PCNTX7

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Example

Definitions

Comments

1. The property identification number must be that of an existing PCONT Bulk Data Entry. Only one PCNTX7 property extension can be associated with a particular PCONT.
2. PCNTX7 is only applied in geometric nonlinear analysis subcases which are defined by ANALYSIS = EXPDYN. It is ignored for all other subcases.
3. If FRIC is not explicitly defined on the PCONTX/PCNTX# entries, the MU1 value on the CONTACT or PCONT entry is used for FRIC in the /INTER entries for Geometric Nonlinear Analysis. Otherwise, FRIC on PCONTX/PCNTX# overwrites the MU1 value on CONTACT/PCONT.
4. In implicit analysis, different contact formulations are used for contact where secondary and main set do not overlap and where they overlap (self-contact).

   In the case of self-contact, the gap cannot be zero and a constant gap is used. For small initial gaps, the convergence will be more stable and faster if GAP is larger than the initial gap.

   In implicit analysis, sometimes a stiffness with scaling factor reduction (for example, STFAC = 0.01) or reduction in impacted thickness (if rigid one) might reduce unbalanced forces and improve convergence, particularly in shell structures under bending where the effective stiffness is much lower than membrane stiffness; but it should be noted that too low of a value could also lead to divergence.

5. If ISTF ≠ 1, the interface stiffness K is computed from the main segment stiffness Km and/or the secondary segment stiffness Ks.

   The main stiffness is computed from Km = STFAC * B * S * S/V for solids, Km = 0.5 * STFAC * E * t for shells.

   The secondary stiffness is an equivalent nodal stiffness computed as Ks = STFAC * B * V-3 for solids, Ks = 0.5 * STFAC * E * t for shells.

   In these equations, B is the Bulk Modulus, S is the segment area, and V is the volume of a solid. There is no limitation to the value of stiffness factor (but a value larger than 1.0 can reduce the initial time step).

   The interface stiffness is then K = max (STMIN, min (STMAX, K1)) with:

   • ISTF = 0, K1 = Km
   • ISTF = 2, K1 = 0.5 * (Km + Ks)
   • ISTF = 3, K1 = max (Km, Ks)
   • ISTF = 4, K1 = min (Km, Ks)
   • ISTF = 5, K1 = Km * Ks / (Km + Ks)
6. The default for the constant gap (IGAP = CONST) is the minimum of:
   • t, average thickness of the main shell elements
   • l/10, l - average side length of the main solid elements
   • lmin/2, lmin - smallest side length of all main segments (shell or solid)
7. If IGAP = VAR, the variable gap is computed as gs + gm

   If IGAP = VAR2, the variable gap is computed as max(GAP, min(GAPFAC * (gs+gm), GAPMAX)

   If IGAP = VAR3, the variable gap is computed as max(GAP, min(GAPFAC * (gs+gm), MESHSIZE * (gsl+gml), GAPMAX)

   with:

   • gm - main element gap, with:

     gm = t/2, t: thickness of the main element for shell elements.

     gm = 0 for solid elements.

   • gs - secondary node gap:

     gs = 0 if the secondary node is not connected to any element or is only connected to solid or spring elements.

     gs = t/2, t - largest thickness of the shell elements connected to the secondary node.

     gs = 1/2√S for truss and beam elements, with S being the cross-section of the element.

   • gml - length of the smaller edge of element.
   • gsl - length of the smaller edge of elements connected to the secondary nodes.

   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.

8. If ICURV = 1, a spherical curvature is defined for the gap with node_ID1 (center of the sphere).

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

   If ICURV = 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 large change in curvature, this formulation might become unstable (will be improved in future version).

   
   
   Figure 1.

9. In case of adaptive meshing and IADM =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.

10. In case of adaptive meshing and IADM =2:

    If the contact occurs in a zone (main side) whose radius of curvature is lower than NRadm 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 Angladm and the percentage of penetration is greater than Padm, the element on the secondary side will be divided (if not yet at maximum level).

    
    
    Figure 3.

11. The coefficients NRADM, PADM, and ANGLADM are used only adaptive meshing and IADM = 2.
12. INACTI = 3, is only recommended for small initial penetrations and should be used with caution because:
    • the coordinate change is irreversible
    • it may create other initial penetrations if several surface layers are defined in the interfaces
    • it may create initial energy if the node belongs to a spring element

    INACTI = 5 is recommended for airbag simulation deployment.

