# SPH Cells Distribution

The particles should be created in a hexagonal compact, face centered cubic or a cubic net packing.

The hexagonal compact net and face centered cubic are recommended for use in Radioss and give similar results. A face center cubic particle distribution can be created using the HyperMesh SPH panel. A HyperMesh Tcl macro to generate hexagonal compact net is available from the Altair Connect website.

## Hexagonal Compact Net

The hexagonal compact net distribution can be created in HyperMesh using a Tcl script
available by searching in Altair Connect for the
Hexagonal Compact Net Tcl script. When using this
script, the pitch or distance between any particle and its closest neighbor is
entered as `h`_{0}.

The mass of the particle `m`_{p} is defined in the property
/PROP/SPH.

The SPH particle mass relates to the material density
$\rho $
and the pitch `h`_{0} of the hexagonal compact net. This particle mass can be
calculated as:

Since the space can be partitioned into polyhedras surrounding each particle of the net, each one with a volume:

Due to discretization differences in the volume, the mass can be more accurately represented by:

- $V$
- Total volume filled by the particles.
- $n$
- Total number of particles distributed in the volume.

For hexagonal compact net, the recommended smoothing length `h` in
/PROP/SPH is the pitch `h`_{0} which is the smallest distance between the particles. A smoothing length smaller
than this can only be used when there is no tension physical problems material. If
the material does include tensile behavior, then a smoothing length larger than `h`_{0} can be used to increase stability, but there will be an increase in the
computational cost.

`h`in /PROP/SPH are used. The accuracy and computational cost of the simulation improves as the smooth length increases.

Distance d | Number of particles at distance d | Number of particles within distance d |
---|---|---|

h_{0} |
12 | 12 |

$\sqrt{2}{h}_{0}$ | 6 | 18 |

$\sqrt{3}{h}_{0}$ | 24 | 42 |

2h_{0} |
12 | 54 |

$\sqrt{5}{h}_{0}$ | 24 | 78 |

## Face Centered Cubic

Similar to hexagonal compact net, each particle has 12 neighbors and the mass of a particle is:

For face centered cubic, the recommended smoothing length `h` in
`/PROP/SPH` is the pitch entered when created the sph mesh in
HyperMesh. The pitch `h`_{0} is the smallest distance between the particles. A smoothing length smaller than
`h`_{0} can only be used when there is no tension physical problems material. If the
material does include tensile behavior, then a smoothing length larger than `h`_{0} can be used to increase stability but there will be an increase in the
computational cost.

## Simple Cubic Net

`c`the side length of each elementary cube into the net.

The mass of the particles `m`_{p} should relate to the density of the material
$\rho $
and to the size `c` of the net, with respect to the following equation:

Distance d | Number of particles at distance d | Number of particles within distance d |
---|---|---|

c | 6 | 6 |

$\sqrt{2}c$ | 12 | 18 |

$\sqrt{3}c$ | 8 | 26 |

2c | 6 | 32 |

$\sqrt{5}c$ | 24 | 56 |

$\sqrt{6}c$ | 24 | 80 |

$\sqrt{2}c$ | 12 | 92 |

3c | 6 | 98 |

From experience using cubic net, a higher smoothing length compared to face centered cubic or hexagonal compact net is needed to solve the tension instability. This higher smoothing length increases the computational cost since more neighbor particles have to be included in the calculation for each particle.

For cubic net, a smoothing length `h` between 1.25c and 1.5c is
recommended in /PROP/SPH.