/INTER/LAGDT/TYPE7

Description

Format

Definitions

Flags for Deactivation of Boundary Conditions: IBC

Definitions

Comments

1. For the flag I_bag, refer to the monitored volume option (Monitored Volumes (Airbags)).
2. Flag I_del = 1 has a CPU cost higher than I_del = 2.
3. If I_gap = 2, the variable gap is computed as:(1)
   $$\text{max}\left\{{\mathit{Gap}}_{\text{min}},\text{min}\left[{\mathit{Fscale}}_{\mathit{gap}}\cdot \left(g_s+g_m\right),{\mathit{Gap}}_{\text{max}}\right]\right\}$$

   The values given in Line 4 are ignored if I_gap ≠ 2.

4. Contact stiffness computed as:
   • For I_stf = 0, stiffness

     $K=K_m$

   • For I_stf > 1, stiffness(2)
     $$K=\text{max}\left[S{t}_{\text{min}},\text{min}\left(S{t}_{\text{max}},K_n\right)\right]$$
     Where,

     • $K_n$ is computed from both main segment stiffness $K_m$ and secondary node stiffness $K_s$

       I_stf = 2, $K_n=\frac{K_m+K_s}{2}$

       I_stf = 3, $K_n=\text{max}\left(K_m,K_s\right)$

       I_stf = 4, $K_n=\text{min}\left(K_m,K_s\right)$

       I_stf = 5, $K_n=\frac{K_m\cdot K_s}{K_m+K_s}$

     • $K_m$ is main segment stiffness and computed as:

       When main segment lies on a shell or is shared by shell and solid(3)

       $$K_m=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$$
       When main segment lies on a solid:(4)

       $$K_m=B\cdot \frac{S^2}{V}$$
       Where,

       $S$

       Segment area

       $V$

       Volume of the solid

       $B$

       Bulk modulus

       $K_s$

       An equivalent nodal stiffness considered for interface TYPE7, and computed as:

       • When node is connected to a shell element:(5)
         $$K_s=\mathit{Stfac}\cdot \frac{1}{2}\cdot E\cdot t$$
       • When node is connected to a solid element:(6)
         $$K_s=\mathit{Stfac}\cdot B\cdot \sqrt[3]{V}$$

   There is no limitation to the value of stiffness factor (but a value larger than 1.0 can reduce the initial time step).

5. The values given in Line 5 are ignored if I_stf < 1.
6. A default value for Gap_min is computed as the minimum of:(7)
   $$Ga{p}_{\text{min}}=\text{min}\left(t,\frac{l}{10},\frac{l_{\text{min}}}{2}\right)$$
   Where,

   $t$

   Average thickness of the main shell elements

   $l$

   Average side length of the main brick elements

   $l_{\min }$

   The smallest side length of all main segments (shell or brick)

7. The gap is computed for each impact as:(8)
   $${\mathit{Fscale}}_{gap}\cdot \left(g_s+g_m\right)$$
   Where,

   • $g_m$ : main element gap:(9)
     $$g_m=\frac{t}{2}$$

     with $t$ : thickness of the main element for shell elements

     $g_m$ = 0 for brick elements

   • $g_s$ : secondary node gap:
     $g_s$ = 0 if the secondary node is not connected to any element or is only connected to brick or spring elements.(10)

     $$g_s=\frac{t}{2}$$

     With $t$ being the largest thickness of the shell elements connected to the secondary node.

     $g_s=\frac{1}{2}\sqrt{S}$ for truss and beam elements, with $S$ being the cross section of the element.

   If the secondary node is connected to multiple shells and/or beams or trusses, the largest computed secondary gap is used.

   The variable gap is always at least equal to Gap_min.

8. Deactivation of the boundary condition is applied to secondary nodes group (grnd_ID_s)
9. Inacti = 3 may create initial energy if the node belongs to a spring element.

   Inacti = 5 is recommended for airbag simulation deployment

   Inacti = 6 is recommended instead of Inacti =5, in order to avoid high frequency effects into the interface.

   
   
   Figure 1.

