PCONTX

Format

Example

Definitions

Comments

1. The property identification number must be that of an existing PCONT Bulk Data Entry. Only one PCONTX property extension can be associated with a particular PCONT.
2. PCONTX 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 slave and master 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, = 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 I ≠ 1, the interface stiffness K is computed from the master segment stiffness Km and/or the slave segment stiffness Ks.

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

   The slave 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 K = max (STMIN, min (STMAX, K1)) with

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

   • gm - master element gap with

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

     gm = 0 for solid elements.

   • gs - slave node gap:

     gs = 0 if the slave 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 slave node.

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

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

8. = 3, 4 are 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.
   = 5 works as:

   
   
   Figure 1.

9. I defines the friction model.

   I = COUL - Coulomb friction with F_T ≤ FRIC * F_N.

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

   The following formulations are available:

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

     $\mu =C_1+\left(C_3-C_1\right)\cdot \frac{V}{C_5}\cdot \left(2-\frac{V}{C_5}\right)$	0 ≤ V ≤ C
     $\mu =C_3-\left(\left(C_3-C_4\right)\cdot {\left(\frac{V-C_5}{C_6-C_5}\right)}^2\cdot \left(3-2\cdot \frac{V-C_5}{C_6-C_5}\right)\right)$	C ≤ V ≤ C
     $\mu =C_2-\frac{1}{\frac{1}{C_2-C_4}+{\left(V-C_6\right)}^2}$	C ≤ 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 (C ≠ 0). It also must be lower than the second critical velocity V_cr2 (C < C).
   • The static friction coefficient C and the dynamic friction coefficient C, must be lower than the maximum friction C (C ≤ C) and C ≤ C).
   • The minimum friction coefficient C, must be lower than the static friction coefficient C and the dynamic friction coefficient C (C ≤ C and C ≤ C).
10. I selects two types of contact friction penalty formulation.
    The viscous (total) formulation (I = VISC) computes an adhesive force as:(4)

    $$\begin{array}{l}{\text{F}}_{\text{adh}}=\text{VISF}*\surd (2\text{KM})*{\text{V}}_{\text{T}}\\ {\text{F}}_{\text{T}}=\text{min}({\mu \text{F}}_{\text{N}},{\text{F}}_{\text{adh}})\\ \end{array}$$
    The stiffness (incremental) formulation (I = STIFF) computes an adhesive force as:(5)

    $$\begin{array}{l}{\text{F}}_{\text{adh}}={\text{F}}_{\text{Told}}+\Delta {\text{F}}_{\text{T}}\hfill \\ \Delta {\text{F}}_{\text{T}}=\text{K}*{\text{V}}_{\text{T}}*\text{dt}\hfill \\ {\text{F}}_{\text{Tnew}}=\text{min}({\mu \text{F}}_{\text{N}},{\text{F}}_{\text{adh}})\hfill \end{array}$$
11. I defines the method for computing the friction filtering coefficient. If I ≠ NO, the tangential friction forces are smoothed using a filter:(6)
    $${\text{F}}_{\text{T}}=\alpha *{\text{F}\prime }_{\text{T}}+(1-\alpha )*{\text{F}\prime }_{\text{T}-1}$$

    Where,

    F_T is the tangential force

    F'_T is the tangential force at time t

    F'_T-1 is the tangential force at time t-1

    α is the filtering coefficient

    I = SIMP - α = FFAC

    I = PER - α = 2πdt/FFAC, where dt/T = FFAC, T is the filtering period

    I = CUTF - α = 2π * FFAC * dt, where FFAC is the cutting frequency

12. This card is represented as an extension to a PCONT property in HyperMesh.