/MAT/LAW108 (SPR_GENE)

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

Deformation, force and energy-based failure criteria are available. The general spring material is often used to model a joint connection between two parts. This material must be assigned to a /PART that references the spring property /PROP/TYPE23 (SPR_MAT).

Format


(1)	(2)	(3)
/MAT/LAW108/`mat_ID`/`unit_ID` or /MAT/SPR_GENE/`mat_ID`/`unit_ID`
`mat_title`
$ρ$
`I`_fail	`I`_equil	`I`_fail2

Loading index=1: Translation in X


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

Loading index=2: Translation in Y


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

Loading index=3: Translation in Z


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

Loading index=4: Rotation in X


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

Loading index=5: Rotation in Y


(1)	(2)	(3)	(4)	(5)	(7)	(9)
`K`₅		`C`₅		`A`₅	`B`₅	`D`₅
`fct_ID`₁₅	`H`₅	`fct_ID`₂₅	`fct_ID`₃₅	`fct_ID`₄₅	$θ_{min}^{5}$	$θ_{max}^{5}$
`F`₅		`E`₅		`Ascale`₅	`Hscale`₅

Loading index=6: Rotation in Z


(1)	(2)	(3)	(4)	(5)	(7)	(9)
`K`₆		`C`₆		`A`₆	`B`₆	`D`₆
`fct_ID`₁₆	`H`₆	`fct_ID`₂₆	`fct_ID`₃₆	`fct_ID`₄₆	$θ_{min}^{6}$	$θ_{max}^{6}$
`F`₆		`E`₆		`Ascale`₆	`Hscale`₆

Filtering force


(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`F`_smooth	`F`_cut

Definition


Field	Contents	SI Unit Example
`prop_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`prop_title`	Material title. (Character, maximum 100 characters)
$ρ$	Density. (Real)	$[\frac{kg}{m^{3}}]$
`I`_fail	Failure criteria. = 0 Uni-directional criteria. = 1 Multi-directional criteria. (Integer)
`I`_equil	Equilibrium flag. 5 6 = 0 No equilibrium. = 1 Force and moment equilibrium. (Integer)
`I`_fail2	Failure model flag. = 0 (Default) Displacement and rotation criteria. = 1 Force criteria (moment criteria). = 3 Internal energy criteria. (Integer)
`K`_i	If $f c t_I D_{1 i} = 0$ : Linear loading and unloading stiffness. If $f c t_I D_{1 i} \neq 0$ : Only used as unloading stiffness for elasto-plastic springs. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Comment 7 (Real)	$[\frac{N}{m}]$ for $i$ =1, 2, 3 $[\frac{Nm}{rad}]$ for $i$ =4, 5, 6
`C`_i	Damping. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF (Real)	$[\frac{N s}{m}]$ for $i$ =1, 2, 3 $[\frac{Nms}{rad}]$ for $i$ =4, 5, 6
`A`_i	Nonlinear stiffness function scale factor. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = 1.0 (Real)	$[N]$ for $i$ =1, 2, 3 $[Nm]$ for $i$ =4, 5, 6
`B`_i	Logarithmic rate effects scale factor. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = 0.0 (Real)	$[N]$ for $i$ =1, 2, 3 $[Nm]$ for $i$ =4, 5, 6
`D`_i	Logarithmic rate effects scale factor. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = 1.0 (Real)	$[\frac{m}{s}]$ for $i$ =1, 2, 3 $[\frac{rad}{s}]$ for $i$ =4, 5, 6
`fct_ID`_1i	Function identifier defining nonlinear stiffness $f ()$ . 7 = 0 Linear spring with stiffness `K` If `H`₁ = 4: Function identifier defining upper yield curve. If `H`₁ = 8: Function is mandatory and defines the force or moment versus spring length. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF (Integer)
`H`_i	Nonlinear Spring Hardening flag for nonlinear spring. =0 Elastic spring. =1 Nonlinear elastic plastic spring with isotropic hardening. =2 Nonlinear elastic plastic spring with uncoupled hardening. =4 Nonlinear elastic plastic spring with kinematic hardening. =5 Nonlinear elastic plastic spring with nonlinear unloading. =6 Nonlinear elastic plastic spring with isotropic hardening and nonlinear unloading. =7 Nonlinear elastic plastic spring with elastic hysteresis. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF (Integer)
`fct_ID`_2i	Function identifier defining force or moment as a function of spring velocity $g ()$ . $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF (Integer)
`fct_ID`_3i	Function identifier. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF If `H`₁ = 4: Defines lower yield curve. If `H`₁ = 5: Defines residual displacement or rotation versus maximum displacement or rotation. If `H`₁= 6: Defines nonlinear unloading curve. If `H`₁= 7: Defines nonlinear unloading curve. (Integer)
`fct_ID`_4i	Function identifier for nonlinear damping $h ()$ . $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF (Integer)
$δ_{\min}^{i}$	Negative translation failure limit. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = -10³⁰ (Real)
	If `I`_fail2=0: Failure displacement	$[m]$
	If `I`_fail2=1: Failure force	$[N]$
	If `I`_fail2=2: Failure internal energy	$[J]$
$θ_{\min}^{i}$	Negative rotational failure limit. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = -10³⁰ (Real)
	If `I`_fail2=0: Failure rotation	$[rad]$
	If `I`_fail2=1: Failure moment	$[N \cdot m]$
	If `I`_fail2=2: Failure internal energy	$[J]$
$δ_{\max}^{i}$	Positive transition failure limit. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = 10³⁰ (Real)
	If `I`_fail2=0: Failure displacement	$[m]$
	If `I`_fail2=1: Failure force	$[N]$
	If `I`_fail2=2: Failure internal energy	$[J]$
$θ_{\max}^{i}$	Positive rotational failure limit. $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = -10³⁰ (Real)
	If `I`_fail2=0: Failure rotation	$[rad]$
	If `I`_fail2=1: Failure moment	$[N \cdot m]$
	If `I`_fail2=2: Failure internal energy	$[J]$
`F`_i	Abscissa scale factor for the damping functions for the $g$ and $h$ . $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = 1.0 (Real)	$[\frac{m}{s}]$ for $i$ =1, 2, 3 $[\frac{rad}{s}]$ for $i$ =4, 5, 6
`E`_i	Ordinate scale factor for the damping function $g$ . $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF (Real)	$[N]$ for $i$ =1, 2, 3 $[Nm]$ for $i$ =4, 5, 6
`Ascale`_i	Abscissa scale factor for the stiffness function $f$ . $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = 1.0 (Real)	$[m]$ for $i$ =1, 2, 3 $[rad]$ for $i$ =4, 5, 6
`Hscale`_i	Ordinate Scale factor for the damping function $h$ . $i$ =1, 2, 3 are translation DOF $i$ =4, 5, 6 are rotation DOF Default = 1.0 (Real)	$[N]$ for $i$ =1, 2, 3 $[Nm]$ for $i$ =4, 5, 6
`F`_smooth	Smooth strain rate flag. =0(Default) Strain rate smoothing is inactive. =1 Strain rate smoothing is active. (Integer)
`F`_cut	Strain rate cutting frequency. Default = 10³⁰ (Real)	$[Hz]$

