/PROP/TYPE44 (SPR_CRUS)

Block Format Keyword This is a spring element property, which represents a simple macro model of a crushable frame in compression, tension, torsion and bending.

Originally, this element was developed in cooperation with PSA PEUGEOT CITROËN.

Format

(1)	(2)	(3)	(4)	(5)	(7)	(8)	(9)
/PROP/TYPE44/`prop_ID`/`unit_ID` or /PROP/SPR_CRUS/`prop_ID`/`unit_ID`
`prop_title`
`Mass`/ `L`		`Inertia` / `L`		`K`_inter	`Skew_ID`	`I`_coupling	`I`_filtr
`K`₁₁`L`		`K`₄₄`L`		`K`₅₅`L`	`K`₆₆`L`		`I`_damp
`K`_5b`L`		`K`_6c`L`
`fct_X`_+i	`fct_X`_-i	`fct_X`_-r		`Fscale_X`_Y
`fct_XX`_+i	`fct_XX`_--i	`fct_XX`_+r	`fct_XX`_--r	`Fscale_XX`_Y
`fct_YY1`_+i	`fct_YY1`_-i	`fct_YY1`_+r	`fct_YY1`_-r	`Fscale_YY1`_Y
`fct_ZZ1`_+i	`fct_ZZ1`_-i	`fct_ZZ1`_+r	`fct_ZZ1`_-r	`Fscale_ZZ1`_Y
`fct_YY2`_+i	`fct_YY2`_-i	`fct_YY2`_+r	`fct_YY2`_-r	`Fscale_YY2`_Y
`fct_ZZ2`_+i	`fct_ZZ2`_-i	`fct_ZZ2`_+r	`fct_ZZ2`_-r	`Fscale_ZZ2`_Y
`X_lim_g`		`X_lim`		`XX_lim`
`YY1_lim`		`ZZ1_lim`		`YY2_lim`	`ZZ2_lim`

If I_damp = 1,

(1)	(2)	(4)
`fct_D_x`	`Dscale_x`	`F_x`
`fct_D_y`	`Dscale_y`	`F_y`
`fct_D_z`	`Dscale_z`	`F_z`
`fct_D_xx`	`Dscale_xx`	`F_xx`
`fct_D_yy`	`Dscale_yy`	`F_yy`
`fct_D_zz`	`Dscale_zz`	`F_zz`

