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The classical theory of univalent functions and quasistatic crack propagation


Oleaga Apadula, Gerardo Enrique (2006) The classical theory of univalent functions and quasistatic crack propagation. European Journal of Applied Mathematics, 17 (02). pp. 233-255. ISSN 0956-7925


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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.

Item Type:Article
Uncontrolled Keywords:Crack propagation; Mode III; Univalent functions; Loewner equation; Schifferd´s method
Subjects:Sciences > Mathematics > Differential equations
ID Code:12568
Deposited On:11 Apr 2011 15:13
Last Modified:06 Feb 2014 09:27

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