/INTER/TYPE23
Block Format Keyword Defines a contact interface for airbag fabrics, modeling contact between a main surface and a secondary surface which are supposed to belong to an airbag.
This is a soft penalty contact which can deal with penetrations and intersections often coming in the folded airbag mesh. This interface can be used for selfimpacting.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/INTER/TYPE23/inter_ID/unit_ID  
inter_title  
surf_ID_{s}  surf_ID_{m}  I_{stf}  I_{gap}  I_{bag}  I_{del}  
Fscale_{gap}  Gap_{max}  Fpenmax  
St_{min}  St_{max}  
Stfac  Fric  Gap_{min}  T_{start}  T_{stop}  
I_{BC}  Inacti  VIS_{s}  Bumult  
I_{fric}  I_{filtr}  X_{freq} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

C_{1}  C_{2}  C_{3}  C_{4}  C_{5} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

C_{6}  
Blank  
Blank  
Blank 
Definitions
Field  Contents  SI Unit Example 

inter_ID  Interface identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

inter_title  Interface title. (Character, maximum 100 characters) 

surf_ID_{s}  Secondary surface
identifier. (Integer) 

surf_ID_{m}  Main surface
identifier. (Integer) 

I_{stf}  Stiffness definition flag.
(Integer) 

I_{gap}  Gap/element option flag. 3
(Integer) 

I_{bag}  Airbag vent holes closure flag in case
of contact.
(Integer) 

I_{del}  Node deletion flag.
(Integer) 

Fscale_{gap}  Gap scale factor. Default = 1.0 (Real) 

Gap_{max}  Maximum gap.
(Real) 
$\left[\text{m}\right]$ 
Fpenmax  Maximum fraction of initial penetration.
4 (Real) 

St_{min}  Minimum stiffness. (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
St_{max}  Maximum stiffness. Default = 10^{30} (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
Stfac  Interface stiffness (if I_{stf} = 1). Default set to 0.0 (Real) 
$\left[\frac{\text{N}}{\text{m}}\right]$ 
Stiffness scale factor for the interface
(if I_{stf} = 0). Default = 1.0 (Real) 

Fric  Coulomb friction. (Real) 

Gap_{min}  Minimum gap for impact
activation. (Real) 
$\left[\text{m}\right]$ 
T_{start}  Start time. (Real) 
$\left[\text{s}\right]$ 
T_{stop}  Time for temporary
deactivation. (Real) 
$\left[\text{s}\right]$ 
I_{BC}  Deactivation flag of boundary conditions
at impact. (Boolean) 

Inacti  Stiffness deactivation flag of stiffness
in case of initial penetrations. 4
(Integer) 

VIS_{s}  Critical damping coefficient on
interface stiffness. Default set to 1.0 (Real) 

Bumult  Sorting factor. 5
6
Default set to 0.20 (Real) 

I_{fric}  Friction formulation flag. 8
9
(Integer) 

I_{filtr}  Friction filtering flag. 10
(Integer) 

X_{freq}  Filtering coefficient. A value should be between 0 and 1. (Real) 

C_{1}  Friction law
coefficient. (Real) 

C_{2}  Friction law
coefficient. (Real) 

C_{3}  Friction law
coefficient. (Real) 

C_{4}  Friction law
coefficient. (Real) 

C_{5}  Friction law
coefficient. (Real) 

C_{6}  Friction law
coefficient. (Real) 
Flags for Deactivation of Boundary Conditions: IBC
(1)1  (1)2  (1)3  (1)4  (1)5  (1)6  (1)7  (1)8  (1)9  (1)10 

I_{BCX}  I_{BCY}  I_{BCZ} 
Definitions
Field  Contents  SI Unit Example 

I_{BCX}  Deactivation flag of X boundary
condition at impact.
(Boolean) 

I_{BCY}  Deactivation flag of Y boundary
condition at impact.
(Boolean) 

