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

Abstract

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.