Calculus of Variations and Geometric Measure Theory

G. Lazzaroni - R. Toader

A model for crack propagation based on viscous approximation

created by lazzaroni on 09 Jun 2010
modified on 05 Oct 2012


Published Paper

Inserted: 9 jun 2010
Last Updated: 5 oct 2012

Journal: Math. Models Methods Appl. Sci.
Volume: 21
Pages: 2019-2047
Year: 2011



In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack needs not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.