Oleaga Apadula, Gerardo Enrique (2006) The classical theory of univalent functions and quasistatic crack propagation. European Journal of Applied Mathematics, 17 (02). pp. 233255. ISSN 09567925

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Official URL: http://journals.cambridge.org/action/displayJournal?jid=EJM
Abstract
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 energyshape relationship. By means of a special family of trial paths generated by the socalled Löwner equation we impose a stability condition on the field which derives in a local crack propagation criterion. We called this the antisymmetry principle, being closely related to the well known symmetry principle for the inplane 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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