Geodesic
Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening
Almi, Stefano1
1 SISSA, Via Bonomea 265, 34136 Trieste, Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 791-826

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In the setting of planar linearized elasticity, we study a fracture model depending on the crack opening. Assuming that the crack path is known a priori and sufficiently smooth, we prove that the energy release rate is well defined. Then, we consider the problem of quasi-static evolution for our model. Thanks to a vanishing viscosity approach, we show the existence of such an evolution satisfying a weak Griffith’s criterion.

DOI : 10.1051/cocv/2016014
Classification : 49Q10, 35J20, 35Q74, 74R99, 74G65
Keywords: Variational models, free-discontinuity problems, energy release rate, energy derivative, cohesive fracture, crack propagation, quasi-static evolution, local minimizers, Griffith’s criterion, vanishing viscosity

Almi, Stefano 1

1 SISSA, Via Bonomea 265, 34136 Trieste, Italy. 
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     author = {Almi, Stefano},
     title = {Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {791--826},
     publisher = {EDP-Sciences},
     volume = {23},
     number = {3},
     year = {2017},
     doi = {10.1051/cocv/2016014},
     mrnumber = {3660449},
     zbl = {1373.49011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016014/}
}
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Almi, Stefano. Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 791-826. doi: 10.1051/cocv/2016014

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