/PROP/TYPE25 (SPR_AXI)

Block Format Keyword This property set is used to define the axisymmetric spring property set.

Format

(1)	(3)	(5)	(6)	(7)	(8)	(9)	(10)
/PROP/TYPE25/`prop_ID`/`unit_ID` or /PROP/SPR_AXI/`prop_ID`/`unit_ID`
`prop_title`
`Mass`	`Inertia`	`Skew_ID`	`sens_ID`	`I`_sflag	`I`_fail	`I`_leng	`I`_fail2

Loading index=1: Tension/Compression

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(9)
`K`₁		`C`₁		`A`₁		`B`₁	`D`₁
`fct_ID`₁₁	`H`₁	`fct_ID`₂₁	`fct_ID`₃₁	`F`₁		$δ_{min}^{1}$	$δ_{max}^{1}$
`Ascale`₁		`E`₁		`fct_ID`₄₁	`Hscale`₁

Loading index=2: Shear (Radial)

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(9)
`K`₂		`C`₂		`A`₂		`B`₂	`D`₂
`fct_ID`₁₂	`H`₂	`fct_ID`₂₂	`fct_ID`₃₂	`F`₂		$δ_{min}^{2}$	$δ_{max}^{2}$
`Ascale`₂		`E`₂		`fct_ID`₄₂	`Hscale`₂

Loading index=3: Torsion

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(9)
`K`₃		`C`₃		`A`₃		`B`₃	`D`₃
`fct_ID`₁₃	`H`₃	`fct_ID`₂₃	`fct_ID`₃₃	`F`₃		$θ_{min}^{3}$	$θ_{max}^{3}$
`Ascale`₃		`E`₃		`fct_ID`₄₃	`Hscale`₃

Loading index=4: Bend (Radial)

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(9)
`K`₄		`C`₄		`A`₄		`B`₄	`D`₄
`fct_ID`₁₄	`H`₄	`fct_ID`₂₄	`fct_ID`₃₄	`F`₄		$θ_{min}^{4}$	$θ_{max}^{4}$
`Ascale`₄		`E`₄		`fct_ID`₄₄	`Hscale`₄

(1)	(3)	(5)	(7)
$v_{0}$	$ω_{0}$
`C`₁	`n`₁	$α_{1}$	$β_{1}$
`C`₂	`n`₂	$α_{2}$	$β_{2}$
`C`₃	`n`₃	$α_{3}$	$β_{3}$
`C`₄	`n`₄	$α_{4}$	$β_{4}$

