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Initiation and propagation of fracture in the models of Griffith and Barenblatt

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Abstract.

In the setting of the simplest debonding problem we give a systematic comparison of the fracture models due to Griffith and Barenblatt. We prove that the Griffith model represents an asymptotic \(\Gamma\)-limit of the Barenblatt model, when the ratio of the external and internal lengths increases indefinitely. We then illustrate the character of convergence by solving explicitly two sample problems with “initially rigid” and “initially elastic” cohesive energies. The geometrical simplicity of the setting allows us to study the small parameter dependence of both global and local minimizers of the total energy.

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Authors and Affiliations

  1. LPMTM, UPR-CNRS 9001, Université Paris-Nord, 93430, Villetaneuse, France

    J.-J. Marigo

  2. LMS, UMR-CNRS 7649, École Polytechnique, 91128, Palaiseau, France

    L. Truskinovsky

Authors
  1. J.-J. Marigo
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  2. L. Truskinovsky
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Correspondence to J.-J. Marigo.

Additional information

Communicated by W.H. Müller

Received: 22 April 2003, Accepted: 12 September 2003, Published online: 9 January 2004

PACS:

62.20.Mk, 68.35.Md, 81.40.Jj, 83.50.Lh

Correspondence to: J.-J. Marigo

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Marigo, JJ., Truskinovsky, L. Initiation and propagation of fracture in the models of Griffith and Barenblatt. Continuum Mech. Thermodyn. 16, 391–409 (2004). https://doi.org/10.1007/s00161-003-0164-y

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  • DOI: https://doi.org/10.1007/s00161-003-0164-y

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