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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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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 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 |
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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: | 12 Dec 2018 15:07 |

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