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.

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

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@article{COCV_2017__23_3_791_0, 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://archive.numdam.org/articles/10.1051/cocv/2016014/} }

TY - JOUR AU - Almi, Stefano TI - Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 791 EP - 826 VL - 23 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016014/ DO - 10.1051/cocv/2016014 LA - en ID - COCV_2017__23_3_791_0 ER -

%0 Journal Article %A Almi, Stefano %T Energy release rate and quasi-static evolution via vanishing viscosity in a fracture model depending on the crack opening %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 791-826 %V 23 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016014/ %R 10.1051/cocv/2016014 %G en %F COCV_2017__23_3_791_0

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, Volume 23 (2017) no. 3, pp. 791-826. doi : 10.1051/cocv/2016014. http://archive.numdam.org/articles/10.1051/cocv/2016014/

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