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
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.
|Uncontrolled Keywords:||Crack propagation; Mode III; Univalent functions; Loewner equation; Schifferd´s method|
|Subjects:||Sciences > Mathematics > Differential equations|
|Deposited On:||11 Apr 2011 17:13|
|Last Modified:||27 Nov 2012 16:16|
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