/INTER/TYPE23

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 self-impacting.

Format

Definitions

Flags for Deactivation of Boundary Conditions: IBC

Definitions

Comments

1. 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

2. 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).
3. If I_gap = 1, variable gap is computed as:(1)
   $$\max \left[Ga{p}_{\min },\min \left(Fscal{e}_{gap}\cdot g_s,\mathit{G}a{p}_{\max }\right)\right]$$

   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.

4. Inacti = 6 is recommended, in order to avoid numerical (high frequency) effects into the interface before inflation.

   
   
   Figure 1.

   If Inacti = 5 or 6 and if Fpenmax is not equal to zero, nodes stiffness is deactivated if:(2)

   $$\mathit{Penetration}\ge \mathit{Fpenmax}\cdot \mathit{Gap}$$
5. The sorting factor, Bumult is used to speed up the sorting algorithm.
6. The sorting factor Bumult is machine dependent.
7. One node can belong to the two surfaces at the same time.
8. 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 $\mu =\text{μ}(\rho ,V)$
     Where,

     $p$

     Pressure of the normal force on the main segment

     $V$

     Tangential velocity of the secondary node relative to the main segment

9. Currently, the coefficients C₁ through C₆ 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 $V\in \left[0,C_5\right]$

     $\mu =C_3-\left(\left(C_3-C_4\right)\cdot {\left(\frac{V-C_5}{C_6-C_5}\right)}^2\cdot \left(3-2\cdot \frac{V-C_5}{C_6-C_5}\right)\right)$ 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,

     $C_1={\mu }_s$	$C_4={\mu }_{\min }$
     $C_2={\mu }_d$	$C_5=V_{\mathit{cr}1}$
     $C_3={\mu }_{\max }$	$C_6=V_{cr2}$

   • 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

   Ifric	Fric	C1	C2	C3	C4	C5	C6
   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						$\left[\frac{\text{m}}{\text{s}}\right]$	$\left[\frac{\text{m}}{\text{s}}\right]$

10. Friction filtering
    If 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.

11. The type of friction penalty formulation is based on the incremental stiffness formulation:
    The friction forces are:(6)

    $$F_t^{new}=\min \left(\mu F_n,F_{adh}\right)$$

    While an adhesion force is computed as:

    $F_{adh}=F_t^{old}+\text{Δ}{F}_t$ with $\text{Δ}{F}_t=K\cdot V_t\cdot dt$

    Where, $V_t$ is the tangential velocity of the secondary node relative to the main segment.