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Journal Articles Journal de l'École polytechnique — Mathématiques Year : 2015

## Energy release rate for non smooth cracks in planar elasticity

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• Function : Author
• PersonId : 867900
Antonin Chambolle
Antoine Lemenant

#### Abstract

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.

#### Domains

Mathematics [math] Analysis of PDEs [math.AP]

### Dates and versions

hal-01015179 , version 1 (26-06-2014)

### Identifiers

• HAL Id : hal-01015179 , version 1
• ARXIV :

### Cite

Jean-François Babadjian, Antonin Chambolle, Antoine Lemenant. Energy release rate for non smooth cracks in planar elasticity. Journal de l'École polytechnique — Mathématiques, 2015, 2, pp.117-152. ⟨hal-01015179⟩

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