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 -limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.
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Simone Racca, Rodica Toader, A variational model for the quasi-static growth of fractional dimensional brittle fractures. Interfaces Free Bound. 16 (2014), no. 4, pp. 509–538DOI 10.4171/IFB/328