2014•Interfaces and Free Boundaries Mathematical Analysis Computation and ApplicationsRequires access

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

Simone Racca, Rodica Toader

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.

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Key concepts: Brittleness, Mathematics, Applied mathematics, Growth model, Calculus (dental), Materials science, Mathematical economics, Composite material