Interfaces and Free Boundaries


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Volume 16, Issue 4, 2014, pp. 509–538
DOI: 10.4171/IFB/328

Published online: 2014-12-10

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

Simone Racca[1] and Rodica Toader[2]

(1) SISSA, Trieste, Italy
(2) Università di Udine, Italy

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, energy minimization, von Koch curve, crack propagation, quasi-static evolution, brittle fractures

Racca Simone, Toader Rodica: A variational model for the quasi-static growth of fractional dimensional brittle fractures. Interfaces Free Bound. 16 (2014), 509-538. doi: 10.4171/IFB/328