Definition

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`	Spring mass. If `I`_leng = 0, $M$ If `I`_leng = 1, $M \cdot l_{0}$ (Real)	$[kg]$ or $[kg \cdot m]$
`Inertia`	Spring inertia. If `I`_leng = 0, $I$ If `I`_leng = 1, $I \cdot l_{0}$ (Real)	$[m^{2} kg]$ or $[m^{3} kg]$
`Skew_ID`	Skew system identifier. (Integer)
`sens_ID`	Sensor identifier. (Integer)
`I`_sflag	Sensor flag. 4 =0 Spring element activated. =1 Spring element deactivated. (Integer)
`I`_fail	Failure criteria. = 0 Uni-directional criteria. = 1 Multi-directional criteria. (Integer)
`I`_leng	Input per unit length flag. 2 = 0 The force in the spring is computed as previously detailed formula. = 1 All input are per unit length. (Integer)
`I`_fail2	Failure model flag. = 0 (Default) Displacement (or rotation) criteria. = 1 Displacement (or rotation) criteria considering velocity effect. = 2 Force (or moment) criteria. = 3 Internal energy criteria. (Integer)
`K`_i	Stiffness $K$ with `I`_leng=0 or $\frac{K}{l_{0}}$ with `I`_leng=1. If $i$ =1 Stiffness for tension/compression. If $i$ =2 Stiffness for shear (radial). (Real)	$[\frac{N}{m}]$ or $[\frac{N}{m^{2}}]$
`K`_i	Stiffness $K$ with `I`_leng=0 or $\frac{K}{θ_{0}}$ with `I`_leng=1. If $i$ =3 Stiffness for torsion. If $i$ =4 Stiffness for bending (radial). (Real)	$[\frac{Nm}{rad}]$ or $[\frac{N m}{r a d^{2}}]$
`C`_i	Damping $C$ with `I`_leng=0 or $\frac{C}{l_{0}}$ with `I`_leng=1. If $i$ =1 Damping for tension/compression. If $i$ =2 Damping for shear (radial). (Real)	$[\frac{Ns}{m}]$ or $[N s]$
`C`_i	Damping $C$ with `I`_leng=0 or $\frac{C}{θ_{0}}$ with `I`_leng=1. If $i$ =3 Damping for torsion. If $i$ =4 Damping for bending (radial). (Real)	$[\frac{Nms}{rad}]$ or $[Nms]$
`A`_i	Coefficient for strain rate effect. If $i$ =1 Coefficient for tension/compression. If $i$ =2 Coefficient for shear (radial). Default = 1.0 (Real)	$[N]$
`A`_i	Coefficient for strain rate effect. If $i$ =3 Coefficient for torsion. If $i$ =4 Coefficient for bending (radial). Default = 1.0 (Real)	$[Nm]$
`B`_i	Logarithmic coefficient for strain rate effect. If $i$ =1 Coefficient for tension/compression. If $i$ =2 Coefficient for shear (radial). Default = 0.0 (Real)	$[N]$
`B`_i	Logarithmic coefficient for strain rate effect. If $i$ =3 Coefficient for torsion. If $i$ =4 Coefficient for bending (radial). Default = 0.0 (Real)	$[Nm]$
`D`_i	Strain coefficients for velocity. If $i$ =1 Coefficient for tension/compression. If $i$ =2 Coefficient for shear (radial). Default = 1.0 (Real)	$[\frac{m}{s}]$
`D`_i	Strain coefficients for velocity. If $i$ =3 Coefficient for torsion. If $i$ =4 Coefficient for bending (radial). Default = 1.0 (Real)	$[\frac{rad}{s}]$
`fct_ID`₁₁	Stiffness function identifier. = 0 Linear spring. ≠ 0 Nonlinear spring. If $i$ =1 Stiffness function $f (δ)$ in tension/compression. If $i$ =2 Stiffness function $f (δ)$ in shear (radial). If `H`_i =4: Function $f (δ)$ defining upper yield curve for load index. (Integer)
`fct_ID`₁₁	Stiffness function identifier. = 0 Linear spring. ≠ 0 Nonlinear spring. If $i$ =3 Stiffness function $f (θ)$ in torsion. If $i$ =4 Stiffness function $f (θ)$ in bending (radial). If `H`_i =4: Function $f (θ)$ defining upper yield curve for load index. (Integer)
`H`_i	Hardening flag for nonlinear spring in different load cases with load index $i$ =1,2,3,4. = 0 Nonlinear elastic spring. = 1 Nonlinear elasto-plastic spring with isotropic hardening. = 2 Nonlinear elasto-plastic spring with decoupled hardening in tension and compression. = 4 Nonlinear elastic plastic spring with 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_ID`_2i	Function defining the change in force with spring displacement rate in $g (\dot{δ})$ . If $i$ =1 Function $g (\dot{δ})$ in tension/compression. If $i$ =2 Function $g (\dot{δ})$ in shear (radial). (Integer)
`fct_ID`_2i	Function defining the change in moment with spring rotation rate in $g (\dot{θ})$ . If $i$ =3 Function $g (\dot{θ})$ in torsion. If $i$ =4 Function $g (\dot{θ})$ in bending (radial). (Integer)
`fct_ID`_3i	Function used only for unloading in transition direction loading index $i$ =1,2. If `H`_i=4 Function identifier defining lower yield curve (transitional). If `H`_i=5 Function identifier defining residual displacement versus maximum displacement. If `H`_i=6 Function identifier defining nonlinear unloading curve. If `H`_i=7 Function identifier defining nonlinear unloading curve (relative displacement). (Integer)
