The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2339–2351 | Cite as

Cracks in random brittle solids:

From fiber bundles to continuum mechanics
Review
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications

Abstract

Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.

Keywords

Critical Load European Physical Journal Special Topic Energy Release Rate Continuum Limit Fracture Process Zone 

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Laboratoire PMMH, ESPCI/CNRS-UMR 7636/Univ. Paris 6 UPMC/Univ. Paris 7 DiderotParis Cedex 05France
  2. 2.Institutt for fysikk, NTNUTrondheimNorway
  3. 3.LMT-Cachan, ENS-Cachan/CNRS/PRES UniverSud ParisCachan CedexFrance

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