Crack growth by vanishing viscosity in planar elasticity

Stefano Almi; Giuliano Lazzaroni; Ilaria Lucardesi; Stefano Almi; Giuliano Lazzaroni; Ilaria Lucardesi

doi:10.3934/mine.2020008

Mathematics in Engineering

2020, Volume 2, Issue 1: 141-173. doi: 10.3934/mine.2020008

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Crack growth by vanishing viscosity in planar elasticity

1.
Universität Wien, Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
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

Received: 21 June 2019 Accepted: 25 November 2019 Published: 09 December 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.
- free-discontinuity problems,
- brittle fracture,
- crack propagation,
- vanishing viscosity,
- local minimizers,
- energy derivative,
- Griffith’s criterion,
- energy release rate,
- stress intensity factor
Citation: Stefano Almi, Giuliano Lazzaroni, Ilaria Lucardesi. Crack growth by vanishing viscosity in planar elasticity[J]. Mathematics in Engineering, 2020, 2(1): 141-173. doi: 10.3934/mine.2020008

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Abstract

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.

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