=7
Nonlinear spring with elastic hysteresis.

(Integer)

 
fct_ID24 Function identifier defining g ( θ ) , rotational for torsion in X.

(Integer)

 
fct_ID34 Function used only for unloading for torsion in X.

If H4 = 4: Function identifier defining lower yield curve, rotational

If H4 = 5: Function identifier defining residual displacement vs maximum displacement

If H4 = 6: Function identifier defining nonlinear unloading curve

If H4= 7: Function identifier defining unloading curve of moment vs rotation

(Integer)

 
fct_ID44 Function identifier defining h ( θ ˙ ) for torsion in X.

(Integer)

 
θ min 4 Negative failure rotation.

Default = -1030 (Real)

[ rad ]
θ max 4 Positive failure rotation

Default = 1030 (Real)

[ rad ]
F4 Scale factor for θ , rotational for torsion in X.

(Real)

[ rad s ]
E4 Coefficient for strain rate effect for torsion in X (homogeneous to a moment).

(Real)

[ Nm ]
Ascale4 Abscissa scale factor for θ for torsion in X (fct_ID14 and fct_ID34).

Default = 1 (Real)

[ rad ]
Hscale4 Coefficient for fct_ID44 for torsion in X (homogeneous to a force).

Default = 1 (Real)

[ Nm ]
K5 Rotational stiffness (for linear spring) or unloading stiffness (for elasto-plastic spring) for rotation in Y.

(Real)

[ Nm rad ]
C5 Rotational damping for rotation in Y.

(Real)

[ Nm rad ]
A5 Coefficient for strain rate effect, rotation in Y (homogeneous to a moment).

Default = 1.0 (Real)

[ Nm ]
B5 Logarithmic coefficient for strain rate effect, rotation in Y (homogeneous to a moment).

(Real)

[ Nm ]
D5 Scale coefficients for rotation velocity in Y.

Default = 1.0 (Real)

[ rad s ]
fct_ID15 Function identifier defining f( θ ), rotational for torsion in Y.
= 0
Linear spring

If H5 = 4: Function identifier defining upper yield curve

(Integer)

 
H5 Rotational hardening flag.
=0
Nonlinear elastic spring.
=1
Nonlinear elastic plastic spring.
=2
Nonlinear elasto-plastic spring with decoupled hardening in tension and compression.
=4
Nonlinear elastic plastic spring "kinematic" hardening.
=5
Nonlinear elasto-plastic spring with nonlinear unloading.
=6
Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading.
=7
Nonlinear spring with elastic hysteresis.

(Integer)

 
fct_ID25 Function identifier defining g ( θ ) , rotation for in Y.

(Integer)

 
fct_ID35 Function used only for unloading for rotation in Y.

If H5 = 4: Function identifier defining lower yield curve, rotational

If H5 = 5: Function identifier defining residual rotation vs maximum rotation

If H5 = 6: Function identifier defining nonlinear unloading curve

If H5= 7: Function identifier defining unloading curve for moment vs rotation

(Integer)

 
fct_ID45 Function identifier defining h ( θ ˙ ) for rotation in Y.

(Integer)

 
θ min 5 Negative failure rotation.

Default = -1030 (Real)

[ rad ]
θ max 5 Positive failure rotation.

Default = 1030 (Real)

[ rad ]
F5 Scale factor for θ , rotational for rotation in Y.

(Real)

[ rad s ]
E5 Coefficient for strain rate effect in rotation in Y (homogeneous to a moment).

(Real)

[ Nm ]
Ascale5 Abscissa scale factor for θ for rotation in Y (fct_ID15 and fct_ID35).

Default = 1 (Real)

[ rad ]
Hscale5 Coefficient for fct_ID45 for rotation in Y (homogeneous to a force).

Default = 1 (Real)

[ Nm ]
K6 Rotational stiffness (for linear spring) or unloading stiffness (for elasto-plastic spring) for rotation in Z.

(Real)

[ Nm rad ]
C6 Rotational damping for rotation in Z.

(Real)

[ Nms rad ]
A6 Coefficient for strain rate effect, rotation Z (homogeneous to a moment).

Default = 1.0 (Real)

[ Nm ]
B6 Logarithmic coefficient for strain rate effect, rotation in Z (homogeneous to a moment).

(Real)

[ Nm ]
D6 Scale coefficients for rotation in Z.

Default = 1.0 (Real)

[ rad s ]
fct_ID16 Function identifier defining f( θ ), rotation in Z.
= 0
Linear spring.

If H6 = 4: Function identifier defining upper yield curve

(Integer)

 
H6 Rotational hardening flag.
=0
Nonlinear elastic spring.
=1
Nonlinear elastic plastic spring.
=2
Nonlinear elasto-plastic spring with decoupled hardening in tension and compression.
=4
Nonlinear elastic plastic spring "kinematic" hardening.
=5
Nonlinear elasto-plastic spring with nonlinear unloading.
=6
Nonlinear elasto-plastic spring with isotropic hardening and nonlinear unloading.
=7
Nonlinear spring with elastic hysteresis.

