Crack growth by vanishing viscosity in planar elasticity
Stefano Almi, 1 Universität Wien, Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria, Giuliano Lazzaroni, Ilaria Lucardesi, 2 Università degli Studi di Firenze, Dipartimento di Matematica e Informatica “Ulisse Dini”, Viale Morgagni 67/a, 50134 Firenze, Italy, 3 Université de Lorraine, Institut Élie Cartan de Lorraine, BP 70239, 54506 Vandoeuvre-lès-Nancy, France, <sup>†</sup><b>This contribution is part of the Special Issue:</b> Variational Models in Elasticity, Guest Editors: Lucia De Luca; Marcello Ponsiglione, Link: <a href="https://www.aimspress.com/newsinfo/1369.html" target="_blank">https://www.aimspress.com/newsinfo/1369.html</a> · Mathematics in Engineering · 2019
We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. Differently from previous works, the crack is not prescribed a priori and is selected in a class of (unions of) regular curves. To prove the result, it is crucial to analyze the properties of the energy release rate showing that it is independent of the crack extension.