/INTER/TYPE25

Solid elements have zero contact gap thickness. Contact inputs can be defined as a single surface, surface to surface, or nodes to surface.

This contact interface can replace interface TYPE3, TYPE5, TYPE7, TYPE19 or TYPE24.

This interface is not available with the implicit solution.

Format

Definitions

Flags for Deactivation of Boundary Conditions: IBC

Definitions

Comments

1. Contact main/secondary pairs can be defined in three ways:
   • Single self-impacting surface only: surf_ID₁ > 0, and surf_ID₂ = 0
   • Symmetric surface to surface: surf_ID₁ > 0, and surf_ID₂ > 0
   • Nodes to surface: grnd_ID_s > 0, surf_ID₁ = 0, and surf_ID₂ > 0

   grnd_ID_s > 0 is used to define node to surface contact type, but it may also be used in other contact types. In that case, the node group will be added simply as supplementary secondary nodes, which is useful when users want to add spring element nodes, main node of rigid body, etc. into the contact (as secondary nodes).

   If the surface is defined with shells, two contact segments (shifted by half thickness (t)) with opposite normal directions will be generated:

   
   
   Figure 1.

   In case of SPMD, each main segment defined by surf_ID_i (i=1, 2) must be associated to an element (possibly to a void element).

   In cases where quadratic elements are used, it is recommended to define the surfaces by using /SURF/PART/EXT as in that case, middle nodes of quadratic elements are used in the contact treatment.

   The surface definition /SURF/PART/ALL is not available with TYPE25.

2. Contact stiffness, $K$ is computed as:(1)
   $$K=\max \left[S{t}_{\min },\min \left(S{t}_{\max },K_n\right)\right]$$
   Where, $K_n$ depends on I_stf:

   • I_stf = 1000, $K_n=K_m$
   • 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, $K_n=\frac{K_m\cdot K_s}{K_m+K_s}$
   $K_m$ : main segment stiffness and computed as:

   • $K_m=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$ , when the main segment lies on a shell.
   • $K_m=\mathit{Stfac}\cdot B\cdot \frac{S^2}{V}$ , when main segment lies on a solid.
   • $K_m=\max \left(\mathit{Stfac}\cdot 0.5\cdot E\cdot t,\mathit{Stfac}\cdot B\cdot \frac{S^2}{V}\right)$ , when main segment is shared by shell and solid.
   $K_s$ : Secondary node stiffness is an equivalent nodal stiffness considered for interface TYPE25, and computed as:

   • $K_m=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$ , when node is connected to a shell element,
   • $K_s=Stfac\cdot B\cdot \sqrt[3]{V}$ , when node is connected to solid element.
   Where,

   $S$

   Segment area

   $V$

   Volume of the solid

   $B$

   Bulk modulus

   $t$

   Thickness of the shell

   The Stfac value can be larger than 1.0. There is no limitation value to the stiffness factor (a value larger 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.

3. The gap is computed automatically for each impact as:
   • If I_gap = 1, variable gap is computed as:(2)
     $$\min (g_s,Gap\_\max \_s)+\min (g_m,Gap\_\max \_m)$$
   • If I_gap=2, variable gap is computed as:(3)
     $$\min (g_s,Gap\_\max \_s)+\min (g_m,Gap\_\max \_m)$$
     with deactivation of secondary nodes when the element size is smaller than gap values:

     
     
     Figure 2.

     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.

   • If I_gap= 3, variable gap is computed as:(4)
     $$\min \left[\min (g_s,Gap\_\max \_s)+\min (g_m,Gap\_\max \_m),\%mesh\_size\cdot \left(g_{s\_l}+g_{m\_l}\right)\right]$$
     Where,

     • $g_m$ : main element gap:

       $g_m=Gap\_scale*\frac{t}{2}$ , with $t$ is 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.

       $g_s=Gap\_scale*\frac{t}{2}$ , if the secondary node is connected to a shell element, with $t$ being the largest thickness of the shell elements connected to the secondary node.

       $g_s=Gap\_scale*\frac{\sqrt{S}}{2}$ , if the secondary node is connected to truss or beam elements, with $S$ being the cross section of the 1D element.

       If the gap modification flag for secondary shell nodes on the free edges I_gap0 is set to 1: $g_s$ is reset to zero if the secondary node lies on the free edges of the secondary surface. The gap modification flag for secondary shell nodes on the free edges has no effect if the secondary node is defined through the optional node group (grnod_IDs).

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

   • $gm\_l$ : length of the smallest edge of the main segment.
   • $gs\_l$ : if the secondary node belongs to the main surface, $gs\_l$ is the length of the smallest edge of main segments connected to the secondary node, $gs\_l$ =1E+30, otherwise.

     In any case, $g_m$ and $g_s$ are limited separately by Gap_max_m and Gap_max_s before the gap is computed.

     If the secondary node does not belong to the main surface, the gap remains (5)

     $$\min (g_s,Gap\_\max \_s)+\min (g_m,Gap\_\max \_m)$$
4. For node to surface contact, the gap never extends more than the secondary node gap out of the surface external border. I_shape determines if the shape of this gap is square or round and the contact force (normal) direction. I_shape has no effect on the gap and its shape for edge to edge contact.
   Depending on I_shape the gap used for contact at the main surface external border and resulting force direction.

