/INTER/TYPE7

Description

Format

Definitions

Flags for Deactivation of Boundary Conditions: IBC

Definitions

Comments

1. In case of SPMD, each mainr segment defined by surf_ID_m must be associated to an element (possibly to a void element).
2. For the flag I_bag, refer to the monitored volume option (Monitored Volumes (Airbags)).
3. Contact stiffness, K is computed as:
   If I_stf =1:(1)

   $$K=Stfac$$
   If I_stf = 2, 3, 4 or 5:(2)

   $$K=\text{max}\left[S{t}_{\text{min}},\text{min}\left(S{t}_{\text{max}},K_n\right)\right]$$
   If I_stf =1000:(3)

   $$K=K_m$$

   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 the main segment stiffness and computed as:

   When the main segment lies on a shell or is shared by shell and solid:(4)

   $$K_m=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$$
   When the main segment lies on a solid:(5)

   $$K_m=\mathit{Stfac}\cdot B\cdot \frac{S^2}{V}$$
   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 the node is connected to a shell element:(6)

   $$K_s=\frac{1}{2}\cdot E\cdot t$$
   When the node is connected to a solid element:(7)

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

   There is no limitation to the value of stiffness scale factor Stfac (but, a value greater than 1.0 can 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.

4. I_stf = 2, 3, 4, or 5 are not compatible with SPH formulation.
5. If I_curv = 1, a spherical curvature is defined for the gap with node_ID₁ (center of the sphere).

   If I_curv = 2, a cylindrical curvature is defined for the gap with node_ID₁ and node_ID₂ (on the axis of the cylinder).

   If I_curv = 3, the main surface shape is obtained with a bicubic interpolation, respecting continuity of the coordinates and the normal from one segment to the other. In case of a fast and large change in curvature, this formulation might become unstable (will be improved in future version).

   
   
   Figure 1.

6. In case of adaptive meshing and I_adm = 1:
   If the contact occurs in a zone (main side) whose radius of curvature is lower than the element size (secondary side), the element on the secondary side will be divided (if not yet at maximum level).

   
   
   Figure 2.

7. In case of adaptive meshing and I_adm = 2:

   If the contact occurs in a zone (main side) whose radius of curvature is lower than NR_adm times the element size (secondary side), the element on the secondary side will be divided (if not yet at maximum level).

   If the contact occurs in a zone (main side) where the angles between the normals are greater than Angl_adm and the percentage of penetration is greater than P_adm, the element on the secondary side will be divided (if not yet at maximum level).

   
   
   Figure 3.

8. The coefficients NR_adm, P_adm, and Angl_adm are used only if adaptive meshing and I_adm=2.
9. If Gap_max=0, there is no maximum value for the gap.
10. If Gap_min=0 or blank, a default value is computed as:

    If main segments are shell and solid elements, Gap_min = min ( $t{}_m$ , $\frac{l_{\min }}{2}$ ).

    Where,

    $t{}_m$

    The average thickness of the main shell elements, for I_gap=0

    $t{}_m$

    The minimum thickness of the main shell elements, for I_gap=1, 2, or 3

    $l_{\min }$

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

    If main segments are all solid elements Gap_min = $\frac{l_{\min }}{10}$

    Where, $l_{\min }$ being the smallest side of all main brick segments.

11. Variable gap:
    If I_gap =1, variable gap is computed as:(8)

    $$\text{max}\left[{\mathit{Gap}}_{\text{min}},\left(g_s+g_m\right)\right]$$
    If I_gap =2, variable gap is computed as:(9)

    $$\text{max}\left\{{\mathit{Gap}}_{\text{min}},\text{min}\left[\mathit{Fscal}{e}_{gap}\cdot \left(g_s+g_m\right),{\mathit{Gap}}_{\text{max}}\right]\right\}$$
    If I_gap =3, variable gap is computed for self-contact as:(10)

    $$\text{max}\left\{{\mathit{Gap}}_{\text{min}},\text{min}\left[\mathit{Fscal}{e}_{\mathit{gap}}\cdot \left(g_s+g_m\right),\%mesh\_size\cdot \left(g_{s\_l}+g_{m\_l}\right),{\mathit{Gap}}_{\text{max}}\right]\right\}$$
    Where,

    • $g_m$ : main element gap

      $g_m=\frac{t}{2}$ : with $t$ being the 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 $t$ 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

    • $g_{m\_l}$ : length of the smaller edge of element
    • $g_{s\_l}$ : length of the smaller edge of elements connected to the secondary node

    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.

