/INTER/TYPE7

Description

Format

Definitions

Flags for Deactivation of Boundary Conditions: IBC

Definitions

Comments

1. In case of SPMD, each master 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 master segment stiffness $K_m$ and slave 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 master segment stiffness and computed as:

   When the master 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 master 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 master 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 (master side) whose radius of curvature is lower than the element size (slave side), the element on the slave 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 (master side) whose radius of curvature is lower than NR_adm times the element size (slave side), the element on the slave side will be divided (if not yet at maximum level).

   If the contact occurs in a zone (master 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 slave 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 master segments are shell and solid elements, Gap_min = min ( $t{}_m$ , $\frac{l_{\min }}{2}$ ).

    Where,

    $t{}_m$

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

    $t{}_m$

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

    $l_{\min }$

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

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

    Where, $l_{\min }$ being the smallest side of all master 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,

    • $g_m$ : master element gap

      $g_m=\frac{t}{2}$ : with $t$ being the thickness of the master element for shell elements

      $g_m=0$ : for brick elements

    • $g_s$ : slave node gap

      $g_s=0$ : if the slave 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 slave 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 slave node

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

    The variable gap is always at least equal to Gap_min.

12. Deactivation of the boundary condition is applied to slave 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. Slave nodes removed from node to surface contact

    For self-impact contact, when Curvilinear Distance (from a node of the master segment to a slave node) is smaller than $\sqrt{2}\cdot Gap$ (in initial configuration), this slave node will not be taken into account by this master segment, and it will not be deleted from the contact for the other master 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 slave and master:(13)

    $$T_{\mathit{interface}}=\frac{T_{\mathit{slave}}+T_{\mathit{master}}}{2}$$

    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 master segment

    $V$

    Tangential velocity of the slave node relative to the master 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,

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

    • 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 less than the second critical velocity $V_{cr2}=C_6\left(C_5<C_6\right)$ .
    • 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		$\left[\frac{1}{Pa}\right]$	$\left[\frac{\text{s}}{\text{m}}\right]$	$\left[\frac{\text{s}}{\text{Pa}\cdot \text{m}}\right]$	$\left[\frac{1}{{\text{Pa}}^2}\right]$	$\left[\frac{{\text{s}}^2}{{\text{m}}^2}\right]$
    2			$\left[\frac{\text{s}}{\text{m}}\right]$		$\left[\frac{\text{s}}{\text{m}}\right]$		$\left[\frac{\text{s}}{\text{m}}\right]$
    3						$\left[\frac{\text{m}}{\text{s}}\right]$	$\left[\frac{\text{m}}{\text{s}}\right]$

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

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

    • If I_filtr = 1: $\alpha =X_{freq}$ , simple numerical filter.
    • If I_filtr = 2: $\alpha =\frac{2\cdot \pi }{X_{freq}}$ , standard -3dB filter, with $X_{\mathit{freq}}=\frac{dt}{T}$ , 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.

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

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 slave node relative to the master segment.

      I_form = 2 is recommended for implicit and low speed impact 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 master 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 master 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 slave side and master 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):
        Slave side: (25)

        $$Q_{\mathit{Fric}}={\mathit{Fheat}}_s\cdot \frac{\left(F_{\mathit{adh}}-F_t\right)}{K}\cdot F_t$$
        Master 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):
        Slave side: (27)

        $$Q_{\mathit{Fric}}={\mathit{Fheat}}_s\cdot C\cdot {V_t}^2\cdot dt$$
        Master 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 slave node to the master 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 slave 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 slave surface

    ${\epsilon }_2$

    Emissivity of master surface

23. If the time step of a slave node in this contact becomes less than dtmin, the slave 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.