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

Jean-Jacques Marigo (1) , Lev Truskinovsky (2)

1 LPMTM - Laboratoire des Propriétés Mécaniques et Thermodynamiques des Matériaux
2 LMS - Laboratoire de mécanique des solides

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 Γ-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.

Mots clés: fracture mechanics; variational methods; gamma-convergence; pull-out test; Barenblatt model

Domaines: Mécanique [physics.med-ph]

Jean-Jacques Marigo, Lev Truskinovsky. Initiation and propagation of fracture in the models of Griffith and Barenblatt. Continuum Mechanics and Thermodynamics, 2004, 16, pp.391-409. ⟨10.1007/s00161-003-0164-y⟩. ⟨hal-00111432⟩