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Brittle fracture in linearly elastic plates

Part of: Fracture and damage Equilibrium (steady-state) problems Existence theories Thin bodies, structures

Published online by Cambridge University Press:  19 November 2021

Stefano Almi Open the ORCID record for Stefano Almi [Opens in a new window]  and
Emanuele Tasso Open the ORCID record for Emanuele Tasso [Opens in a new window]
Stefano Almi
Affiliation:
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria (stefano.almi@univie.ac.at)
Emanuele Tasso
Affiliation:
Technische Universität Dresden, Faculty of Mathematics, 01062 Dresden, Germany (emanuele.tasso@tu-dresden.de)
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Abstract

In this work we derive by $\Gamma$-convergence techniques a model for brittle fracture linearly elastic plates. Precisely, we start from a brittle linearly elastic thin film with positive thickness $\rho$ and study the limit as $\rho$ tends to $0$. The analysis is performed with no a priori restrictions on the admissible displacements and on the geometry of the fracture set. The limit model is characterized by a Kirchhoff-Love type of structure.

Keywords

Dimension reductionΓ-convergencebrittle fracturefree discontinuity problems

MSC classification

Primary: 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 74R10: Brittle fracture 74G65: Energy minimization 74K15: Membranes
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 1 , February 2023 , pp. 68 - 103
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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