Calculus of Variations and Geometric Measure Theory

J. F. Babadjian - A. Chambolle - A. Lemenant

Energy release rate for non smooth cracks in planar elasticity

created by lemenant on 27 Jun 2014



Inserted: 27 jun 2014
Last Updated: 27 jun 2014

Year: 2014


This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with density $1/2$ at the tip. First, the blow-up limit of the displacement is analyzed, and the convergence to the corresponding positively $1/2$-homogenous function in the cracked plane is established. Then, the energy release rate is obtained as the derivative of the elastic energy with respect to an infinitesimal additional crack increment.