The stress intensity factor for non-smooth fractures in antiplane elasticity

@article{Chambolle2011TheSI,
  title={The stress intensity factor for non-smooth fractures in antiplane elasticity},
  author={A. Chambolle and Antoine Lemenant},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2011},
  volume={47},
  pages={589-610}
}
  • A. ChambolleA. Lemenant
  • Published 21 October 2011
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
Motivated by some questions arising in the study of quasistatic growth in brittle fracture, we investigate the asymptotic behavior of the energy of the solution u of a Neumann problem near a crack in dimension 2. We consider non smooth cracks K that are merely closed and connected. At any point of density 1/2 in K, we show that the blow-up limit of u is the usual “cracktip” function $${C\sqrt{r}\sin(\theta/2)}$$ , with a well-defined coefficient (the “stress intensity factor” or SIF). The… 
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11 Citations
Background Citations
8
Results Citations
2

11 Citations

Quasistatic crack growth based on viscous approximation: a model with branching and kinking

Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is…

Quasistatic crack growth based on viscous approximation: a model with branching and kinking

Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is…

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

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…

Regularity up to the Crack-Tip for the Mumford-Shah problem

We prove that if $(u,\Gamma)$ is a minimizer of the functional $$ J(u,\Gamma)=\int_{B_1(0)\setminus \Gamma}|\nabla u|^2dx +\H^1(\Gamma) $$ and $\Gamma$ connects $\partial B_1(0)$ to a point in the…

A rigidity result for global Mumford–Shah minimizers in dimension three

A selective review on Mumford–Shah minimizers

This is a review paper on the Mumford-Shah functional, with particular interest in blow-up limits, low dimensions (2 and 3), and connection with fracture theory. It includes in particular a sketch…

A selective review on Mumford–Shah minimizers

  • A. Lemenant
  • Mathematics
    Bollettino dell'Unione Matematica Italiana
  • 2016
This is a review paper on the Mumford-Shah functional, with particular interest in blow-up limits, low dimensions (2 and 3), and connection with fracture theory. It includes in particular a sketch…

Energy release rate for non smooth cracks in planar elasticity

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…

Crack growth by vanishing viscosity in planar elasticity

We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not…

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

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…

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