/INTER/TYPE21

Description

Format

Definition

Comments

1. In case of SPMD, each main segment defined by surf_ID_m must be associated to an element (possibly to a void element).
2. Contact gap
   • If I_gap = 0 (constant gap),

     Gap is constant over the secondary surface and along the time, equal to Gap_min. And a default value for Gap_min is computed as $t/2$ , $t$ being the average thickness of the secondary shell elements.

     In case of constant gap, Gap_max and Fscale_gap will not be used.

   If contact thickness of the part is not defined in input /PART:

   • If I_gap = 1, variable gap over the secondary surface is computed as:(1)
     $$\max \left[Ga{p}_{\min },\min \left(Fscal{e}_{gap}\cdot g_s,Ga{p}_{\max }\right)\right]$$
   • If I_gap = 2, variable gap over the secondary surface and along the time is computed at each time, as:(2)
     $$\max \left[Ga{p}_{\min },\min \left(Fscal{e}_{gap}\cdot g_s,Ga{p}_{\max }\right)\right]$$

     and will vary along the time according to the variation of shells and 3-node shells thickness, on the secondary side.

     Where,

     $g_s$

     Secondary node gap

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

     with $t$ is thickness of the secondary element for shell elements

     $g_s=0$

     For brick elements

   If contact thickness of the part is defined in input /PART:

   • If I_gap = 1, variable gap is computed as:(3)
     $$\max \left[Ga{p}_{\min },\min \left(Fscal{e}_{gap}\cdot \frac{t_{part}}{2},Ga{p}_{\max }\right)\right]$$
   • If I_gap = 2, variable gap is computed as:(4)
     $$\max \left[Ga{p}_{\min },\min \left(Fscal{e}_{gap}\cdot \frac{t-t_0+t_{part}}{2},Ga{p}_{\max }\right)\right]$$
     Where,

     $t_{part}$

     Maximum thickness of the parts linked to the secondary node

     $t$

     Current thickness of the secondary node

     $t_0$

     Initial thickness of the secondary node

   If I_gap = 1 or 2, the variable gap is always at most equal to Gap_max and default value for Gap_max will be set to 10³⁰ and is always at least equal to Gap_min (but there is no default value for Gap_min).

3. In case of adaptive meshing:
   • 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 1.

   • 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 2.

4. The interface allows secondary nodes to cross the main surface; if a secondary node gets into the main surface from a distance greater than DEPTH, no contact force is computed on the node.

   
   
   Figure 3.

   A default value for DEPTH is computed as the maximum of:

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

   If the input value is not equal to 0, DEPTH will be raised up to the upper value of the gap (at time 0) among all nodes.

   Too large of a DEPTH will decrease the performances of search algorithms for contact.

5. Maximum contact pressure due to thickening. P_max is used only if I_gap = 2.
   • It can be used for limiting the contact force in case of thickening.
   • It can be used for limiting the normal contact force in case of thickening according to the following equation:(5)
     $$F_n\le P_{\max }\cdot S$$
   • The tangent contact force is also limited when the flag I_Tlim = 0 by the following equation:(6)
     $$F_t\le P_{\max }\cdot \frac{S}{\sqrt{3}}$$

   Where, $S$ is the extrapolated surface of segments connected to the secondary node.

6. $F=K$

   
   
   Figure 4.

7. Stfac can be larger than 1.0.
8. Deactivation of the boundary condition is applied to secondary nodes.
9. Inacti = 3 may create initial energy if the node belongs to a spring element.

   Inacti = 5 or Inacti = 6, the gap is initially reduced and recovers its computed value as the secondary node depenetrates.

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

   
   
   Figure 5.

10. 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.
11. There is no limitation value to the stiffness factor (but a value larger than 1.0 can reduce the initial time step).
12. 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 $\mu$ is Coulomb Friction coefficient.

