/INTER/TYPE19

Format

Definitions

Flags for Deactivation of Boundary Conditions: IBC

Definitions

Comments

1. The contact main and secondary surfaces and be defined in the following ways.
   Single surface self-impacting and edge to edge self-impacting contact:

   • surf_ID_s > 0 and surf_ID_m = 0
   • surf_ID_s = 0 and surf_ID_m > 0
   Symmetric surface to surface and edge to edge contact

   • surf_ID_s > 0 and surf_ID_m > 0
2. When sens_ID is defined for activation/deactivation of the interface, T_start and T_stop are not taken into account.
3. In case of SPMD, each main segment defined by surf_ID_m must be associated to an element (possibly to a void element).
4. For flag I_bag, refer to the monitored volume option (Monitored Volumes (Airbags)).
5. Flag I_del = 1 has a CPU cost higher than I_del = 2.
6. Variable gap is computed as:
   • If I_gap = 1:(1)
     $$\max \left[Ga{p}_{\min },\left(g_s+g_m\right)\right]$$
   • If I_gap = 3:(2)
     $$\max \left\{Ga{p}_{\min },\min \left[Fscal{e}_{gap}\cdot \left(g_s+g_m\right),\%mesh\_size\cdot \left(g_{s\_l}+g_{m\_l}\right),Ga{p}_{\max }\right]\right\}$$
   • If I_gap = 4:
     Node to surface contact uses variable gap(3)

     $$\max \left\{Ga{p}_{\min },\min \left[Fscal{e}_{gap}\cdot \left(g_s+g_m\right),Ga{p}_{\max }\right]\right\}$$

     For self-contact, if element size < gap value, then secondary nodes are deactivated for nearby main segments. This is the same as using /INTER/TYPE7, Irem_gap = 2. Edge to edge contact uses a constant gap as defined by Gap_min.

   • Where,

     • $g_m$ : main element gap

       $g_m=\frac{t}{2}$ , 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.

       $g_s=\frac{t}{2}$ , with $t$ : 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.

     • $g_{m\_l}$ : length of the smaller edge of 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.

7. A default value for Gap_min is computed as:(4)
   $$Ga{p}_{\min }=g_{m\_\min }+g_{s\_\min }$$
   While,

   $g_{m\_\min }=\min \left(t,\frac{l}{20},\frac{l_{\min }}{2}\right)$

   Main surface gap

   $t$

   Average thickness of the main elements for shell elements

   $l$

   Average side length of the main brick elements

   $l_{\min }$

   Smallest side length of all main segments (shell or brick)

   $g_{s\_\min }$

   Secondary surface gap.

   Computation identical to $g_{m\_\min }$ , except that it is applied on secondary side elements.

8. Contact stiffness:
   For node to 3-node and 4-node segments or 2-node segments to 2-node segments contacts computation as:(5)

   $$K=\max \left[S{t}_{\mathit{min}},\mathit{min}\left(S{t}_{\max },K_n\right)\right]$$
   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, $K_n=\max \left(K_m,K_s\right)$

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

     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:(6)

     $$K_m=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$$
     When main segment lies on a solid:(7)

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

     $S$

     Segment area

     $V$

     Volume of the solid

     $B$

     Bulk modulus

   • $K_s$ is an equivalent nodal stiffness considered for interface TYPE7, and computed as:
     When node is connected to a shell element:(8)

     $$K_s=\frac{1}{2}\cdot E\cdot t$$
     When node is connected to solid element:(9)

     $$K_s=B\cdot \sqrt[3]{V}$$

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

   When using /PROP/VOID and /MAT/VOID, material properties and thickness for the VOID material must be entered; otherwise, the contact stiffness of the void elements will be zero. This is especially important if VOID shell elements share elements with solid elements as the stiffness of the shell elements is used in the contact calculation.

9. The values given in Line 4 are ignored, if I_gap ≠ 3.
10. The values given in Line 5 are ignored, if I_stf ≤ 1.
11. Spherical curvature (I_curv = 1) is defined with node_ID₁ (center of the sphere).
12. The node_ID₂ given in Line 6 is ignored, if I_curv = 1.
13. Cylindrical curvature (I_curv = 2) is defined with node_ID₁ and node_ID₂ (on the axis of the cylinder).
14. Inacti = 3 may create initial energy if the node belongs to a spring element.
    Inacti = 6 is recommended instead of Inacti =5, to avoid high frequency effects into the interface.

