# RD-E: 0901 - Billiards (Pool)

A pool game is modeled to show the transmission of momentum between one impacting ball and 15 impacted balls.

The purpose of this example is to investigate the transmission of momentum between several balls. Contact with the various interfaces using the Penalty and Lagrange Multipliers' method is analyzed.

## Options and Keywords Used

- 16-node thick shell and sphere mesh (/PROP/TYPE20 (TSHELL))
- TYPE7 interface using the Lagrange Multipliers method and the Penalty method (/INTER/TYPE7)
- TYPE16 sliding and tied interface, and quadratic surface contact (/INTER/LAGMUL/TYPE16)
- Elastic shock
- Momentum transmission and shock wave
- Initial velocities (/INIVEL)

^{-1}in X direction is applied to all nodes of the white (cue) ball.

All nodes of the lower face of the table are completely fixed (translations and rotations).

## Input Files

- Billiard_game/Interface_16
- <install_directory>/hwsolvers/demos/radioss/example/09_Billiards/Billiards_model/BILLARD*

## Model Description

^{-1}. Elastic rebounds are observed.

Units: mm, g, N, MPa.

**Material Properties: Balls (pheonolic resin)**- Initial density
- 0.00137 g.mm
^{-3} - Young's modulus
- 10500 $\left[\mathrm{MPa}\right]$
- Poisson ratio
- 0.3

**Material Properties: Frame (polymer)**- Initial density
- 0.001 g.mm
^{-3} - Young's modulus
- 1000 $\left[\mathrm{MPa}\right]$
- Poisson ratio
- 0.49

**Material Properties: Plate (slate)**- Initial density
- 0.0028 g.mm
^{-3} - Young's modulus
- 62000 $\left[\mathrm{MPa}\right]$
- Poisson ratio
- 0

### Model Method

Secondary nodes (red) are extracted from the external surfaces of the parts.