### Abstract

The A-CD^{2} method gives a mechanical description for instantaneous collisions between rigid bodies. This method considers a solid that moves with constant velocity in the intervals [t_{1}, t_{c}[ and ]t_{c}, t_{2}]. The contact points at t_{c} are computed with the current position and the new velocities, due to the collision at t_{c}, are calculated by means of a constrained optimization problem. Several applications have used this method. When the solid is governed by a torque free motion, the velocities are not necessarily constants, because depend on the moments of inertia. This behavior is not included in the ACD^{2} method, since constant velocities are considered. An extension includes the use of the Euler equations for modeling the angular velocities, when the body is torque free. Therefore, non constant angular velocities are obtained when the moments of inertia are different. An important result is the reduction in the computational complexity of the original algorithm, from O(N^{2}) to O(N), mainly due to the contact detection stage. This reduction allows to handle problem 20 times larger than the original. Numerical simulations for granular layers motion are presented.

Original language | English |
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Title of host publication | Proceedings of the 6th European Conference on Computational Mechanics |

Subtitle of host publication | Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 |

Editors | Roger Owen, Rene de Borst, Jason Reese, Chris Pearce |

Publisher | International Centre for Numerical Methods in Engineering, CIMNE |

Pages | 1896-1905 |

Number of pages | 10 |

ISBN (Electronic) | 9788494731167 |

Publication status | Published - 1 Jan 2020 |

Event | 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 - Glasgow, United Kingdom Duration: 11 Jun 2018 → 15 Jun 2018 |

### Publication series

Name | Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 |
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### Conference

Conference | 6th ECCOMAS European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th ECCOMAS European Conference on Computational Fluid Dynamics, ECFD 2018 |
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Country | United Kingdom |

City | Glasgow |

Period | 11/06/18 → 15/06/18 |

### Keywords

- Computational complexity
- Contact detection
- Rigid body collision

### ASJC Scopus subject areas

- Computer Science Applications
- Computational Theory and Mathematics
- Mechanics of Materials
- Mechanical Engineering

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## Cite this

^{2}method. In R. Owen, R. de Borst, J. Reese, & C. Pearce (Eds.),

*Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018*(pp. 1896-1905). (Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018). International Centre for Numerical Methods in Engineering, CIMNE.