Title | Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case |

Publication Type | Journal Article |

Year of Publication | 1999 |

Authors | Braides, A, Dal Maso, G, Garroni, A |

Journal | Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58 |

Abstract | Starting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included. |

URL | http://hdl.handle.net/1963/3371 |

DOI | 10.1007/s002050050135 |

## Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case

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