   
   
   Figure 3. I_shape=1 (Square Gap)

   
   
   Figure 4. I_shape=2 (Round Gap)

   I_shape =1 is not available with I_gap =3 and will then be reset to I_shape =2.

5. For shell element edge to edge contact, the gap is round. The main side contact gap on the free edge is shifted so that the edge does not extend out of the shell segment.

   
   
   Figure 5. Edge contact main side

   The secondary side contact gap on the free edge behavior depends on the value of I_gap0 as shown in figure xyz.

   
   
   Figure 6. Edge contact secondary side

6. For solid elements when I_edge=11 and I_edge=13, the secondary side consists of only the sharp edges with angle smaller than Edge_angle. For I_edge=22, all edges from solid elements are considered on secondary side. On the main side, all edges from solid elements are included for all 3 I_edge cases.

   
   
   Figure 7. Secondary side edges for I_edge=11 and I_edge=13

7. 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.
   The friction forces are:(6)

   $$F_t^{new}=\min \left(\mu F_n,F_{adh}\right)$$

   While an adhesion force is computed as:

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

   Where, $\mu$ is the Coulomb friction coefficient and is defined as:

   • For flag I_fric by default:

     $\mu =Fric$ with $F_T\le \mu \cdot F_N$ (Coulomb friction)

   • For flag I_fric > 1, 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

   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):(7)
     $$\mu =\mathit{Fric}+C_1\cdot p+C_2\cdot V+C_3\cdot p\cdot V+C_4\cdot p^2+C_5\cdot V^2$$
   • I_fric = 2 (Modified Darmstad law):(8)
     $$\mu =Fric+C_1\cdot e^{\left(C_{2}V\right)}\cdot p^2+C_3\cdot e^{\left(C_{4}V\right)}\cdot p+C_5\cdot e^{\left(C_{6}V\right)}$$
   • 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,

     • $C_1={\mu }_s$ , 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
     • $C_4={\mu }_{\min }$ , minimum coefficient of friction
     • $C_5=V_{cr1}\ne 0$ , first critical velocity, must be > 0
     • $C_6=V_{cr2}$ , second critical velocity, must be $>V_{cr1}$

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

8. Friction filtering
   If I_filtr = 1, 2 or 3, the tangential forces are smoothed using a filter:(9)

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

   • If I_filtr = 1: α = X_freq, simple numerical filter
   • If I_filtr = 2: $\alpha =\frac{2\cdot \pi }{X_{freq}}$ , standard -3dB filter, with $X_{freq}=\frac{dt}{T}$ , and T = filtering period
   • If I_filtr = 3: $\alpha =2\cdot \pi \cdot X_{\mathit{freq}}\cdot dt$ , standard -3dB filter, with X_freq = cutting frequency

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

9. Inacti and Ipen_max, initial penetration treatment:
   • Inacti = 1000: The initial penetrations are ignored: no contact force is applied, but the nodes are not deactivated from the contact; if the node goes out of the contact and later gets back into contact, contact forces are then applied.

     
     
     Figure 8.

   • Inacti = -1: Initial forces are applied on all penetrating nodes. High initial penetrations should be avoided, as they might generate high contact forces and lead to high energy error at the beginning of the computation.
   • Inacti = 5: The main segment is shifted by the initial penetration value ( $P_0$ ); therefore, at time zero no initial forces are applied.

   The main segment position is restored only in case of rebound larger than $P_0$ .

   In the opposite case, when secondary node continues to penetrate, the penetration is computed as:(10)

   $$P\text{'}=P-P_0$$

   
   
   Figure 9.

   • Intersections and large initial penetration (Inacti= -1 and 5):

     Shells: initial intersections should be avoided, as they will lead to wrong direction of contact force and possible secondary nodes anchorage.

10. When sens_ID is defined for activation/deactivation of the interface, T_start and T_stop are not taken into account.
11. For output forces:

    When the contact type is asymmetric surface to surface, the output normal contact forces in Time History are calculated correctly, if the two surfaces are well separated.

12. IVIS2=-1: is used to add adhesion in the normal direction and viscous resistive forces in the tangential direction. This can be used to model thermoplastic composite forming.
    When used, half of the contact gap is considered an adhesive zone and the other half a physical contact zone. Therefore, to maintain the same physical contact gap, the contact thickness should be doubled using Gap_scale.

    
    
    Figure 10.

    The adhesive force is only applied after secondary nodes have entered the physical contact zone and then move back into the adhesion zone. The adhesive force acts to prevent the node from moving out of the adhesion zone and is applied in the normal direction.(11)

    $$F_N=\frac{SigMaxAdh\cdot Area}{\frac{1}{2}Gap}(\frac{1}{2}Gap-P_{adh})$$

    Where,

    $Area$

    Area of the secondary surface

    $P_{adh}$

    Penetration into the adhesion zone

    $Gap$

    Contact gap as calculated in Comment 3

    The adhesive spring ruptures as the node exits the adhesion zone and will be recreated if the node enters the contact zone again.

    Viscous resistive forces are applied in the tangential direction when the secondary nodes enter into the adhesion zone. A viscous tangential opposing force is applied instead of a friction force and is calculated as:(12)

    $$F_T=-(ViscAdhFact)\frac{ViscFluid\cdot Area}{\frac{1}{2}Gap}{V}_{rel}$$

    Where,

    $Area$

    Area of the secondary surface

    $V_{rel}$

    Penetration into the adhesion zone

    $Gap$

    Contact gap

    
    
    Figure 11.