@article {almi2017energy, 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}, volume = {23}, number = {3}, year = {2017}, month = {05/2017}, pages = {791{\textendash}826}, publisher = {EDP Sciences}, abstract = {

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{\textquoteright}s criterion.

}, doi = {10.1051/cocv/2016014}, url = {https://www.esaim-cocv.org/component/article?access=doi\&doi=10.1051/cocv/2016014}, author = {Stefano Almi} }