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`/ `L`	Frame mass per unit length. (Real)	$[kgm]$
`Inertia`/ `L`	Frame inertia per unit length. (Real)	$[kgm]$
`K`_inter	Contact interface stiffness $K_{i n t e r} = \frac{A E}{L}$ . 2 A Frame area E Young's modulus L Frame length (Real)	$[\frac{N}{m}]$
`Skew_ID`	Skew system identifier. (Integer)
`I`_coupling	Coupling flag. 3 = 0 Each element is computed independently. = 1 Coupling of force and moment in any direction. (Integer)
`K`₁₁`L`	Tensile / Compression stiffness, multiplied by L. (Real)	$[\frac{N}{m}]$
`K`₄₄`L`	Torsional stiffness around X axis, multiplied by L. (Real)	$[{Nm}^{2}]$
`K`₅₅`L`	Bending Y stiffness around Y axis, multiplied by L. (Real)	$[{Nm}^{2}]$
`K`₆₆`L`	Bending Z stiffness around Z axis, multiplied by L. (Real)	$[{Nm}^{2}]$
`K`_5b`L`	Shear Bending XY stiffness axis, multiplied by L. (Real)	$[{Nm}^{2}]$
`K`_6c`L`	Shear Bending XZ stiffness axis, multiplied by L. (Real)	$[{Nm}^{2}]$
`fct_X`_+i	Tensile force function versus strain in X direction. (Integer)
`fct_X`_-i	Initial compression force function versus strain in X-direction. Used for elements in the initial state. 4 (Integer)
`fct_X`_-r	Residual compression force function versus strain in X direction. Used for elements in the residual state. 4 (Integer)
`Fscale_X`_Y	Ordinate scale factor for tensile functions. Default = 1 (Real)
`fct_XX`_+i	Initial torsion moment function versus torsion angle in the positive direction. Used for elements in the initial state. (Integer)	$[N]$
`fct_XX`_-i	Initial torsion moment function versus torsion angle in the negative direction. Used for elements in the initial state. (Integer)
`fct_XX`_+r	Residual torsion moment function versus torsion angle in the positive direction. Used for elements in the residual state. (Integer)
`fct_XX`_-r	Residual torsion moment function versus torsion angle in the negative direction. Used for elements in the residual state. (Integer)
`Fscale_XX`_Y	Ordinate scale factor for torsion moment functions. Default = 1 (Real)	$[{Nm}^{2}]$
`fct_YY1`_+i	Initial bending Y moment function versus bending angle in the positive direction for node 1. Used for elements in the initial state. (Integer)
`fct_YY1`_-i	Initial bending Y moment function versus bending angle in the negative direction for node 1. Used for elements in the initial state. (Integer)
`fct_YY1`_+r	Residual bending Y moment function versus bending angle in the positive direction for node 1. Used for elements in the residual state. (Integer)
`fct_YY1`_-r	Residual bending Y moment function versus bending angle in the negative direction for node 1. Used for elements in the residual state. (Integer)
`Fscale_YY1`_Y	Ordinate scale factor for bending Y moment functions for node 1. Default = 1 (Real)	$[Nm]$
`fct_ZZ1`_+i	Initial bending Z moment function versus bending angle in the positive direction for node 1. Used for elements in the initial state. (Integer)
`fct_ZZ1`_-i	Initial bending Z moment function versus bending angle in the negative direction for node 1. Used for elements in the initial state. (Integer)
`fct_ZZ1`_+r	Residual bending Z moment function versus bending angle in the positive direction for node 1. Used for elements in the residual state. (Integer)
`fct_ZZ1`_-r	Residual bending Z moment function versus bending angle in the negative direction for node 1. Used for elements in the residual state. (Integer)
`Fscale_ZZ1`_Y	Ordinate scale factor for bending Z moment functions for node 1. Default = 1 (Real)	$[Nm]$
`fct_YY2`_+i	Initial bending Y moment function versus bending angle in the positive direction for node 2. Used for elements in the initial state. (Integer)
`fct_YY2`_-i	Initial bending Y moment function versus bending angle in the negative direction for node 2. Used for elements in the initial state. (Integer)
`fct_YY2`_+r	Residual bending Y moment function versus bending angle in the positive direction for node 2. Used for elements in the residual state. (Integer)
`fct_YY2`_-r	Residual bending Y moment function versus bending angle in the negative direction for node 2. Used for elements in the residual state. (Integer)
`Fscale_YY2`_Y	Ordinate scale factor for bending Y moment functions for node 2. Default = 1 (Real)	$[Nm]$