      • If fct_ID_F = 0

        Fric is Coulomb friction

        $\mu =\mathit{Fric}$

      • If fct_ID_F ≠ 0

        Fric becomes a scale factor of Coulomb friction coefficient which depends on the temperature.(7)

        $$\mu =\mathit{Fric}\cdot {\mathrm{f}}_F\left(Ascal{e}_F,T_{interface}\right)$$
        While, $T_{interface}$ is the interface temperature which is taken as the mean temperature of secondary and main:(8)

        $$T_{interface}=\frac{T_{secondary}+T_{main}}{2}$$
    • For flag I_fric > 0, new friction models are introduced. In this case, the friction coefficient is set by a function.(9)
      $$\mu =\mu (p,V)$$
      Where,

      $p$

      Pressure of the normal force on the main segment

      $V$

      Tangential velocity of the secondary node relative to the main segment

13. Currently, the coefficients C₁ through C₆ are used (if I_fric = 0) and C₆ is not used (if I_fric = 1) to define a variable friction coefficient $\mu$ for new friction formulations.
    The following formulations are available:

    • I_fric = 1 (Generalized Viscous Friction Law):(10)
      $$\mu =\mathit{Fric}+C_1\cdot p+C_2\cdot V+C_3\cdot p\cdot V+C_4\cdot p^2+C_5\cdot V^2$$
    • I_fric = 2 (Modified Darmstad Law):(11)
      $$\mu =Fric+C_1\cdot e^{\left(C_{2}V\right)}\cdot p^2+C_3\cdot e^{\left(C_{4}V\right)}\cdot p+C_5\cdot e^{\left(C_{6}V\right)}$$
    • 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,

      $C_1={\mu }_s$

      $C_2={\mu }_d$

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

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

      $C_5=V_{cr1}$

      $C_6=V_{cr2}$

      First critical velocity $V_{cr1}=C_5$ must be different to 0 ( $C_5\ne 0$ ).

      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 $C_4\le C_2$ ).

    • I_fric = 4 (Exponential decay friction law)
      The frictional coefficient is assumed to be dependent on the relative velocity $V$ of the surfaces in contact according to:(12)

      $$\mu =C_1+\left(Fric-C_1\right)\cdot e^{\left(-C_2\left|V\right|\right)}$$

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

14. The formulation for friction is a stiffness (incremental) formulation, and the friction forces are:(13)
    $$F_t^{new}=\min \left(\mu F_n,F_{adh}\right)$$

    While an adhesion force is computed as:

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

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

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

    $$F_{Tf}=\alpha F_T(t)+\left(1-\alpha \right)F_{Tf}(t-dt)$$
    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, $\alpha$ coefficient is calculated from, if:

    • I_filtr =1 ➤ $\alpha =X_{freq}$ , simple numerical filter with a value between 0 and 1.
    • I_filtr =2 ➤ $\alpha =\frac{2\cdot \pi }{X_{freq}}$ , standard -3dB filter, with the number of time steps to filter defined as $X_{freq}=\frac{dt}{T}$ , and T = filtering period
    • I_filtr =3 ➤ $\alpha =2\cdot \pi \cdot X_{freq}\cdot dt$ standard -3dB filter, with X_freq = cutting frequency

16. 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. So the nodal temperature of main side will be considered.

    If I_the = 2, Heat transfer is computed using thermal conductance K_the only for the secondary side. The temperature of the main side is not assumed to be a constant but is calculated from the temperature field defined on each main node. These nodal temperatures can vary over time and space which are defined using /IMPTEMP.

    Thermal conduction

    I_the = 1 needs the material of the secondary side to be a thermal material using finite element formulation for heat transfer (/HEAT/MAT).