`fct_ID`_3i	Function used only for unloading in rotational direction loading index $i$ =3,4. If `H`_i=4 Function identifier defining lower yield curve (rotational). If `H`_i=5 Function identifier defining residual rotation versus maximum rotation. If `H`_i=6 Function identifier defining nonlinear unloading curve. If `H`_i=7 Function identifier unloading curve for moment versus rotation (relative rotation). (Integer)
`fct_ID`_4i	Function to consider velocity or deformation velocity dependency damping in $h (\dot{δ})$ . If $i$ =1 Function $h (\dot{δ})$ in tension/compression. If $i$ =2 Funciton $h (\dot{δ})$ in shear (radial). (Integer)
`fct_ID`_4i	Function to consider velocity or deformation velocity dependency damping in $h (\dot{θ})$ . If $i$ =3 Function $h (\dot{θ})$ in torsion. If $i$ =4 Function $h (\dot{θ})$ in bending (radial). (Integer)
`Hscale`_i	Scale factor to homogeneous a force for $h (\dot{δ})$ (`fct_ID`_4i function). If $i$ =1 In tension/compression. If $i$ =2 In shear (radial). Default = 1.0 (Real)	$[N]$
`Hscale`_i	Scale factor to homogeneous a moment for $h (\dot{θ})$ (`fct_ID`_4i function). If $i$ =3 In torsion. If $i$ =4 In bending (radial). Default = 1.0 (Real)	$[Nm]$
`F`_i	Scale factor for $\dot{δ}$ (abscissa of `fct_ID`_2i function for $g (\dot{δ})$ ) in function. If $i$ =1 In tension/compression. If $i$ =2 In shear (radial). (Real)	$[\frac{m}{s}]$
`F`_i	Scale factor for $\dot{θ}$ (abscissa of `fct_ID`_2i function for $g (\dot{θ})$ ) in function. If $i$ =3 In torsion. If $i$ =4 In bending (radial). (Real)	$[\frac{rad}{s}]$
$δ_{min}^{i}$	Loading index $i$ =1, 2. Negative transitional failure limit. Default = -10³⁰ (Real)
	If `I`_fail2 = 0, 1: Failure displacement in transitional direction.	$[m]$
	If `I`_fail2 = 2: Failure force in transitional direction.	$[N]$
	If `I`_fail2 = 3: Failure internal energy related to transitional direction.	$[J]$
$θ_{\min}^{i}$	Loading index $i$ = 3, 4. Negative rotational failure limit. Default = -10³⁰ (Real)
	If `I`_fail2 = 0, 1: Failure rotation in rotational direction.	$[rad]$
	If `I`_fail2 = 2: Failure moment in rotational direction.	$[N \cdot m]$
	If `I`_fail2 = 3: Failure internal energy related to rotational direction.	$[J]$
$δ_{max}^{i}$	Loading index $i$ =1, 2. Positive transitional failure limit. Default = 10³⁰ (Real)
	If `I`_fail2 = 0, 1: Failure displacement in transitional direction.	$[m]$
	If `I`_fail2 = 2: Failure force in transitional direction.	$[N]$
	If `I`_fail2 = 3: Failure internal energy related to transitional direction.	$[J]$
$θ_{max}^{i}$	Loading index $i$ = 3, 4. Positive rotational failure limit. Default = 10³⁰ (Real)
	If `I`_fail2 = 0, 1: Failure rotation in rotational direction.	$[rad]$
	If `I`_fail2 = 2: Failure moment in rotational direction.	$[N \cdot m]$
	If `I`_fail2 = 3: Failure internal energy related to rotational direction.	$[J]$
`Ascale`_i	Scale factor for $δ$ (abscissa of `fct_ID`_1i and `fct_ID`_3i function for $f (δ)$ ). If $i$ =1 In tension/compression. If $i$ =2 In shear (radial). Default = 1.0 (Real)	$[m]$
`Ascale`_i	Scale factor for $θ$ (abscissa of `fct_ID`_1i and `fct_ID`_3i function for $f (θ)$ ). If $i$ =3 In torsion. If $i$ =4 In bending (radial). Default = 1.0 (Real)	$[rad]$
`E`_i	Scale factor for $g (\dot{δ})$ (`fct_ID`_2i function). It is the coefficient for strain rate effect (homogeneous to a force). If $i$ =1 In tension/compression. If $i$ =2 In shear (radial). (Real)	$[N]$
`E`_i	Scale factor for $g (\dot{θ})$ (`fct_ID`_2i function). It is the coefficient for strain rate effect (homogeneous to a moment). If $i$ =3 In torsion. If $i$ =4 In bending (radial). (Real)	$[Nm]$
$v_{0}$	Reference translational velocity. Default = 1.0 (Real)	$[\frac{m}{s}]$
$ω_{0}$	Reference rotational velocity. Default = 1.0 (Real)	$[\frac{rad}{s}]$
`c`_i	Relative velocity coefficient in different load case (with load index $i$ =1,2,3,4). Default = 0.0 (Real)
	If `I`_fail2=0,1: Coefficient for failure displacement with $i$ =1,2. Coefficient for failure rotation with $i$ =3,4.	$[m]$ or $[rad]$
	If `I`_fail2=2: Coefficient for failure force $i$ =1,2,3. Coefficient for failure moment $i$ =3,4.	$[N]$ or $[N \cdot m]$
	If `I`_fail2=3: Coefficient for failure internal energy $i$ =1,2,3,4.	$[J]$
`n`_i	Relative velocity exponent. If $i$ =1 In tension/compression. If $i$ =2 In shear (radial). If $i$ =3 In torsion. If $i$ =4 In bending (radial). Default = 0.0 (Real)
$α_{i}$	"Mult" factor. If $i$ =1 In tension/compression. If $i$ =2 In shear (radial). If $i$ =3 In torsion. If $i$ =4 In bending (radial). Default = 1.0 (Real)
$β_{i}$	Exponent. If $i$ =1 In tension/compression. If $i$ =2 In shear (radial). If $i$ =3 In torsion. If $i$ =4 In bending (radial). Default = 2.0 (Real)