`fct_ZZ2`_+i	Initial bending Z moment function versus bending angle in the positive direction for node 2. Used for elements in the initial state. (Integer)
`fct_ZZ2`_-i	Initial bending Z moment function versus bending angle in the negative direction for node 2. Used for elements in the initial state. (Integer)
`fct_ZZ2`_+r	Residual bending Z moment function versus bending angle in the positive direction for node 2. Used for elements in the residual state. (Integer)
`fct_ZZ2`_-r	Residual bending Z moment function versus bending angle in the negative direction for node 2. Used for elements in the residual state. (Integer)
`Fscale_ZZ2`_Y	Ordinate scale factor for bending Z moment functions for node 2. Default = 1 (Real)	$[Nm]$
`X_lim_g`	Global strain limit in X direction to switch the elements and neighboring frame elements from initial into residual state. This indicates the frame element is completely collapsed. (Real)
`X_lim`	Same as before, but the switch occurs when strains in the X-direction exceed the limit. (Real)
`XX_lim`	Same as before, but the switch occurs when shear strains in the XX-direction (torsion) exceeds the limit. (Real)	$[rad]$
`YY1_lim`	Same as before, but the switch occurs when shear strains in the YY-direction on node 1 exceeds the limit. For neighboring element sharing node 1, all DOFs linked to the node will be switched to the residual state. (Real)	$[rad]$
`ZZ1_lim`	Same as before, but the switch occurs when shear strains in the ZZ-direction on node 1 exceeds the limit. For neighboring element sharing node 1, all DOFs linked to the node will be switched to the residual state. (Real)	$[rad]$
`YY2_lim`	Same as before, but the switch occurs when shear strains in the YY-direction on node 2 exceeds the limit. For neighboring element sharing node 2, all DOFs linked to the node will be switched to the residual state. (Real)	$[rad]$
`ZZ2_lim`	Same as before, but the switch occurs when shear strains in the ZZ-direction on node 2 exceeds the limit. For neighboring element sharing node 2, all DOFs linked to the node will be switched to the residual state. (Real)	$[rad]$
`I`_filtr	Strain rate filtering flag. = 0 No strain rate filtering. = 1 With strain rate filtering. (Integer)
`I`_damp	Damping flag. = 0 No damping. = 1 With damping. (Integer)
`fct_D_x`	Damping force-elongation rate curve for X - DOF.
`fct_D_y`	Damping force-elongation rate curve for Y - DOF.
`fct_D_z`	Damping force-elongation rate curve for Z - DOF.
`fct_D_xx`	Damping force-elongation rate curve for XX - DOF.
`fct_D_yy`	Damping force-elongation rate curve for YY - DOF.
`fct_D_zz`	Damping force-elongation rate curve for ZZ - DOF.
`Dscale_x`	Linear damping or function damping scale factor for X – DOF. Default = 1 (See Comment 10) (Real)	$[\frac{kg}{s}]$ or $[N]$
`Dscale_y`	Linear damping or function damping scale factor for Y – DOF. Default = 1 (See Comment 10) (Real)	$[\frac{kg}{s}]$ or $[N]$
`Dscale_z`	Linear damping or function damping scale factor for Z – DOF. Default = 1 (See Comment 10) (Real)	$[\frac{kg}{s}]$ or $[N]$
`Dscale_xx`	Linear damping or function damping scale factor for XX – DOF. Default = 1 (See Comment 10) (Real)	$[\frac{k g \cdot m}{s}]$ or $[Nm]$
`Dscale_yy`	Linear damping or function damping scale factor for YY – DOF. Default = 1 (See Comment 10) (Real)	$[\frac{k g \cdot m}{s}]$ or $[Nm]$
`Dscale_zz`	Linear damping or function damping scale factor for ZZ – DOF. Default = 1 (See Comment 10) (Real)	$[\frac{k g \cdot m}{s}]$ or $[Nm]$
`F_x`	Abscissa scale factor on Force-elongation rate curve X - DOF. Default = 1 (See Comment 10) (Real)	$[\frac{m}{s}]$
`F_y`	Abscissa scale factor on Force-elongation rate curve Y - DOF. Default = 1 (See Comment 10) (Real)	$[\frac{m}{s}]$
`F_z`	Abscissa scale factor on Force-elongation rate curve Z - DOF. Default = 1 (See Comment 10) (Real)	$[\frac{m}{s}]$
`F_xx`	Abscissa scale factor on Force-elongation rate curve XX - DOF. Default = 1 (See Comment 10) (Real)	$[\frac{1}{s}]$
`F_yy`	Abscissa scale factor on Force-elongation rate curve YY - DOF. Default = 1 (See Comment 10) (Real)	$[\frac{1}{s}]$
`F_zz`	Abscissa scale factor on Force-elongation rate curve ZZ - DOF. Default = 1 (See Comment 10) (Real)	$[\frac{1}{s}]$