    
    
    Figure 1.

15. With Irem_gap = 2, it allows to have the element size smaller than gap values:

    
    
    Figure 2. Secondary nodes removed from node to surface contact

    
    
    Figure 3. Secondary lines removed from edge to edge contact

    In case of self-impact contact, when Curvilinear is smaller than $\sqrt{2}\cdot Gap$ (in initial configuration), then this secondary entity (node / line) will not be taken into account by this main entity (surface / line). The secondary entity will not be deleted from the contact for other other main entities. This also applies both nodes to surface and edge to edge contact as stated in the /INTER/TYPE7 and /INTER/TYPE11 comments.

16. The sorting factor, Bumult is used to speed up the sorting algorithm.
17. The sorting factor, Bumult is machine dependent.
18. One node can belong to the two surfaces at the same time.
19. If fric_ID is defined, the contact friction is defined in /FRICTION and the friction inputs (I_fric, C₁, etc.) in this input card are not used.
    For friction formulation:

    • Whatever the friction flag I_fric, the Coulomb friction coefficient used in the TYPE11 interface is:
      (10)

      $$\mu =Fric$$
    • The friction flag I_fric only applies to the TYPE7 interface(s).
    • If the friction flag I_fric = 0 (default), the old static friction formulation is used:
      (11)

      $$F_t\le \mu \cdot F_n$$

      While, $\mu =\mathit{Fric}$ with $\mu$ 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 relative to the main segment

20. Currently, the coefficients C₁ through C₆ are used to define a variable friction coefficient $\mu$ for new friction formulations.
    • I_fric = 1 (Generalized Viscous Friction law):(12)
      $$\mu =\mathit{Fric}+C_1\cdot p+C_2\cdot V+C_3\cdot p\cdot V+C_4\cdot p^2+C_5\cdot V^2$$
    • I_fric = 2 (Modified Darmstad law): (13)
      $$\mu =Fric+C_1\cdot e^{\left(C_{2}V\right)}\cdot p^2+C_3\cdot e^{\left(C_{4}V\right)}\cdot p+C_5\cdot e^{\left(C_{6}V\right)}$$
    • I_fric = 3 (Renard law):

      $\mu =C_1+\left(C_3-C_1\right)\cdot \frac{V}{C_5}\cdot \left(2-\frac{V}{C_5}\right)$ 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 less than the maximum friction $C_3$ ( $C_1\le C_3$ and $C_2\le C_3$ ).
    • The minimum friction coefficient $C_4$ , must be less than the static friction coefficient $C_1$ and the dynamic friction coefficient $C_2$ ( $C_4\le C_1$ and $C_4\le C_2$ ).

    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		$\left[\frac{1}{{\text{Pa}}^2}\right]$	$\left[\frac{\text{s}}{\text{m}}\right]$	$\left[\frac{1}{\text{P}\text{a}}\right]$	$\left[\frac{\text{s}}{\text{m}}\right]$		$\left[\frac{\text{s}}{\text{m}}\right]$
    3						$\left[\frac{\text{m}}{\text{s}}\right]$	$\left[\frac{\text{m}}{\text{s}}\right]$

21. Friction filtering:
    If I_filtr ≠ 0, the tangential forces are smoothed using a filter:(14)

    $$F_t=\alpha \cdot {F^{\prime }}_t+\left(1-\alpha \right)\cdot F_t^{-1}$$
    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.

22. Friction penalty formulation I_form
    • If I_form = 1, (default) viscous formulation, the friction forces are:(15)
      $$F_t=\min \left(\mu F_n,F_{adh}\right)$$

      While an adhesion force is computed as:

      $F_{adh}=C\cdot V_t$ with $C=VI{S}_F\cdot \sqrt{2Km}$

    • If I_form = 2, stiffness formulation, the friction forces are:(16)
      $$F_t^{new}=\min \left(\mu F_n,F_{adh}\right)$$

      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.

