Consider a microcrack in an infinite lattice stretched in the *y* direction
(Figure 1).
The easiest way to compute the displacements of atoms is by a
^{-2}.
Nevertheless, except in a small neighborhood around the microcrack,
the atoms experience a smooth (elastic)
deformation field which leads to the idea of
applying continuum elasticity models far from the defect.

The approach of

The most common solution is a so-called

Finally, a

Refereed Articles

2016 | |

[12] | Analysis of an optimization-based atomistic-to-continuum coupling method for point defects , ESAIM: Mathematical Modelling and Numerical Analysis, volume 50, 2016. [bibtex] [doi] [arXiv] |

[11] | Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations , volume 222, 2016. [bibtex] [doi] [arXiv] |

[10] | An optimization based coupling method for multiscale problems , Multiscale Model. Simul., Society for Industrial and Applied Mathematics, volume 14, 2016. [bibtex] [pdf] [doi] |

2014 | |

[9] | Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method , Computer Methods in Applied Mechanics and Engineering, volume 268, 2014. [bibtex] [pdf] [doi] [arXiv] |

[8] | (In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods , Multiscale Model. Simul., volume 12, 2014. [bibtex] [pdf] [doi] [arXiv] |

[7] | An optimization-based atomistic-to-continuum coupling method , SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, volume 52, 2014. [bibtex] [arXiv] |

2013 | |

[6] | Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice , Math. Comp., volume 82, 2013. [bibtex] [doi] [arXiv] |

[5] | A Priori and A Posteriori $W^1,infty$ Error Analysis of a QC Method for Complex Lattices , SIAM J. Numer. Anal., volume 51, 2013. [bibtex] [doi] [arXiv] |

2012 | |

[4] | Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions , SIAM J. Sci. Comput., volume 34, 2012. [bibtex] [doi] [arXiv] |

[3] | The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain , Multiscale Model. Simul., volume 10, 2012. [bibtex] [doi] [arXiv] |

[2] | Numerical Methods for Multilattices , Multiscale Model. Simul., volume 10, 2012. [bibtex] [doi] [arXiv] |

2011 | |

[1] | Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions , Multiscale Model. Simul., volume 9, 2011. [bibtex] [doi] [arXiv] |