(Integer)

 
fct_ID26 Function identifier defining g ( θ ) , rotation in Z.

(Integer)

 
fct_ID36 Function used only for unloading for rotation in Z.

If H6 = 4: Function identifier defining lower yield curve, rotational

If H6 = 5: Function identifier defining residual rotation vs maximum rotation

If H6 = 6: Function identifier defining nonlinear unloading curve

If H6= 7: Function identifier defining unloading curve for moment vs rotation

(Integer)

 
fct_ID46 Function identifier defining h ( θ ) for rotation in Z.

(Integer)

 
θ min 6 Negative failure rotation.

Default = -1030 (Real)

[ rad ]
θ max 6 Positive failure rotation.

Default = 1030 (Real)

[ rad ]
F6 Scale factor for θ , rotational for rotation in Z.

(Real)

[ rad s ]
E6 Coefficient for strain rate effect rotation in Z (homogeneous to a moment).

(Real)

[ Nm ]
Ascale6 Abscissa scale factor for θ for rotation in Z (fct_ID16 and fct_ID36).

Default = 1 (Real)

[ rad ]
Hscale6 Coefficient for fct_ID46 for rotation in Z (homogeneous to a force).

Default = 1 (Real)

[ Nm ]
Fsmooth Smooth strain rate flag.
=0(Default)
Strain rate smoothing is inactive.
=1
Strain rate smoothing is active.

(Integer)

 
Fcut Strain rate cutting frequency.

Default = 1030

(Real)

[Hz]

Comments

  1. The spring has six DOF computed in a skew system frame: δ X , δ Y , δ Z , θ X , θ Y , θ Z

    clip0116
    Figure 1.
    • The six DOF are independent. If initial length is not equal to zero, the equilibrium is insured for forces, but not for moments. It is then recommended to use spring elements TYPE8 with a zero length or with one of the two nodes fixed in all directions.
    • If δ is a translational DOF, the force in direction δ is computed as:

      Linear spring:

      F ( δ ) = K i δ i + C i δ ˙ i for i = 1, 2, 3

      Nonlinear spring:

      F ( δ ) = f ( δ i Ascale i ) [ A i + B i ln | δ ˙ i D i | + E i g ( δ ˙ i F i ) ] + C i δ ˙ i + Hscale i h ( δ ˙ i F i ) for i= 1, 2, 3

    • If θ is a rotational DOF, the moment is computed as:

      Linear spring:

      M ( θ ) = K i θ i + C i θ ˙ i for i = 4, 5, 6

      Nonlinear spring:

      M ( θ ) = f ( θ i Ascale i ) [ A i + B i ln | θ ˙ i D i | + E i g ( θ ˙ i F i ) ] + C i θ ˙ i + Hscale i h ( θ ˙ i F i ) for i = 4, 5, 6

      linear_spring
      Figure 2. Linear Spring

      nonlinear_spring_0
      Figure 3. Nonlinear Elastic Spring, Hi=0

      nonlinear_spring_1
      Figure 4. Nonlinear Elastic Plastic Spring, Hi=1

      nonlinear_spring_2
      Figure 5. Nonlinear Elasto- plastic Spring with Decoupled Hardening in Tension and Compression, Hi= 2

      nonlinear_spring_4
      Figure 6. Nonlinear Elastic Plastic Spring "kinematic" Hardening, Hi= 4

      nonlinear_spring_5
      Figure 7. Nonlinear Elastic Plastic Spring "kinematic" Hardening, Hi= 5

      nonlinear_spring_6
      Figure 8. Nonlinear Elasto-Plastic Spring with Isotropic Hardening and Nonlinear Unloading, Hi= 6
      nonlinear_spring_7 Figure 9. Nonlinear Spring with Elastic Hysteresis, Hi=7

      With i =1, 2, 3, 4, 5, 6

  2. If Iequil = 0, then:(1)
    f ( θ ) = M 2 y = M 1 y

    M 2 y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGnbWaaS baaSqaaiaaikdacaWG5baabeaaaaa@3916@ is moment in Y by N2

    M 1 y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGnbWaaS baaSqaaiaaikdacaWG5baabeaaaaa@3916@ is moment in Y by N1

  3. If Iequil = 1, then:(2)
    M 1 y M 2 y M 1 z M 2 z
    (3)
    f ( θ ) = M 2 y M 1 y 2

    M 2 y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGnbWaaS baaSqaaiaaikdacaWG5baabeaaaaa@3916@ is moment in Y by N2

    M 1 y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGnbWaaS baaSqaaiaaikdacaWG5baabeaaaaa@3916@ is moment in Y by N1

    M 2 z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGnbWaaS baaSqaaiaaikdacaWG5baabeaaaaa@3916@ is moment in Z by N2

    M 1 z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGnbWaaS baaSqaaiaaikdacaWG5baabeaaaaa@3916@ is moment in Z by N1

  4. Failure criterion:
    • If the failure criterion is uni-directional, Ifail=0, the spring fails as soon as one of the criteria is met in one direction.

