/FRICTION

This friction model is compatible with contact interfaces: TYPE7, TYPE11, TYPE19, TYPE24 and TYPE25.

Format

Definitions

Comments

1. The friction defined in /FRICTION overrides any friction defined in the contact interface.
2. Default values listed in the first section are used for any parts whose friction is not specifically defined in the repeating section using grpart_ID1, grpart_ID2, part_ID1, and part_ID2.
3. If friction between parts is defined more than one time in the model, the friction defined in the last position are used.
4. The friction value $\mu$ is defined.
   • I_fric = 0 (Coulomb friction):(1)
     $$\mu =\mathit{Fric}$$
   • I_fric = 1 (Generalized Viscous Friction law):
     (2)

     $$\mu =\mathit{Fric}+C_1.p+C_2\cdot V+C_3.p\cdot V+C_4\cdot p^2+C_5\cdot V^2$$
     Where,

     $p$

     Pressure of the normal force on the master segment

     $V$

     Tangential velocity of the slave node

   • I_fric = 2 (Modified Darmstad law):(3)
     $$\mu =\mathit{Fric}+C_1.e^{\left(C_{2}V\right)}.p^2+C_3.e^{\left(C_{4}V\right)}.p+C_5.e^{\left(C_{6}V\right)}$$
     Where,

     $p$

     Pressure of the normal force on the master segment

     $V$

     Tangential velocity of the slave node

   • • I_fric = 3 (Renard law):(4)
       $$\mu =C_1+\left(C_3-C_1\right)\cdot \frac{V}{C_5}\cdot \left(2-\frac{V}{C_5}\right)\hspace{0.17em}\text{if}\hspace{0.17em}V\in \left[0,C_5\right]$$
       (5)
       $$\begin{array}{l}\mu =C_3-\left((C_3-C_4\right)\cdot {\left(\frac{V-C_5}{C_6-C_5}\right)}^2\cdot \left(3-2\cdot \frac{V-C_5}{C_6-C_5}\right)\hspace{0.17em})\hspace{0.17em}\text{if}\hspace{0.17em}V\in [C_5{C}_6]\\ \end{array}$$
       (6)
       $$\mu =C_2-\frac{1}{\frac{1}{C_2-C_4}+{\left(V-C_6\right)}^2}\text{if}V\ge C_6$$
     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 of Friction Formulation

     Ifric	Fric	C1	C2	C3	C4	C5	C6
     1		$\left[\frac{1}{\text{Pa}}\right]$	$\left[\frac{\text{s}}{\text{m}}\right]$	$\left[\frac{\text{s}}{\text{Pa}\cdot \text{m}}\right]$	$\left[\frac{1}{{\text{Pa}}^2}\right]$	$\left[\frac{{\text{s}}^2}{{\text{m}}^2}\right]$
     2			$\left[\frac{\text{s}}{\text{m}}\right]$		$\left[\frac{\text{s}}{\text{m}}\right]$		$\left[\frac{\text{s}}{\text{m}}\right]$
     3						$\left[\frac{\text{m}}{\text{s}}\right]$	$\left[\frac{\text{m}}{\text{s}}\right]$

5. Friction filtering
   If I_filtr ≠ 0, the tangential forces are smoothed using a filter:(7)

   $$F_t=\alpha \cdot {F^{\prime }}_t+\left(1-\alpha \right)\cdot {{F^{\prime }}_t}^{-1}$$
   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 $X_{freq}=\frac{dt}{T}$ , 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.

6. Friction penalty formulation I_form:
   • If I_form = 1 (default) viscous formulation, the friction forces are:(8)
     $$F_t=\text{min}\left(\mu F_n,F_{\text{adh}}\right)$$
     While an adhesion force is computed as:(9)

     $$F_{\text{adh}}=C\cdot V_t\text{with}C={\mathit{VIS}}_F\cdot \sqrt{2\mathit{Km}}$$
   • If I_form = 2, stiffness formulation, the friction forces are:(10)
     $$F_t^{\mathit{new}}=\text{min}\left(\mu F_n,F_{\mathit{adh}}\right)$$
     While an adhesion is computed as:(11)

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

     Where, $V_t$ is the contact tangential velocity.

     I_form = 2 is recommended for implicit and low speed impact explicit analysis.

7. Orthotropic friction for shell elements, if Idir = 1.
   • Two sets of friction coefficients must be defined after the line that contains Idir
   • The orthotropic directions are defined only on the master contact surface
   • The 2 ways to define the orthotropic friction direction
     • Use the orthotropic direction from the shell element as defined in /PROP/TYPE9, /PROP/TYPE10, /PROP/TYPE11, /PROP/TYPE17, /PROP/TYPE51, or /PROP/PCOMPP.

       Direction 1 from element.

       Direction 2 is orthogonal to Direction 1 in the segment plane.

     • Use Direction 1 defined from the vector $V$ and angle $\varphi$ defined in /FRIC_ORIENT.
   • Not supported for solid element, beam, truss or spring elements or edge to edge contact.