Example (Spotweld - No Rupture)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. LOCAL_UNIT_SYSTEm:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/2
units for material and property
                  kg                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/PROP/TYPE23/6680004/2
SPOTWELD_NO_RUPTURE
#    Imass                          Area             Inertia   skew_ID   sens_ID    Isflag     
         2                          8E+3                .002         0         0         0 
/MAT/LAW108/6680004/2
TYPE8
#            Density
                1E-6
#    Ifail    Iequil    Ifail2
                   0             
#              KTens               CTens               ATens               BTens               DTens
                 1.8                   0                   0                   0                   0
#  fct_ID1     HTens   fct_ID2   fct_ID3   fct_ID4                 delta_minTens       delta_maxTens
                   0         0         0         0                             0                   0
#                  F                   E              Ascale             Hscalex
                   0                   0                   0                   0
#              KTens               CTens               ATens               BTens               DTens
                  .3                   0                   0                   0                   0
#  fct_ID1     HTens   fct_ID2   fct_ID3   fct_ID4                 delta_minTens       delta_maxTens
                   0         0         0         0                             0                   0
#                  F                   E              Ascale             Hscalex
                   0                   0                   0                   0
#              KTens               CTens               ATens               BTens               DTens
                 1.8                   0                   0                   0                   0
#  fct_ID1     HTens   fct_ID2   fct_ID3   fct_ID4                 delta_minTens       delta_maxTens
                   0         0         0         0                             0                   0
#                  F                   E              Ascale             Hscalex
                   0                   0                   0                   0
#                  K                   C                   A                   B                   D
    114.649681528662                   0                   0                   0                   0
#       N1         H        N2        N3        N4                     theta_min           theta_max
                   0         0         0         0                             0                   0
#                  F                   E              Ascale             Hscalex
                   0                   0                   0                   0
#                  K                   C                   A                   B                   D
    114.649681528662                   0                   0                   0                   0
#       N1         H        N2        N3        N4                     theta_min           theta_max
                   0         0         0         0                             0                   0
#                  F                   E              Ascale             Hscalex
                   0                   0                   0                   0
#                  K                   C                   A                   B                   D
    114.649681528662                   0                   0                   0                   0
#       N1         H        N2        N3        N4                     theta_min           theta_max
                   0         0         0         0                             0                   0
#                  F                   E              Ascale             Hscalex