10. The sorting factor, Bumult is used to speed up the sorting algorithm.
11. The default value for Bumult is automatically increased to 0.30 for models which have more than 1.5 million nodes and to 0.40 for models with more than 2.5 million of nodes.
12. One node can belong to the two surfaces at the same time.
13. There is no limitation value to the stiffness factor (but a value larger than 1.0 can reduce the initial time step).
14. 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,

      $\rho$

      Pressure of the normal force on the main segment

      $V$

      Tangential velocity of the secondary node

15. 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):(11)
      $$\mu =\mathit{Fric}+C_1\cdot p+C_2\cdot V+C_3\cdot p\cdot V+C_4\cdot p^2+C_5\cdot V^2$$
    • I_fric = 2 (Darmstad law):(12)
      $$\mu =C_1\cdot e^{(C_{2}V)}\cdot p^2+C_3\cdot e^{\left(C_{4}V\right)}\cdot p+C_5\cdot e^{\left(C_{6}V\right)}$$
    • I_fric = 3 (Renard law):(13)
      $$\mu =C_1+\left(C_3-C_1\right)\cdot \frac{V}{C_5}\cdot \left(2-\frac{V}{C_5}\right)\hspace{0.17em}\text{if}\hspace{0.17em}V\in \left[0,C_5\right]$$
      (14)
      $$\mu =C_3-\left(\left(C_3-C_4\right)\cdot {\left(\frac{V-C_5}{C_6-C_5}\right)}^2\cdot \left(3-2\cdot \frac{V-C_5}{C_6-C_5}\right)\right)\hspace{0.17em}\text{if}\hspace{0.17em}V\in \left[C_5,C_6\right]$$
      (15)
      $$\mu =C_2-\frac{1}{\frac{1}{C_2-C_4}+{\left(V-C_6\right)}^2}\hspace{0.17em}\text{if}\hspace{0.17em}V\ge C_6$$

      Where,

      $C_1={\mu }_s$

      $C_2={\mu }_d$

      $C_3={\mu }_{\max }$

      $C_4={\mu }_{\min }$

      $C_5=V_{cr1}$

      $C_6=V_{cr2}$

    • First critical velocity $V_{cr1}=C_5$ = must be different to 0 (C₅ ≠ 0).
    • First critical velocity $V_{cr1}=C_5$ must be lower than the second critical velocity $V_{\mathit{cr}2}=C_6(C_5<C_6)$ .
    • The static friction coefficient C₁ and the dynamic friction coefficient C₂, must be lower than the maximum friction coefficient C₂ (C₄ ≤ C₁ and C₄ ≤ C₂).
16. Friction Filtering
    If I_filtr ≠ 0 , the tangential forces are smoothed using a filter:(16)

    $$F_t=\alpha \cdot {F^{\prime }}_t+\left(1-\alpha \right)\cdot {F^{\prime }}_t{}^{-1}$$
    Where α coefficient is calculated from:

    • If I_filtr = 1 ➤ $\alpha =X_{freq}$ , 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 ➤ $\alpha =2\cdot \pi \cdot X_{\mathit{freq}}\cdot \mathit{dt}$ standard -3dB filter, with X_freq is cutting frequency

    The filtering coefficient X_freq should have a value between 0 and 1.

17. Friction penalty formulation I_form
    • If I_form = 1, (default) viscous formulation, the friction forces are:(17)
      $$F_t=\min \left(\mu F_n,F_{\text{adh}}\right)$$
    • While an adhesion force is computed as:(18)
      $$F_{\mathit{adh}}=C\cdot V_t\text{with}C={\mathit{VIS}}_F\cdot \sqrt{2\mathit{Km}}$$
    • If I_form = 2, stiffness formulation, the friction forces are:(19)
      $$F_t^{\mathit{new}}=\min \left(\mu F_n,F_{\mathit{adh}}\right)$$
    • While an adhesion force is computed as:(20)
      $$F_{\mathit{adh}}=F_t^{\mathit{old}}+\mathrm{\text{Δ}}{F}_t\text{with}\mathrm{\text{Δ}}{F}_t=K\cdot V_t\cdot {\delta }_t$$

      Where, $V_t$ is contact tangential velocity.