%0 Journal Article
%A Oleaga Apadula, Gerardo Enrique
%T The classical theory of univalent functions and quasistatic crack propagation
%D 2006
%@ 0956-7925
%U https://hdl.handle.net/20.500.14352/49652
%X We study the propagation of a crack in critical equilibrium for a brittle material in a Mode III field. The energy variations for small virtual extensions of the crack are handled in a novel way: the amount of energy released is written as a functional over a family of univalent functions on the upper half plane. Classical techniques developed in connection to the Bieberbach Conjecture are used to quantify the energy-shape relationship. By means of a special family of trial paths generated by the so-called Löwner equation we impose a stability condition on the field which derives in a local crack propagation criterion. We called this the anti-symmetry principle, being closely related to the well known symmetry principle for the in-plane fields.
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