    INACTI = 6 is recommended instead of INACTI = 5, in order to avoid high frequency effects into the interfaces.

    
    
    Figure 4.

    If FPENMAX is not equal to zero, nodes stiffness is deactivated if penetration > FPENMAX*GAP, regardless of the value of INACTI.

13. IFRIC defines the friction model.

    IFRIC = COUL - Coulomb friction with F_T < FRIC * F_N.

    For IFRIC > 0 the friction coefficient is set by a function ( $\mu$ = $\mu$ (p, V)), where p is the pressure of the normal force on the main segment and V is the tangential velocity of the secondary node.

    The following formulations are available:

    • IFRIC = 1 - Generalized viscous friction law(1)
      $$\mu =\text{FRIC}+\text{C}1*\text{p}+\text{C}2*\text{V}+\text{C}3*\text{p}*\text{v}+\text{C}4*{\text{p}}^2+\text{C}5*{\text{v}}^2$$
    • IFRIC = 2 - Darmstad law(2)
      $$\mu ={\text{C}}_1*{\text{e}}^{(\text{C}{\hspace{0.17em}}_2\text{V})}*{\text{p}}^2+{\text{C}}_3*{\text{e}}^{(\text{C}{\hspace{0.17em}}_4\text{V})}*\text{p}+{\text{C}}_5*{\text{e}}^{(\text{C}{\hspace{0.17em}}_6\text{V})}$$
    • IFRIC = 3 - Renard law

      $\mu =C_1+\left(C_3-C_1\right)·\frac{V}{C_5}·\left(2-\frac{V}{C_5}\right)$	0 ≤ V ≤ C5
      $\mu =C_3-\left(\left(C_3-C_4\right)·{\left(\frac{V-C_5}{C_6-C_5}\right)}^2·\left(3-2·\frac{V-C_5}{C_6-C_5}\right)\right)$	C5 ≤ V ≤ C6
      $\mu =C_2-\frac{1}{\frac{1}{C_2-C_4}+{\left(V-C_6\right)}^2}$	C6 ≤ V

      Where,

      (3)
      $$\begin{array}{l}{C}_1=C1={\mu }_s,C_2=C2={\mu }_d\hfill \\ C_3=C3={\mu }_{\text{max}},C_4=C4={\mu }_{\text{min}}\hfill \\ C_5=C5=V_{cr1},C_6=C6=V_{cr2}\hfill \end{array}$$
    • The first critical velocity V_cr1 must not be 0 (C5 ≠ 0). It also must be lower than the second critical velocity V_cr2 (C5 < C6).
    • The static friction coefficient C1 and the dynamic friction coefficient C2, must be lower than the maximum friction C3 (C1 ≤ C3) and C2 ≤ C3).
    • The minimum friction coefficient C4, must be lower than the static friction coefficient C1 and the dynamic friction coefficient C2 (C4≤ C1 and C4 ≤ C2).
14. IFILTR defines the method for computing the friction filtering coefficient. If IFILT ≠ NO, the tangential friction forces are smoothed using a filter:(4)
    $${\text{F}}_{\text{T}}=\alpha ·{\text{F}\prime }_{\text{T}}+(1-\alpha )·{\text{F}\prime }_{\text{T}-1}$$
    Where,

    F_T

    Tangential force

    F'_T

    Tangential force at time t

    F'_T-1

    Tangential force at time t-1

    α

    Filtering coefficient

    • IFILTR = SIMP conref="../../bank/solvers_symbols_equations_r_b.dita#reference_xh2_vkk_pw/o2_sym_alpha" id="pcntx7_bulk_r_ph_dmj_vtb_k1b"/> = FFAC
    • IFILTR = PER conref="../../bank/solvers_symbols_equations_r_b.dita#reference_xh2_vkk_pw/o2_sym_alpha" id="pcntx7_bulk_r_ph_dwt_vtb_k1b"/> = 2πdt/FFAC, where dt/T = FFAC, T is the filtering period
    • IFILTR = CUTF conref="../../bank/solvers_symbols_equations_r_b.dita#reference_xh2_vkk_pw/o2_sym_alpha" id="pcntx7_bulk_r_ph_stz_vtb_k1b"/> = 2π * FFAC * dt, where FFAC is the cutting frequency
15. IFORM selects two types of contact friction penalty formulation.
    The viscous (total) formulation (IFORM = VISC) computes an adhesive force as:(5)