I_{BCZ}  Deactivation flag of Z boundary
condition at impact.
(Boolean) 
Comments
 For contact stiffness:
$K=\mathit{Stfac}\cdot {K}_{s}$ if I_{stf} = 0.
While,
${K}_{s}$ is an equivalent nodal stiffness of the secondary component computed as:
${K}_{s}=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$ when node is connected to a shell element.
Where, $E$
 Young's modulus
 $B$
 Bulk modulus of the secondary component
 $t$
 Shell thickness
 $V$
 Solid element volume
 If Gap_{min} is not specified or set to zero, a default value is computed as the minimum of $t$ (average thickness of the secondary shell elements).
 If I_{gap} = 1, variable gap is
computed as:
(1) $$\mathrm{max}\left[Ga{p}_{\mathrm{min}},\mathrm{min}\left(Fscal{e}_{gap}\cdot {g}_{s},\mathit{G}a{p}_{\mathrm{max}}\right)\right]$$While,
g_{s}: secondary node gap:
${g}_{s}=\frac{t}{2}$ with $t$ is the largest thickness of the shell elements connected to the secondary node.
If the secondary node is connected to multiple shells, the largest computed secondary gap is used.
The variable gap is always at least equal to Gap_{min}.
 Inacti = 6 is recommended, in
order to avoid numerical (high frequency) effects into the interface before inflation.
If Inacti = 5 or 6 and if Fpenmax is not equal to zero, nodes stiffness is deactivated if:
(2) $$\mathit{Penetration}\ge \mathit{Fpenmax}\cdot \mathit{Gap}$$  The sorting factor, Bumult is used to speed up the sorting algorithm.
 The sorting factor Bumult is machine dependent.
 One node can belong to the two surfaces at the same time.
 For friction formulation
 If the friction flag I_{fric} = 0 (default), the old
static friction formulation is used:
${F}_{t}\le \mu \cdot {F}_{n}$ with $\mu =\mathit{Fric}$ ( $\mu $ is Coulomb friction coefficient).
 For flag I_{fric} > 0, new friction
models are introduced. In this case, the friction coefficient is set by a function
$\mu =\text{\mu}(\rho ,V)$
Where,
 $p$
 Pressure of the normal force on the main segment
 $V$
 Tangential velocity of the secondary node relative to the main segment
 If the friction flag I_{fric} = 0 (default), the old
static friction formulation is used:
 Currently, the coefficients C_{1} through C_{6} are used to define a variable friction
coefficient
$\mu $
for new friction formulations.The following formulations are available:
 I_{fric} = 1 (generalized
viscous friction law):
(3) $$\mu =\mathit{Fric}+{C}_{1}\cdot p+{C}_{2}\cdot V+{C}_{3}\cdot p\cdot V+{C}_{4}\cdot {p}^{2}+{C}_{5}\cdot {V}^{2}$$  I_{fric} = 2 (Modified
Darmstad law):
(4) $$\mu =Fric+{C}_{1}.{e}^{\left({C}_{2}V\right)}.{p}^{2}+{C}_{3}.{e}^{\left({C}_{4}V\right)}.p+{C}_{5}.{e}^{\left({C}_{6}V\right)}$$  I_{fric} = 3 (Renard law):
$\mu ={C}_{1}+\left({C}_{3}{C}_{1}\right)\cdot \frac{V}{{C}_{5}}\cdot \left(2\frac{V}{{C}_{5}}\right)$ if $V\in \left[0,{C}_{5}\right]$
$\mu ={C}_{3}\left(\left({C}_{3}{C}_{4}\right)\cdot {\left(\frac{V{C}_{5}}{{C}_{6}{C}_{5}}\right)}^{2}\cdot \left(32\cdot \frac{V{C}_{5}}{{C}_{6}{C}_{5}}\right)\right)$ if $V\in \left[{C}_{5},{C}_{6}\right]$
$\mu ={C}_{2}\frac{1}{\frac{1}{{C}_{2}{C}_{4}}+{\left(V{C}_{6}\right)}^{2}}$ if $V\ge {C}_{6}$
Where,${C}_{1}={\mu}_{s}$ ${C}_{4}={\mu}_{\mathrm{min}}$ ${C}_{2}={\mu}_{d}$ ${C}_{5}={V}_{\mathit{cr}1}$ ${C}_{3}={\mu}_{\mathrm{max}}$ ${C}_{6}={V}_{cr2}$  First critical velocity ${V}_{cr1}={C}_{5}$ must be different to 0 ( ${C}_{5}\ne 0$ ).
 First critical velocity ${V}_{cr1}={C}_{5}$ must be lower than the second critical velocity ${V}_{cr2}={C}_{6}$ ( ${C}_{5}<{C}_{6}$ ).
 The static friction coefficient ${C}_{1}$ and the dynamic friction coefficient ${C}_{2}$ , must be lower than the maximum friction ${C}_{3}$ ( ${C}_{1}\le {C}_{3}$ and ${C}_{2}\le {C}_{3}$ ).
 The minimum friction coefficient ${C}_{4}$
Table 1. Units for Friction Formulations I_{fric} Fric C_{1} C_{2} C_{3} C_{4} C_{5} C_{6} 1 $\left[\frac{1}{\text{P}\text{a}}\right]$ $\left[\frac{\text{s}}{\text{m}}\right]$ $\left[\frac{\text{s}}{\text{Pa}\cdot \text{m}}\right]$ $\left[\frac{1}{{\text{Pa}}^{2}}\right]$ $\left[\frac{{\text{s}}^{2}}{{\text{m}}^{2}}\right]$ 2 $\left[\frac{\text{s}}{\text{m}}\right]$ $\left[\frac{\text{s}}{\text{m}}\right]$ $\left[\frac{\text{s}}{\text{m}}\right]$ 3 $\left[\frac{\text{m}}{\text{s}}\right]$ $\left[\frac{\text{m}}{\text{s}}\right]$  I_{fric} = 1 (generalized
viscous friction law):
 Friction filteringIf I_{filtr} ≠ 0, the tangential forces are smoothed using a filter:
(5) $${F}_{t}=\alpha \cdot {{F}^{\prime}}_{t}+\left(1\alpha \right)\cdot {{{F}^{\prime}}_{t}}^{1}$$Where α coefficient is calculated from: If I_{filtr} = 1: $\alpha ={X}_{\mathit{freq}}$ , simple numerical filter
 If I_{filtr} = 2: $\alpha =\frac{2\cdot \pi}{{X}_{\mathit{freq}}}$ , standard 3dB filter, with ${X}_{\mathit{freq}}=\frac{dt}{T}$ , and $T$ is filtering period
 If I_{filtr} = 3:
$\alpha =2\cdot \pi \cdot {X}_{freq}\cdot dt$
, standard 3dB filter, with X_{freq} is cutting frequency
The filtering coefficient X_{freq} should have a value between 0 and 1.
 The type of friction penalty formulation is
based on the incremental stiffness formulation:The friction forces are:
(6) $${F}_{t}^{new}=\mathrm{min}\left(\mu {F}_{n},{F}_{adh}\right)$$While an adhesion force is computed as:
${F}_{adh}={F}_{t}^{old}+\text{\Delta}{F}_{t}$ with $\text{\Delta}{F}_{t}=K\cdot {V}_{t}\cdot dt$
Where, ${V}_{t}$ is the tangential velocity of the secondary node relative to the main segment.