Example

In this example, besides stiffness there are also functions to describe the tension, compression, torsion, bending Y, and bending Z load case.

#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
unit for prop
#              MUNIT               LUNIT               TUNIT
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. GEOMETRICAL SETS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/PROP/TYPE44/2/2
prop44 example
#             MASS/L           INERTIA/L              Kinter   Skew_Id Icoupling   Ifilter
              .01267                  52                   0         0         0         0
#                K11                 K44                 K55                 K66     Idamp
           341270000           645300000         17692570000         27269000000         0
#                K5b                 K6c
           200000000           300000000
#FUNCT_X+I FUNCT_X-I FUNCT_X-R                     FSCALE_XY
      1000      1001      1002                             0
#FUNCTXX+I FUNCTXX-I FUNCTXX+R FUNCTXX-R          FSCALE_XXY
      1010      1011      1012      1013                   0
#FUNCYY1+I FUNCYY1-I FUNCYY1+R FUNCYY1-R          FSCALEYY1Y
      1020      1021      1022      1023                   0
#FUNCZZ1+I FUNCZZ1-I FUNCZZ1+R FUNCZZ1-R          FSCALEZZ1Y
      1030      1031      1032      1033                   0
#FUNCYY2+I FUNCYY2-I FUNCYY2+R FUNCYY2-R          FSCALEYY2Y
      1020      1021      1022      1023                   0
#FUNCZZ2+I FUNCZZ2-I FUNCZZ2+R FUNCZZ2-R          FSCALEZZ2Y
      1030      1031      1032      1033                   0
#            X_lim_g               X_lim              XX_lim
               -.709              -.0455                 .34
#            YY1_lim             ZZ1_lim             YY2_lim             ZZ2_lim
                .137               .1396                .138               .1393
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  3. FUNCTIONS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1000
fct_X+i (tension, initial state)
#                  X                   Y
                  -1               10000                                                            
                   0               10000                                                            
               .0012               44500                                                            
                   1               44500                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1001
fct_X-i (compression, initial state)
#                  X                   Y
                 -.9              -71200                                                            
               -.865              -45100                                                            
               -.777              -27500                                                            
               -.708              -14300                                                            
              -.0488              -14200                                                            
              -.0454              -14700                                                            
              -.0299              -21300                                                            
              -.0238              -39700                                                            
                -.02              -44500                                                            
                   0              -38100                                                            
                   1              -38100                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1002
fct_X-r (compression, collapsed state)
#                  X                   Y
                 -.9              -71300                                                            
               -.865              -45200                                                            
               -.777              -27600                                                            
               -.708              -14000                                                            
                   1              -14000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1010
fct_XX+i (initial state)
#                  X                   Y
                  -1              464000                                                            
                   0              464000                                                            
                 .12              486000                                                            
                 .16              479000                                                            
                 .19              453000                                                            
                 .34              193000                                                            
                  .8               70000                                                            
                 1.6              181000                                                            
                 3.3               84000                                                            
                   5               84000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1011
fct_XX-i (initial state)
#                  X                   Y
                  -5              -84000                                                            
                -3.3              -84000                                                            
                -1.6             -181000                                                            
                 -.8              -70000                                                            
                -.34             -193000                                                            
                -.19             -453000                                                            
                -.16             -479000                                                            
                -.12             -486000                                                            
                   0             -464000                                                            
                   1             -464000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1012
fct_XX+r (collapsed state)
#                  X                   Y
                  -1              193000                                                            
                 .34              193000                                                            
                  .8               70000                                                            
                 1.6              181000                                                            
                 3.3               84000                                                            
                   5               84000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1013
fct_XX-r (collapsed state)
#                  X                   Y
                  -5              -84000                                                            
                -3.3              -84000                                                            
                -1.6             -181000                                                            
                 -.8              -70000                                                            
                -.34             -193000                                                            
                   1             -193000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1020
fct_YY1+i, fct_YY2+i (initial state)
#                  X                   Y
                  -1              800000                                                            
                   0              800000                                                            
                .051              895000                                                            
                .082              799000                                                            
                .135              534000                                                            
                 .24              370000                                                            
                 .32              315000                                                            
                   1              315000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1021
fct_YY1-i, fct_YY2-i (initial state)
#                  X                   Y
                  -1             -315000                                                            
                -.32             -315000                                                            
                -.24             -370000                                                            
               -.135             -534000                                                            
               -.082             -799000                                                            
               -.051             -895000                                                            
                   0             -800000                                                            
                   1             -800000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1022
fct_YY1+r, fct_YY2+r (collapsed state)
#                  X                   Y
                  -1              150000                                                            
                 -.9              150000                                                            
                 -.6              178000                                                            
                -.45              250000                                                            
                 -.3              462000                                                            
                 -.2              663000                                                            
                -.15              717000                                                            
                 -.1              674000                                                            
                .135              534000                                                            
                 .24              370000                                                            
                 .32              315000                                                            
                   1              315000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1023
fct_YY1-r, fct_YY2-r (collapsed state)
#                  X                   Y
                  -1             -315000                                                            
                -.32             -315000                                                            
                -.24             -370000                                                            
               -.135             -534000                                                            
                  .1             -674000                                                            
                 .15             -717000                                                            
                  .2             -663000                                                            
                  .3             -462000                                                            
                 .45             -250000                                                            
                  .6             -178000                                                            
                  .9             -150000                                                            
                   1             -150000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1030
fct_ZZ1+i, fct_ZZ2+i (initial state)
#                  X                   Y
                  -1              500000                                                            
                   0              500000                                                            
               .0255              700000                                                            
                .051              700000                                                            
               .1395              380000                                                            
               .3375              250000                                                            
                   1              250000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1031
fct_ZZ1-i, fct_ZZ2-i (initial state)
#                  X                   Y
                  -1             -250000                                                            
              -.3375             -250000                                                            
              -.1395             -380000                                                            
               -.051             -700000                                                            
              -.0255             -700000                                                            
                   0             -500000                                                            
                   1             -500000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1032
fct_ZZ1+r, fct_ZZ2+r (collapsed state)
#                  X                   Y
                  -1              110000                                                            
                -.45              110000                                                            
                -.15              442000                                                            
                 -.1              491000                                                            
                -.05              478000                                                            
               .1395              380000                                                            
               .3375              250000                                                            
                   1              250000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1033
fct_ZZ1-r, fct_ZZ2-r (collapsed state)
#                  X                   Y
                  -1             -250000                                                            
              -.3375             -250000                                                            
              -.1395             -380000                                                            
                 .05             -478000                                                            
                  .1             -491000                                                            
                 .15             -442000                                                            
                 .45             -110000                                                            
                   1             -110000                                                            
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