12. Deactivation of the boundary condition is applied to secondary nodes group (grnd_ID_s).
13. Inacti = 3 may create initial energy if the node belongs to a spring element.
    Inacti = 6 is recommended instead of Inacti =5, in order to avoid high frequency effects into the interface.

    
    
    Figure 4.

    If Fpenmax is not equal to zero, nodes stiffness is deactivated if:

    $Penetration\ge Fpenmax\cdot Gap$ whatever the value of Inacti.

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

    
    
    Figure 5. Secondary nodes removed from node to surface contact

    For self-impact contact, when Curvilinear Distance (from a node of the main segment to a secondary node) is smaller than $\sqrt{2}\cdot Gap$ (in initial configuration), this secondary node will not be taken into account by this main segment, and it will not be deleted from the contact for the other main segments.

15. One node can belong to the two surfaces at the same time.
16. 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:

    If the friction flag I_fric=0 (default), the old static friction formulation is used:

    $F_t\le \mu \cdot F_n$ with $\mu$ being the Coulomb friction coefficient

    • If fct_ID_F = 0:
      I_fric is the Coulomb friction.(11)

      $$\mu =\mathit{Fric}$$
    • If fct_ID_F ≠ 0:
      Fric becomes a scale factor of Coulomb friction coefficient which depends on the temperature.(12)

      $$\mu =\mathit{Fric}\cdot {\mathrm{f}}_F\left({\mathit{Ascale}}_F,T_{\mathit{interface}}\right)$$
    While $T_{\mathit{interface}}$ is the temperature which is taken as the mean temperature of secondary and main:(13)

    $$T_{\mathit{interface}}=\frac{T_{\mathit{secondary}}+T_{\mathit{main}}}{2}$$

    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

17. 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):(14)
      $$\mu =\mathit{Fric}+C_1.p+C_2\cdot V+C_3.p\cdot V+C_4\cdot p^2+C_5\cdot V^2$$
    • I_fric = 2 (Modified Darmstad law):(15)
      $$\mu =\mathit{Fric}+C_1.e^{\left(C_{2}V\right)}.p^2+C_3.e^{\left(C_{4}V\right)}.p+C_5.e^{\left(C_{6}V\right)}$$
    • I_fric = 3 (Renard law):(16)
      $$\mu =C_1+\left(C_3-C_1\right)\cdot \frac{V}{C_5}\cdot \left(2-\frac{V}{C_5}\right)\hspace{0.17em}\text{if}\hspace{0.17em}V\in \left[0,C_5\right]$$
      (17)
      $$\begin{array}{l}\mu =C_3-\left((C_3-C_4\right)\cdot {\left(\frac{V-C_5}{C_6-C_5}\right)}^2\cdot \left(3-2\cdot \frac{V-C_5}{C_6-C_5}\right)\hspace{0.17em})\hspace{0.17em}\text{if}\hspace{0.17em}V\in [C_5{C}_6]\\ \end{array}$$
      (18)
      $$\mu =C_2-\frac{1}{\frac{1}{C_2-C_4}+{\left(V-C_6\right)}^2}\text{if}V\ge C_6$$
    Where for I_fric=3:

