Inserted: 3 aug 2018
Last Updated: 5 oct 2018
In this work we first analyze the singular behavior of the displacement $u$ of a linearly elastic body in dimension 2 close to the tip of a smooth crack, extending the well-known results for straight fractures to general smooth ones. As conjectured by Griffith, $u$ behaves as the sum of an $H^2$-function and a linear combination of two singular functions whose profile is similar to the square root of the distance from the tip. The coefficients of the linear combination are the so called stress intensity factors. Afterwards, we prove the differentiability of the elastic energy with respect to an infinitesimal fracture elongation and we compute the energy release rate, enlightening its dependence on the stress intensity factors.