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A Model for the Quasi-Static Growth¶of Brittle Fractures:¶Existence and Approximation Results
Open accessAbstract
Abstract We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G. A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although we cannot exclude the possibility that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time-discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the continuous time evolution.
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VI. The phenomena of rupture and flow in solids
Griffith, A. A. (1921) · Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character · doi:10.1098/rsta.1921.0006 · Cited by 11,052
Optimal approximations by piecewise smooth functions and associated variational problems
Mumford, D., & Shah, J. (1989) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160420503 · Cited by 5,208
(1988) · Elsevier eBooks · doi:10.1016/c2013-0-11200-7 · Cited by 5,131
Revisiting brittle fracture as an energy minimization problem
Francfort, G. A., & Marigo, J.-J. (1998) · Journal of the Mechanics and Physics of Solids · doi:10.1016/s0022-5096(98)00034-9 · Cited by 3,530
Fédérer, H. (1996) · Classics in mathematics · doi:10.1007/978-3-642-62010-2 · Cited by 3,019
Operateurs Maximaux Monotones - Et Semi-Groupes De Contractions Dans Les Espaces De Hilbert
(1973) · North-Holland Mathematics Studies · doi:10.1016/s0304-0208(08)x7125-7 · Cited by 2,578
Weakly Differentiable Functions
Ziemer, W. P. (1989) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-1015-3 · Cited by 2,222
Blake, A., & Zisserman, A. (1987) · The MIT Press eBooks · doi:10.7551/mitpress/7132.001.0001 · Cited by 2,105
Variational Methods in Image Segmentation
Morel, J. M., & Solimini, S. (1995) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4684-0567-5 · Cited by 620
Fracture mechanics applied to engineering problems-strain energy density fracture criterion
Sih, G. C., & Macdonald, B. (1974) · Engineering Fracture Mechanics · doi:10.1016/0013-7944(74)90033-2 · Cited by 341
Cited by
Hofacker, M., & Miehe, C. (2013) · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.4387 · Cited by 306
Metadata
- Authors
- Dal Maso, G., & Toader, R.
- Venue
- Archive for Rational Mechanics and Analysis
- Published
- 2002-04
- Volume
- 162
- Issue
- 2
- Pages
- 101-135
- ISSN
- 0003-9527 (ISSN-L)
- 1432-0673
- OpenAlex
- W2030617114
- Cited by
- 310
- References
- 10
- FWCI
- 21.22
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Dal Maso, G., & Toader, R. (2002). A Model for the Quasi-Static Growth¶of Brittle Fractures:¶Existence and Approximation Results. Archive for Rational Mechanics and Analysis. https://doi.org/10.1007/s002050100187
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