## Resumen

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.

Idioma original | Inglés |
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Título de la publicación alojada | Proceedings of the 6th European Conference on Computational Mechanics |

Subtítulo de la publicación alojada | Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018 |

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

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

Páginas | 1896-1905 |

Número de páginas | 10 |

ISBN (versión digital) | 9788494731167 |

Estado | Publicada - 1 ene 2020 |

Evento | 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, Reino Unido Duración: 11 jun 2018 → 15 jun 2018 |

### Serie de la publicación

Nombre | 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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### Conferencia

Conferencia | 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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País/Territorio | Reino Unido |

Ciudad | Glasgow |

Período | 11/06/18 → 15/06/18 |

## Áreas temáticas de ASJC Scopus

- Informática aplicada
- Teoría computacional y matemáticas
- Mecánica de materiales
- Ingeniería mecánica