# RD-V: 0110 Friction

The contact friction forces are studied and compared to an analytical solution.

The contact friction forces are studied between a fixed and moving plate. The friction and reaction forces are used to calculate a displacement which is compared to the applied displacement.

## Options and Keywords Used

• /INTER/TYPE24

## Input Files

Before you begin, copy the file(s) used in this problem to your working directory.

## Model Description

The top plate is 254 mm square and 25.4 mm thick. The parts are modeled using solid elements and linear elastic material. The larger bottom fixed plate is model as a rigid by using a rigid body. The bottom plate is fully constrained. The negative y face of the top plate was constrained in the y direction. The coefficient of friction between the plates is 0.05. The top plate has displacements applied to the positive y and z faces by applying imposed velocities using:
$V=\frac{{V}_{m}}{2}\left[1+\mathrm{sin}\left(\frac{2\pi }{T}t+\frac{3\pi }{2}\right)\right]$
Table 1. Improved Velocity Inputs
${V}_{m}$ $T$ Total Displacement
565 mm/s 0.009 s Y=2.54 mm
-102 mm/s 0.001 s Z=0.0508 mm

The following system is used: mm, s, Mg.

### Simulation Iterations

The contact reaction force was output to the time history file. The reaction force from the imposed velocity applied to the top block’s positive y face were also output to the time history file. The surface to surface /INTER/TYPE24 contact interface was studied.

## Results

The displacement applied to the top block’s positive y face was compared to the displacement using:

$u=\frac{L}{Ewh}\left(F-\frac{R\mu }{2}\right)$

Where,
$u$
Theoretical displacement in the y direction
$L$
Length of the top block
$w$
Width of the top block
$h$
Height of the top block
$E$
Young's modulus
$F$
Total resultant force at the imposed velocity, calculated from /ANIM/VECT/FREAC
$R$
Total contact reaction forces in the z direction from /TH/INTER
$\mu$
Coefficient of friction

The calculated displacement, where the imposed velocity was applied in the y direction was 2.530 mm. When compared to the applied 2.540 mm displacement, there was a numerical error of 0.39%.

### Conclusion

The contact interface friction calculation results in minimum error of 0.39% when compared to theory.

1 Buechler, Miles, Amanda McCarty, Derek Reding, and R. D. Maupin. "Explicit finite element code verification problems." In 22nd SEM International Modal Analysis Conference, Dearborn, MI. 2004