2006
DOI: 10.1016/j.euromechsol.2006.05.002
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Initiation of cracks with cohesive force models: a variational approach

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Cited by 62 publications
(39 citation statements)
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“…This is the penalty to pay in order to recover the Griffith theory via a variational approach, which frees itself from the usual constraints that a pre-existing crack must be assumed a priori. In agreement with other work by Marigo et al [11], this means that if local minima are looked for, the load required to open a crack is infinite and the sound elastic state is always locally stable. This conclusion is in agreement with the most classical and definite tests on glass filaments by Griffith [18], who experimentally showed that brittle materials without pre-existing flaws are practically unbreakable or, more precisely, that their strength approaches the theoretical value of the same order of the elastic modulus.…”
Section: Introductionsupporting
confidence: 86%
See 1 more Smart Citation
“…This is the penalty to pay in order to recover the Griffith theory via a variational approach, which frees itself from the usual constraints that a pre-existing crack must be assumed a priori. In agreement with other work by Marigo et al [11], this means that if local minima are looked for, the load required to open a crack is infinite and the sound elastic state is always locally stable. This conclusion is in agreement with the most classical and definite tests on glass filaments by Griffith [18], who experimentally showed that brittle materials without pre-existing flaws are practically unbreakable or, more precisely, that their strength approaches the theoretical value of the same order of the elastic modulus.…”
Section: Introductionsupporting
confidence: 86%
“…On the other hand, the functional (3.1) does not account for the possibility of pre-existing flaw. For the reasons mentioned at length in the Introduction, already noted by Marigo and his collaborators [11], such functional does not appear appropriate to model the phenomenon of fracture. On the other hand, the approximating functional is consistently applicable.…”
Section: The Proposed Modified Variational Modelmentioning
confidence: 96%
“…For example, a first extension should be to consider prestresses in the composite and hence to develop the procedure in the case of an affine stress-strain relation. Another natural extension could be to consider more general and more realistic contact conditions between matrix and fibers: unilateral contact without friction or cohesive forces [9], for instance. The difficulty would be to solve non linear cell problems, and in such cases the effective behavior would no longer be described by a finite number of coefficients.…”
Section: Discussionmentioning
confidence: 99%
“…An important step will be to apply the MAM in the case of a cohesive crack [Barenblatt 1962;Dugdale 1960;Del Piero and Raous 2010], which automatically contains a critical stress and even a characteristic length. The goal will be to study the influence of the critical stress and characteristic length on the nucleation and the propagation of a crack in the spirit of the previous works based on the variational approach to fracture [Abdelmoula et al 2010;Bourdin et al 2008;Charlotte et al 2006;Del Piero and Truskinovsky 2009;Ferdjani et al 2007;Giacomini 2005;Jaubert and Marigo 2006;Marigo and Truskinovsky 2004].…”
Section: Discussionmentioning
confidence: 99%