Comments

In this spring property, depend on input, Spring Local Coordinate System determined by the input of Node N3, skew or global system.
Force and moment computation:
- In case of I_leng =0, the force in the spring is computed as:
  with $i$ =1,2(1)
  $F (δ) = f (\frac{δ^{i}}{A s c a l e_{i}}) [A_{i} + B_{i} \ln (\max (1, | \frac{{\dot{δ}}^{i}}{D_{i}} |)) + E_{i} g (\frac{{\dot{δ}}^{i}}{F_{i}})] + C_{i} {\dot{δ}}^{i} + H s c a l e_{i} h (\frac{{\dot{δ}}^{i}}{F_{i}})$
  with $i$ =3,4(2)
  $M (θ) = f (\frac{θ^{i}}{A s c a l e_{i}}) [A_{i} + B_{i} \ln (\max (1, | \frac{{\dot{θ}}^{i}}{D_{i}} |)) + E_{i} g (\frac{{\dot{θ}}^{i}}{F_{i}})] + C_{i} {\dot{θ}}^{i} + H s c a l e_{i} h (\frac{{\dot{θ}}^{i}}{F_{i}})$
  
  with $- l_{0} < δ < + \infty$
  Where,
  - $δ^{i}$ (with $- l_{0} < δ^{i} < + \infty$ ) is the difference between the current length $l$ and the initial length $l_{0}$ of the spring element for corresponding translational DOF.
  - $θ^{i}$ is the relative angle for corresponding rotational DOF in radians.
  - For linear springs, $f (δ)$ , $g (\dot{δ})$ , ( $h (\dot{δ}), f (θ), g (\dot{θ})$ and $h (\dot{θ})$ ) are null functions and A_i, B_i, E_i, and Hscale_i are not taken into account.
  - If stiffness function $f (δ)$ (or $f (θ)$ ) is requested, then K is used as a slope for unloading only.
  - If K is lower than the maximum slope of function $f (δ)$ (or $f (θ)$ ), K is not consistent with the maximum slope of the curve), K is set to the maximum slope of the curve.
- If I_leng = 1, all input are per unit length:
  Spring mass = $M \cdot l_{0}$
  
  Spring stiffness = $\frac{K}{l_{0}}$
  
  Spring damping = $\frac{C}{l_{0}}$
  
  Spring inertia = $I \cdot l_{0}$
  
  Where, $l_{0}$ is the spring reference length.
  
  The force in the spring is computed,
  
  with $i$ =1,2(3)
  $F (ε) = f (\frac{ε^{i}}{A s c a l e_{i}}) [A_{i} + B_{i} \ln (\max (1, | \frac{{\dot{ε}}^{i}}{D_{i}} |)) + E_{i} g (\frac{{\dot{ε}}^{i}}{F_{i}})] + C_{i} {\dot{ε}}^{i} + H s c a l e_{i} h (\frac{{\dot{ε}}^{i}}{F_{i}})$
  
  with $i$ =3,4 (4)
  $M (θ) = f (\frac{θ^{i}}{A s c a l e_{i}}) [A_{i} + B_{i} \ln (\max (1, | \frac{{\dot{θ}}^{i}}{D_{i}} |)) + E_{i} g (\frac{{\dot{θ}}^{i}}{F_{i}})] + C_{i} {\dot{θ}}^{i} + H s c a l e_{i} h (\frac{{\dot{θ}}^{i}}{F_{i}})$
  Where, $ε^{i}$ is the engineering strain and defined as: (5)
  $ε^{i} = \frac{δ^{i}}{l_{0}}$
  - Force functions are given versus engineering strain and engineering strain rate.
  - Failure criteria are defined with respect to strain. Input of negative/positive failure limit should be related to initial length.
The decoupled hardening (hardening flag, H_i=2) and kinematic hardening (hardening flag, H_i=4) models are only valid in axial direction (tension and torsion). They are not available in radial direction (shear and bending).
Spring is activated and/or deactivated by sensor:
- If sens_ID ≠ 0 and I_sflag = 0, the spring element is activated by the sens_ID.
- If sens_ID ≠ 0 and I_sflag = 1, the spring element is deactivated by the sens_ID.
- Spring elements with sensor activation or deactivation are mainly used for the pretension model.
- 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.