Calculus of Variations and Geometric Measure Theory

S. Almi - I. Lucardesi

Energy release rate and stress intensity factors in planar elasticity in presence of smooth cracks

created by lucardesi on 03 Aug 2018
modified on 05 Oct 2018


Published Paper

Inserted: 3 aug 2018
Last Updated: 5 oct 2018

Journal: NoDEA
Year: 2018
Doi: 10.1007/s00030-018-0536-4


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.