Calculus of Variations and Geometric Measure Theory

S. Racca - R. Toader

A variational model for the quasi-static growth of fractional dimensional brittle fractures

created by racca on 12 Jul 2013



Inserted: 12 jul 2013
Last Updated: 12 jul 2013

Year: 2013


We propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

Keywords: variational models, quasi-static evolution, Crack propagation, energy minimization, brittle fractures, Von Koch curve