# A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

Rafii-Tabar, Hashem, Lu, Hua and Cross, Mark
(1998)
*A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate.*
Journal of Physics: Condensed Matter, 10 (11).
pp. 2375-2387.
ISSN 0953-8984 (Print), 1361-648X (Online)
(doi:10.1088/0953-8984/10/11/003)

## Abstract

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | modelling, crack propagation |

Subjects: | Q Science > QA Mathematics Q Science > QC Physics Q Science > QD Chemistry |

Pre-2014 Departments: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis > Computational Mechanics & Reliability Group School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis > Computational Science & Engineering Group School of Computing & Mathematical Sciences > Department of Mathematical Sciences |

Related URLs: | |

Last Modified: | 14 Oct 2016 08:59 |

URI: | http://gala.gre.ac.uk/id/eprint/88 |

### Actions (login required)

View Item |