https://doi.org/10.1140/epjst/e2014-02268-9
Review
Cracks in random brittle solids:
From fiber bundles to continuum mechanics
1 Laboratoire PMMH, ESPCI/CNRS-UMR 7636/Univ. Paris 6 UPMC/Univ. Paris 7 Diderot, 10 rue Vauquelin, 75231 Paris Cedex 05, France
2 Institutt for fysikk, NTNU, 7491 Trondheim, Norway
3 LMT-Cachan, ENS-Cachan/CNRS/PRES UniverSud Paris, 61 Av. Président Wilson, 94235 Cachan Cedex, France
a e-mail: sylvain.patinet@espci.fr
b e-mail: damien.vandembroucq@espci.fr
c e-mail: alex.hansen@ntnu.no
d e-mail: stephane.roux@lmt.ens-cachan.fr
Received: 17 April 2014
Revised: 18 August 2014
Published online: 24 October 2014
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.
© EDP Sciences, Springer-Verlag, 2014