      δ i δ max i 1 or | δ i δ min i | 1 with δ max i and δ min i being the failure limits in direction i =1,2,3

      θ i θ max i 1 or | θ i θ min i | 1 with θ max i and θ min i being the failure limits in direction i =4,5,6

    • If the failure criteria is multi-directional, Ifail=1, the spring fails if the following criteria is fulfilled:(4)
      i = 1 , 2 , 3 ( δ i δ f a i l i ) 2 + i = 4 , 5 , 6 ( θ i n i θ f a i l i ) 2 1

      with δ fail i being the failure displacement in direction i = 1, 2, 3; and θ f a i l i being the falure displacement (rotation) in direction i =4,5,6.

    • If δ min i (resp δ max i , with i =1, 2, 3) is 0, no failure in the negative direction (resp positive).
    • The failure model flag Ifail2 allows the 3 types of failure criteria:
      1. If Ifail2= 0, the displacemenet/rotation criterion is activated:(5)
        δ f a i l i = { δ max i , i f ( δ i > 0 ) δ min i , i f ( δ i 0 )
        Where, δ min i and δ max i are the static failure limit in translational DOF.(6)
        θ f a i l i = { θ max i , i f ( θ i > 0 ) θ min i , i f ( θ i 0 )

        Where, θ min i and θ max i are the static failure limit in rotational DOF.

      2. If Ifail2=1, the force/moment criterion is activated:(7)
        δ f a i l i = { δ max i , i f ( δ i > 0 ) δ min i , i f ( δ i 0 )
        Where, δ min i and δ max i are the static force failure limit in translational DOF.(8)
        θ f a i l i = { θ max i , i f ( θ i > 0 ) θ min i , i f ( θ i 0 )

        Where, θ min i and θ max i are the static moment failure limit in rotational DOF.

        In this case, the displacement/rotation values are replaced by failure force/moment values.

      3. If Ifail2=3, the energey criterion is activated:(9)
        δ f a i l i = δ max i
        Where, δ max i is the static energy failure limit in translational DOF.(10)
        θ f a i l i = θ max i

        Where, θ max i is the static energy falure limit in rotational DOF.

        In this case, the displacement/rotation values are replaced by positive failure energy values.

  5. For each direction, δ min i (with i =1, 2, 3) is taken if δ i is negative, otherwise, δ max i is taken if is positive. The δ min i (with i =1, 2, 3) must be negative. Both θ min i (with i =4, 5, 6) and θ max i are expressed in radians.
  6. If Ki (with i =1, 2, 3) is less than the maximum slope of the yield curve (Ki is not consistent with the maximum slope of yield curve), Ki is set to the maximum slope of the curve.

    If Ki (with i=4, 5, 6) is less than the maximum slope of the yield curve (Ki is not consistent with the maximum slope of yield curve), Ki is set to the maximum slope of the curve.

  7. If hardening flag Hi is 4, the loading curve should be positive for all values of abscissa. The unloading curve in this case should be negative for all values of abscissa. For flag 4, these curves represents upper and lower limits of yield force as function of current spring length variation or strain. The force jumps between the curves each time when the direction of deformation changes.
  8. If hardening flag Hi is 5, residual deformation is a function of maximum displacement:

    δ resid = f N 3 ( δ max i ) with i =1, 2, 3

    θ resid = f N 3 ( θ max i ) with i =4, 5, 6

  9. For linear springs, f ( δ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGMbWaae WaceaacqaH0oazaiaawIcacaGLPaaaaaa@3A7A@ and g ( δ ˙ ) (or f ( θ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGMbWaae WaceaacqaH4oqCaiaawIcacaGLPaaaaaa@3A8B@ and g ( θ ˙ ) ) are null functions and Ai, Bi, and Ei, are not taken into account.
  10. The third node in element definition is not used to determine local coordinate system of the spring. The local coordinate system is determined either by setting a skew or by using global coordinate system, when the skew is not given.
  11. Spring is in compression in a given direction of local coordinate system, when projection of direction from initial position of node N1 to current position of node N1 to the direction of the local coordinate system is positive. Otherwise, the spring is in tension in corresponding direction of local coordinate system.
  12. Spring is activated and/or deactivated by sensor:
    • If sens_ID ≠ 0 and Isflag = 0, the spring element is activated by the sens_ID.
    • If sens_ID ≠ 0 and Isflag = 1, the spring element is deactivated by the sens_ID.
    • If sens_ID 0 and Isflag = 2, then:
      • The spring is activated and, or, deactivated by sensor sens_ID (if sensor is ON, spring is ON; if sensor is OFF, spring is OFF)
      • The spring reference length ( l 0 ) is the distance between node N1 and N2 at the time of sensor activation.

    If a sensor is used for activating or deactivating a spring, the reference length of the spring at sensor activation (or deactivation) is equal to the nodal distance at time = 0; except if sensor flag is equal to 2.