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Fracture

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Variational Models and Methods in Solid and Fluid Mechanics

Part of the book series: CISM Courses and Lectures ((CISM,volume 535))

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Abstract

These notes begin with a review of the mainstream theory of brittle fracture, as it has emerged from the works of Griffith and Irwin. We propose a re-formulation of that theory within the confines of the calculus of variations, focussing on crack path prediction. We then illustrate the various possible minimality criteria in a simple 1d-case as well as in a tearing experiment and discuss in some details the only complete mathematical formulation so far, that is that where global minimality for the total energy holds at each time. Next we focus on the numerical treatment of crack evolution and detail crack regularization which turns out to be a good approximation from the standpoint of crack propagation. This leads to a discussion of the computation of minimizing states for a non-convex functional. We illustrate the computational issues with a detailed investigation of the tearing experiment.

Part of these notes has been extracted verbatim from Bourdin et al. (2008)

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Author information

Authors and Affiliations

  1. Louisiana State University, Baton Rouge, LA, 70803, USA

    B. Bourdin

  2. Université Paris-Nord, 93430, Villetaneuse, France

    G. A. Francfort

Authors
  1. B. Bourdin
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  2. G. A. Francfort
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Editor information

Editors and Affiliations

  1. Università “La Sapienza”, Roma, Italy

    Francesco dell’Isola

  2. Polytech Marseille, France

    Sergey Gavrilyuk

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Bourdin, B., Francfort, G.A. (2011). Fracture. In: dell’Isola, F., Gavrilyuk, S. (eds) Variational Models and Methods in Solid and Fluid Mechanics. CISM Courses and Lectures, vol 535. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0983-0_3

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  • DOI: https://doi.org/10.1007/978-3-7091-0983-0_3

  • Publisher Name: Springer, Vienna

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