    • $C_1={\mu }_s$ , static coefficient of friction, must be ${\mu }_{\min }<{\mu }_s<{\mu }_{\max }$
    • $C_2={\mu }_d$ , dynamic coefficient of friction, must be ${\mu }_{\min }<{\mu }_d<{\mu }_{\max }$
    • $C_3={\mu }_{\max }$ , maximum coefficient of friction
    • $C_4={\mu }_{\min }$ , mimimum coefficient of friction
    • $C_5=V_{\mathit{cr}1}$ , first critical velocity, must be > 0
    • $C_6=V_{cr2}$ , second critical velocity, must be $>V_{cr1}$

    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						$\left[\frac{\text{m}}{\text{s}}\right]$	$\left[\frac{\text{m}}{\text{s}}\right]$

18. Friction filtering:
    If I_filtr flag $\ne$ 0, the tangential forces are smoothed using a filter:(19)

    $$F_{Tf}=\alpha F_T(t)+\left(1-\alpha \right)F_{Tf}(t-dt)$$
    Where,

    $F_{Tf}$

    Filtered tangential force.

    $F_T(t)$

    Calculated tangential force at time t before filtering.

    $F_{Tf}(t-dt)$

    Filtered tangential force at the previous time step

    $t$

    Current simulation time

    $dt$

    Current simulation time step

    $\alpha$

    Filtering coefficient

    Where α coefficient is calculated from:

    • If I_filtr = 1: $\alpha =X_{freq}$ , simple numerical filter with a value between 0 and 1.
    • If I_filtr = 2: $\alpha =\frac{2\cdot \pi }{X_{freq}}$ , standard -3dB filter, with the number of time steps to filter defined as $X_{\mathit{freq}}=\frac{dt}{T}$ , and $T$ is the filtering period.
    • If I_filtr = 3: $\alpha =2\cdot \pi \cdot X_{\mathit{freq}}\cdot \mathit{dt}$ , standard -3dB filter, with X_freq = cutting frequency.
19. Friction penalty formulation I_form:
    • If I_form = 1 (default) viscous formulation, the friction forces are:(20)
      $$F_t=\text{min}\left(\mu F_n,F_{\text{adh}}\right)$$
      While an adhesion force is computed as:(21)

      $$F_{\text{adh}}=C\cdot V_t\text{with}C={\mathit{VIS}}_F\cdot \sqrt{2\mathit{Km}}$$
    • If I_form = 2, stiffness formulation), the friction forces are:(22)
      $$F_t^{\mathit{new}}=\text{min}\left(\mu F_n,F_{\mathit{adh}}\right)$$

      While an adhesion 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.

      I_form = 2 is recommended for implicit and explicit analysis.

20. 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:(23)
      $$K=K_{\mathit{the}}\cdot f_K\left({\mathit{Ascale}}_K,P\right)$$
    • While ${\mathrm{f}}_K$ is the function of fct_ID_K.
21. 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:(24)
      $${\mathit{Fheat}}_s+{\mathit{Fheat}}_m\le 1.0$$

      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: (25)

        $$Q_{\mathit{Fric}}={\mathit{Fheat}}_s\cdot \frac{\left(F_{\mathit{adh}}-F_t\right)}{K}\cdot F_t$$
        Main side: (26)

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

        (I_{the_form}= 1)
      • If I_form= 1 (a penalty formulation):
        Secondary side: (27)

        $$Q_{\mathit{Fric}}={\mathit{Fheat}}_s\cdot C\cdot {V_t}^2\cdot dt$$
        Main side: (28)

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

        (I_{the_form}= 1)
22. Radiation:
    Radiation is considered in contact if $F_{rad}\ne 0$ and the distance, $d_{}$ , of the secondary node to the main segment is:(29)

    $$\mathit{Gap}<d<D_{\mathit{rad}}$$
    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:(30)

    $$h_{\mathit{rad}}=F_{\mathit{rad}}\left({T_m}^2+{T_s}^2\right)\cdot \left(T_m+T_s\right)$$
    with(31)

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

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. When sens_ID is defined for activation/deactivation of the interface, T_start and T_stop are not taken into account.