This property is linked to two node spring elements.
K_inter is used to calculate interface stiffness when the frame element is referred in a contact.
If I_coupling =1, moments generated by forces are accounted in the global moment balance for each frame element (similar to I_equil =1 flag for spring /PROP/TYPE8 (SPR_GENE)).
To reproduce buckling behavior of a chain of the crushable frames, it is assumed that each element can be either in initial state or in residual state (collapsed). Initially all crushable frame elements are in the initial state and corresponding "initial" force strain curves are used. When the strain becomes higher than the limit X_lim_g for a particular element, the element is switched into residual state. Afterwards, only "residual" force strain curves are used for this element for all DOFs. At the same time, information is sent to the attached frame elements (left and right, defined with property TYPE44 only) and all directions on the both nodes of these elements switch to the residual state.
When the value X_lim and/or XX_lim are reached, all DOFs on the both elements nodes switch to the residual state. Neighboring elements also switch to residual state.
When the value YYi_lim and/or ZZi_lim are reached, all DOFs linked to the node of the element, i switch to residual state. Neighboring element, which share the node, also switch to residual state.
The function fct_X_+i or fct_XX_+i is linked to both nodes of the frame element.
If skew is defined in the property, the Z-direction is:(1)
$Z = X Λ Y_{s k e w}$
If no skew frame is assigned in the property set, the Z-direction is:(2)
$Z = X Λ Y_{g l o b a l}$
If the damping function is defined, the damping function formula is used instead linear damping.

Force linear damping:

$F_{d a m p} = D_{s c a l e_{i}} \cdot {\dot{δ}}_{i}$ with ( $i = x, y, z, x x, y y, z z$ - DOF)

Force function damping:

$F_{d a m p} = H_{s c a l e_{i}} \cdot h (\frac{{\dot{δ}}_{i}}{F_{i}})$ with ( $i = x, y, z, x x, y y, z z$ - DOF)

Where:

$H_{s c a l e_{i}} = D_{s c a l e_{i}}$

${\dot{δ}}_{i}$

Elongation rate.

$h (\frac{{\dot{δ}}_{i}}{F_{i}})$

Damping Force-elongation rate curve for each DOF.

$F_{i}$

Abscissa scale factor on Force-elongation rate curve for each DOF.