#   ISTRAT             ASTRAT 
         0                   0
#enddata

Comments

When used with /PROP/TYPE23 (SPR_MAT), this material law has the same behavior as spring property /PROP/TYPE8 (SPR_GENE); except that in this material the mass is calculated from the density and volume, or density, area and length.
Inputs repeated for each degree of freedom (DOF) $i$ are defined with the following directions:
- $i$ =1: tension/compression
- $i$ =2: shear xy
- $i$ =3: shear xz
- $i$ =4: torsion
- $i$ =5: bending y
- $i$ =6: bending z
This spring should only be used when the spring has zero initial length or when one of the spring nodes is constrained in all directions. For other situations, the equilibrium is insured for forces, but not for moments. Thus, the moment calculation can be incorrect. If the initial spring length is not zero, use /PROP/TYPE13 (SPR_BEAM) or /MAT/LAW113 (SPR_BEAM).
The spring has six DOF $δ^{1}, δ^{2}, δ^{3}, θ^{4}, θ^{5}, θ^{6}$ computed in a local coordinate system. The local system can be defined for each element using /SPRING Skew_ID. If Skew_ID is not defined for each element, the local system defined in the /PROP/TYPE23 (SPR_MAT) Skew_ID is used. If a system is not defined in the element or property, then the global system is used.
The sign (tension or compression) of the spring force depends on the relative displacement of Node N2 with respect to Node N1. If the movement of node N2 relative to node N1 is in the positive direction of the spring system, then the spring is in tension. If the movement of node N2 relative to node N1 is in the negative direction of the spring system, then the spring is in compression.
If I_equil = 0 (no equilibrium), then:
$f (θ) = M_{2 y} = - M_{1 y}$
$M_{2 y}$ is moment in $Y$ by N₂
$M_{1 y}$ is moment in $Y$ by N₁
If I_equil = 1 (force and moment equilibrium), then:
$- M_{1 y} \neq M_{2 y} - M_{1 z} \neq M_{2 z}$
$f (θ) = \frac{M_{2 y} - M_{1 y}}{2}$
$M_{2 y}$ is moment in $Y$ by N₂
$M_{1 y}$ is moment in $Y$ by N₁
$M_{2 z}$ is moment in $Z$ by N₂
$M_{1 z}$ is moment in $Z$ by N₁
Force and moment computation.
- $δ$ is a translational DOF, the force in direction $δ$ is computed as:
  $F (δ) = f (\frac{δ^{i}}{A s c a l e_{i}}) [A_{i} + B_{i} \ln | \frac{{\dot{δ}}^{i}}{D_{i}} | + E_{i} g (\frac{{\dot{δ}}^{i}}{F_{i}})] + C_{i} {\dot{δ}}^{i} + H s c a l e_{i} h (\frac{{\dot{δ}}^{i}}{F_{i}})$ with $i$ =1,2,3
- $θ$ is a rotational DOF, the moment is computed as:
  $M (θ) = f (\frac{θ^{i}}{A s c a l e_{i}}) [A_{i} + B_{i} \ln | \frac{{\dot{θ}}^{i}}{D_{i}} | + E_{i} g (\frac{{\dot{θ}}^{i}}{F_{i}})] + C_{i} {\dot{θ}}^{i} + H s c a l e_{i} h (\frac{{\dot{θ}}^{i}}{F_{i}})$ with $i$ =4,5,6
  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, $f (δ), g (\dot{δ}), h (\dot{δ})$ and $k (δ) \cdot (f (θ), g (\dot{θ}), h (\dot{θ}) and k (θ))$ are zero functions and $A_{i}$ , $B_{i}$ , $E_{i}$ and $H s c a l e_{i}$ 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 slop 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.
Note that material density and inertia in /PROP/TYPE23 must not be null to ensure that the nodes connected by such a spring get a non-zero mass and inertia, unless they are secondary nodes of a rigid body, in which case unrealistically high stiffness and damping values are avoided.
If the nodes connected by such a spring get a zero mass and inertia, they can still be secondary nodes of a rigid body, except for rigid bodies activated by a sensor. The rigid body cannot be set to OFF in the Radioss Engine.
It is not possible to use elementary time step for springs with null density or null inertia in the model. Nodal Time Step or Advanced Mass Scaling must be used. If control time step is not set to Nodal Time Step, neither Advanced Mass Scaling in the Radioss Engine nor Nodal Time Step will be turned ON automatically.