2014/06/26 by Jean-François Babadjian, Babadjian, Jean-François, Antonin Chambolle +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1406.6981
arxiv created 2014/06/26 · arxiv updated 2014/06/27
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.