23. If the time step of a secondary node in this contact becomes less than dtmin, the secondary node is deleted from the contact and a warning message is printed in the output file. This dtmin value takes precedence over any model interface minimum time step entered in /DT/INTER/DEL.
24. Edges to edge contact flag I_edge:
    • I_edge = 1: only external edges are generated from contact surfaces which defined by SHELL parts, it is recommended for optimized performance. Cannot be used when the surface contains only solid parts which lead to an empty line and then error message will be printed.

      
      
      Figure 4.

    • I_edge = 2: all edges are generated from contact surfaces.

      
      
      Figure 5.

25. Heat exchange:
    By I_the =1 (heat transfer activated) to consider heat exchange and heat friction in contact.

    • If I_{the_form} = 0, then heat exchange is between shell and constant temperature contact T_int.
    • If I_{the_form} = 1, then heat exchange is between all contact pieces.

      T_int is used only when I_{the_form}= 0. In this case, the temperature of main side assumed to be constant (equal to T_int). If I_{the_form}=1, then T_int is not taken into account, for the nodal temperature of main side will be considered.

    Heat exchange coefficient:

    • If fct_ID_K = 0, then K_the is heat exchange coefficient and heat exchange depends only on heat exchange surface.
    • If fct_ID_K ≠ 0, then K_the is a scale factor and the heat exchange will depend on the contact pressure:(17)
      $$K=K_{\mathit{the}}\cdot f_K\left({\mathit{Ascale}}_K,P\right)$$
    • While ${\mathrm{f}}_K$ is the function of fct_ID_K.
26. Heat Friction:
    • Frictional energy is converted into heat when I_the > 0 for interface.
    • Fheat_s and Fheat_m are defined as the fraction of frictional energy and distributed respectively to the secondary side and main side. So generally:(18)
      $${\mathit{Fheat}}_s+{\mathit{Fheat}}_m\le 1.0$$

      When both Fheat_s and Fheat_m are equal to 0, the conversion of the frictional sliding energy to heat is not activated.

    • The frictional heat Q_Fric is defined:
      • If I_form= 2 (a stiffness formulation):
        Secondary side: (19)

        $$Q_{\mathit{Fric}}={\mathit{Fheat}}_s\cdot \frac{\left(F_{\mathit{adh}}-F_t\right)}{K}\cdot F_t$$
        Main side: (20)

        $$Q_{\mathit{Fric}}={\mathit{Fheat}}_m\cdot \frac{\left(F_{\mathit{adh}}-F_t\right)}{K}\cdot F_t$$

        (I_{the_form}= 1)
      • If I_form= 1 (a penalty formulation):
        Secondary side: (21)

        $$Q_{\mathit{Fric}}={\mathit{Fheat}}_s\cdot C\cdot {V_t}^2\cdot dt$$
        Main side: (22)

        $$Q_{\mathit{Fric}}={\mathit{Fheat}}_m\cdot C\cdot {V_t}^2\cdot dt$$

        (I_{the_form}= 1)
27. Radiation:
    Radiation is considered in contact if $F_{rad}\ne 0$ and the distance, $d_{}$ , of the secondary node to the main segment is:(23)

    $$\mathit{Gap}<d<D_{\mathit{rad}}$$
    While $D_{rad}$ is the maximum distance for radiation computation. The default value for $D_{rad}$ is computed as the maximum of:

    • Upper value of the Gap (at time 0) among all nodes
    • Smallest side length of secondary element

    It is recommended not to set the value too high for $D_{rad}$ , which may reduce the performance of Radioss Engine.

    A radiant heat transfer conductance is computed as:(24)

    $$h_{\mathit{rad}}=F_{\mathit{rad}}\left({T_m}^2+{T_s}^2\right)\cdot \left(T_m+T_s\right)$$
    with(25)

    $$F_{\mathit{rad}}=\frac{\sigma }{\frac{1}{{\epsilon }_1}+\frac{1}{{\epsilon }_2}-1}$$
    Where,

    $\sigma =5.669\times {10}^{-8}\left[\frac{\text{W}}{{\text{m}}^2{\text{K}}^4}\right]$

    Stefan Boltzman constant

    ${\epsilon }_1$

    Emissivity of secondary surface

    ${\epsilon }_2$

    Emissivity of main surface