    $$\begin{array}{l}{\text{F}}_{\text{adh}}=\text{VISF}*(\surd 2\text{KM})*{\text{V}}_{\text{T}}\\ {\text{F}}_{\text{T}}=\text{min}({\mu \text{F}}_{\text{N}},{\text{F}}_{\text{adh}})\\ \end{array}$$
    The stiffness (incremental) formulation (IFORM = STIFF) computes an adhesive force as:(6)

    $$\begin{array}{l}{\text{F}}_{\text{adh}}={\text{F}}_{\text{Told}}+\Delta {\text{F}}_{\text{T}}\hfill \\ \Delta {\text{F}}_{\text{T}}=\text{K}*{\text{V}}_{\text{T}}*\text{dt}\hfill \\ {\text{F}}_{\text{Tnew}}=\text{min}({\mu \text{F}}_{\text{N}},{\text{F}}_{\text{adh}})\hfill \end{array}$$
16. Exchange between shell and constant temperature contact TINT.
17. RTHE is the inverse of thermal resistance (units: [W/(m²*K)]).
18. Secondary segment contact is deactivated when the segment kinematic time step calculated for this contact is lower than DTMIN.
19. With IREMGAP = 2, this allows the element size < gap values:

    
    
    Figure 5.

    In case of self-impact contact, when curvilinear distance (from a node of the main segment to a secondary node) is < gap*sqrt(2) (in initial configuration), then 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.

20. When SENSID is defined for activation/deactivation of the interface, TSTART and TSTOP are not taken into account.
21. If FRAD is not equal to zero, and d, the distance from the secondary node to the main segment, is in the range: Gap < d < DRAD, then radiation is calculated. The radiant heat transfer conductance is calculated as:(7)
    $$h_{\mathit{rad}}=F_{\mathit{rad}}\left(T_m^2+T_s^2\right)\left(T_m+T_s\right)$$
    (8)
    $$F_{\mathit{rad}}=\frac{\sigma }{\frac{1}{{\varepsilon }_1}+\frac{1}{{\varepsilon }_2}-1}$$
    Where,

    $\sigma$

    Stefan Boltzman constant

    ${\epsilon }_1$

    Emissivity of the secondary surface

    ${\epsilon }_2$

    Emissivity of the main surface

22. If FRAD is not equals to zero, then the default value of DRAD is calculated as the maximum of:
    • upper value of the gap (at time 0) among all nodes
    • smallest side length of secondary element
23. Frictional energy is converted into heat when heat transfer is activated (ITHE > 0) on the interface. Options FHEATS and FHEATM are used to control this option.

    When FHEATS and FHEATM = 0, the conversion of the frictional sliding energy to heat is not activated. Non-zero values of FHEATS and FHEATM define the fraction of this energy which is converted into heat and transferred to the secondary and main, respectively.

    The frictional heat QFric is defined as:

    If IFORM = 2 (a stiffness formulation):

    • Secondary: (9)
      $$Q_{\mathit{Fric}}={\mathit{Fheat}}_s\cdot \frac{\left(F_{\mathit{adh}}-F_T\right)}{K}\cdot F_T$$
    • Main: (10)
      $$Q_{\mathit{Fric}}={\mathit{Fheat}}_m\cdot \frac{\left(F_{\mathit{adh}}-F_T\right)}{K}\cdot F_T$$

      (ITHEF=1)

    If IFORM = 1 (a penalty formulation):

    • Secondary: (11)
      $$Q_{\mathit{Fric}}={\mathit{Fheat}}_s\cdot C\cdot V_T^2\cdot dt$$
    • Main: (12)
      $$Q_{\mathit{Fric}}={\mathit{Fheat}}_m\cdot C\cdot V_T^2\cdot dt$$
      (ITHEF=1)
24. This card is represented as an extension to a PCONT property in HyperMesh.