2023-11-28T21:08:36Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/496522023-08-25T13:08:10Zcom_20.500.14352_14col_20.500.14352_15
The classical theory of univalent functions and quasistatic crack propagation
Oleaga Apadula, Gerardo Enrique
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 LĂ¶wner 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.
2023-06-20T09:28:27Z
2023-06-20T09:28:27Z
2023-06-20T09:28:27Z
2006
journal article
https://hdl.handle.net/20.500.14352/49652
0956-7925
10.1017/S0956792506006577
http://journals.cambridge.org/action/displayJournal?jid=EJM
eng
BFM 2004-05634
SFB 611
open access
Cambridge University Press