/INTER/TYPE24

Penalty stiffness is constant and therefore, the time step is not affected (for standard penalty stiffness). Solid elements are given a zero gap. Three types of inputs contacts can be defined: single surface, surface to surface, or nodes to surface. This contact interface can replace interface TYPE3, TYPE5, or TYPE7. For implicit solution, this interface TYPE24 is only available with SMP.

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 you 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).

   The surface definition /SURF/PART/ALL is not available with TYPE24.

2. Contact stiffness, K is defined as:(1)
   $$K=\max \left[S{t}_{\min },\min \left(S{t}_{\max },K_n\right)\right]$$
   Where, $K_n$ depends on I_stf
   • If I_stf = 1000, $K_n=K_m$ (Default stiffness)
   • 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, $K_n=\frac{K_m\cdot K_s}{K_m+K_s}$
   • I_stf = 6, $K_n=\min \left(K_m,K_s\right)$ ,

     Soft stiffness. This option is only available with implicit solution.

     For each contact, to make nonlinear iteration convergence easier, smaller initial stiffness is used; for the function of the reaction of the contacting parts (with increasing penetration or rebound), the stiffness will be adjusted, but is always smaller than the input stiffness.

   • I_stf = 12, Nitsche method with $K_n=\frac{K_m+K_s}{2}$
   • I_stf = 13, Nitsche method with $K_n=\max \left(K_m,K_s\right)$
   • I_stf = 14, Nitsche method with $K_n=\min \left(K_m,K_s\right)$

   $K_m$ : main segment stiffness

   • $K_m=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$ , when the main segment lies on a shell
   • $K_m=\max \left(\mathit{Stfac}\cdot 0.5\cdot E\cdot t,\mathit{Stfac}\cdot B\cdot \frac{S^2}{V}\right)$ , when main segment is shared by shell and solid
   • $K_m=\mathit{Stfac}\cdot B\cdot \frac{S^2}{V}$ , when main segment lies on a solid.
   $K_s$ : Secondary node stiffness is an equivalent nodal stiffness considered for interface TYPE24, and computed as:

   • $K_s=\mathit{Stfac}\cdot 0.5\cdot E\cdot t$ , 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.

   If Implicit Analysis is to be considered (defined by /IMPLICIT), the default value is I_stf= 4; I_stf = 6 is recommended for flexible or bending dominated structures.

3. The Nitsche method ¹ is a contact algorithm used to resolve contact equations. This method can be used in place of the traditional penalty contact method. Nitsche method is better at preventing contact penetrations especially for cases of contact between components with different material stiffness such as contact between rubber and metal. For these cases, it is difficult to select a penalty stiffness because using the minimum stiffness may lead to large penetrations and using the maximum contact stiffness may result in highly deformed elements and a decreasing time step. The Nitsche method can improve modeling such problems because the contact forces are computed using the contact stiffness, penetrations, and the element's stresses. The Nitsche method is available only for single surface or surface to surface contact between solids and not edge to edge contact.
4. The gap is computed automatically (similar to the variable gap, I_gap = 1 of TYPE7) for each impact as:(2)
   $$gap=g_m+g_s$$
   While,

   • $g_m$ : main element gap:

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

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

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

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

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

   Limitation concerning I_gap0=1:

   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 (grnd_ID_s).

5. 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:(3)

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

   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):(4)
     $$\mu =\mathit{Fric}+C_1\cdot p+C_2\cdot V+C_3\cdot p\cdot V+C_4\cdot p^2+C_5\cdot V^2$$
   • I_fric = 2 (Modified Darmstad law):(5)
     $$\mu =Fric+C_1\cdot e^{\left(C_{2}V\right)}\cdot p^2+C_3\cdot e^{\left(C_{4}V\right)}\cdot p+C_5\cdot e^{\left(C_{6}V\right)}$$
   • 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 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						$\left[\frac{\text{m}}{\text{s}}\right]$	$\left[\frac{\text{m}}{\text{s}}\right]$

6. Friction filtering
   If I_filtr = 1, 2 or 3, the tangential forces are smoothed using a filter:(6)

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

7. 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 2.

   • 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.

     The contact forces caused by the initial penetration are increased from zero at t=0.0 to full contact force at 10,000 cycles. This slow increase of the contact force allows press fit situations in models to be simulated.

   • 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:(7)

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

   
   
   Figure 3.

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

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

     Solids: by default, the distance which is considered for searching the initial penetration is compute as:(8)

     $$d=\frac{{\displaystyle \sum _{main\begin{array}{c}\end{array}segments}\frac{1}{2}\min \left[\frac{V}{A},{\max }_{edge=1,4}(L_{edge})\right]}}{N\_m\_seg}$$
     While for each main segment,

     $V$

     Volume of the connected solid element

     $A$

     Segment area

     $L_{edge}$

     $edge$ = 1 to 4 are the lengths of the edges of the segment.

     $N\_m\_seg$

     Number of main segments

     $\min \left[\frac{V}{A},{\max }_{edge=1,4}(L_{edge})\right]$

     An estimation of the depth of the solid element connected to the segment (limited to the size of the segment)

     
     
     Figure 4.

   Maximum initial penetration Ipen_max:

   • If a non-zero value is input for Ipen_max, this default value is omitted and initial penetrations will be searched within Ipen_max.
   • Large value of the searching distance might lead to poor performance of Radioss Starter and/or memory allocation failure. Therefore, it is advised not to set a too large value for Ipen_max.
   • Nevertheless, Ipen_max may be used to catch penetrations larger than the computed (default) searching distance, as shown in Figure 5:

     
     
     Figure 5.

8. I_pen0, Initial penetration detection flag:
   • By default, the detection of the penetrations for self-impacts for each part (shell and solid elements only) are always excluded (even if surf_ID₁ is defined in isolation and Inacti =-1 is set).
   • I_pen0 = 1 initial penetrations are taken into account for self-impact for each part and initial forces are set, but in some complex situations, incorrect initial penetrations might be calculated.
9. When sens_ID is defined for activation/deactivation of the interface, T_start and T_stop are not taken into account.
10. When edge to edge contact is activated using $I_{edge}$ =1, the edge to edge contact is symmetric and the edges used in contact are automatically generated from the defined single surface (surf_ID₁) or surface to surface contact (surf_ID₁ and surf_ID₂):
    • For solids and shells

      The edges are considered anywhere the angle between two external segments which share the same edge is smaller than Edge_angle value (by default 135°).

    • For shells
      The edges are considered at the perimeter border of the shell parts.

      
      
      Figure 6.

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. For implicit solution:
    • Interface TYPE24 is only available with SMP
    • The default for I_stf will be set to 4 (I_stf=6 can be used, recommended for flexible or bending dominated structures)
    • The default for Inacti will be set to -1