    Thermal conduction is computed when the secondary node falls into gap:(15)

    $$gap=\max \left[Ga{p}_{\min },\min \left(\mathit{Fscal}{e}_{gap}\cdot g_s,Ga{p}_{\max }\right)\right]$$
    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, K_the is a scale factor and heat exchange depends on contact pressure:(16)
      $$\mathrm{K}=K_{the}\cdot {\mathrm{f}}_K\left(Ascal{e}_K,P\right)$$

      While ${\mathrm{f}}_K$ is the function of fct_ID_K.

17. Radiation:
    Radiation is considered in contact if $F_{rad}\ne 0$ and the distance, $d_{}$ , of the secondary node to the main segment is:(17)

    $$\mathit{Gap}<d<D_{\mathit{rad}}$$
    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:(18)

    $$h_{\mathit{rad}}=F_{\mathit{rad}}\left({T_m}^2+{T_s}^2\right)\cdot \left(T_m+T_s\right)$$
    with(19)

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

18. Heat Friction
    • Frictional energy is converted into heat when I_the > 0 for interface
    • Fheat is defined as the fraction of this energy which is converted into heat and transferred to the secondary side.
    • The frictional heat Q_Fric is so defined for a stiffness formulation:(20)
      $$Q_{\mathit{Fric}}=Fheat\cdot \frac{\left(F_{adh}-F_t\right)}{K}\cdot F_t$$
19. Critical damping factors allow for the reduction of dynamic effects, especially for those tools where a loading is applied. This can be used to model the hydraulic press system:

    A damping force (resp. torque) is applied to the tool:

    $F_d=-Cv$ (resp.) $m_d=-C_r{v}_r$

    With $C=Damp\cdot \sqrt{2\cdot Mass\cdot K}$ resp. $C_r=Dam{p}_r\cdot \sqrt{2\cdot I\cdot K_r}$

    Where,

    $C$

    Percentage of the critical damping with the tool mass Mass (resp. inertia $I$ ).

    $K$

    Total interface stiffness (resp. rotational stiffness $K_r$ ).

    $v$ (resp. ) $v_r$

    Translational (resp. rotational) velocity of the tool, if ID_ref is equal to 0; otherwise, it is the relative velocity with respect to tool of interface ID_ref.

20. When sens_ID is defined for activation/deactivation of the interface, T_start and T_stop are not taken into account.
21. If Invn = 1, Radioss will check if main normal are oriented towards the blank or not. Not well oriented normal may cause big penetrations and wrong results. If this happens, it is important to stop computation when this problem is detected. This option used to check if secondary node is contacting the main segment from the correct side (Figure 6) at the time of first impact. If not, the computation is stopped with an error message.

    
    
    Figure 6.

    • Main normal is well oriented: First impact is from correct side (penetration is smaller than Gap).
    • Main normal is not well oriented: First impact is from wrong side (penetration is almost equal to DEPTH).

    This option is only available for shells and must be used with a special care, because the computation can be stopped even if the normals are well oriented when there are large initial penetrations.

22. When fct_ID_c ≠0, the heat transfer coefficient can change as function of distance d when Gap < d ≤ Dcond.

    Abscises and ordinates of this function must be between 0 and 1.

    The heat transfer coefficient is computed as:(21)

    $$K=K_{the}\left(P=0\right)*fct\text{}\_I{D}_c\left(\frac{d-Gap}{Dcond-Gap}\right)$$

    The maximum value of $K$ is equal to the value of K_the when K_the is constant. Otherwise, in case of K_the depending on pressure, the maximum is equal to value of K_the for contact pressure $P$ =0.

    $K$ drops to zero when distance is equal to Dcond.

23. When fct_ID_c≠0, the heat transfer is computed as:
    • Conductive heat transfer when d < Gap
    • Conductive and radiative heat transfer when Gap < d ≤ Dcond.
    • Radiative heat transfer when Dcond < d ≤ Drad
24. When fct_ID_c ≠ 0 and Dcond = 0, then Dcond=D_rad.

    When F_rad ≠ 0, fct_ID_c ≠ 0, and D_rad = 0, then D_rad = Dcond.