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Research Article | Open Access

On some non-local approximation of nonisotropic Griffith-type functionals

Fernando Farroni1, Giovanni Scilla2, Francesco Solombrino1( )
Dipartimento di Matematica ed Applicazioni "R. Caccioppoli", Università di Napoli Federico II, Via Cintia Monte Sant'Angelo, 80126 Napoli, Italy
Dipartimento di Scienze di Base e Applicate per l'Ingegneria (SBAI), Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy
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Abstract

The approximation in the sense of Γ-convergence of nonisotropic Griffith-type functionals, with p −growth ( p > 1) in the symmetrized gradient, by means of a suitable sequence of non-local convolution type functionals defined on Sobolev spaces, is analysed.

Keywords

non-local approximationsΓ-convergenceGriffith functionalbrittle fracture

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Mathematics in Engineering
Volume 4 Issue 4,
August 2022
Pages 1-22
DOI: 10.3934/mine.2022031

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Cite this article:
Farroni F, Scilla G, Solombrino F. On some non-local approximation of nonisotropic Griffith-type functionals. Mathematics in Engineering, 2022, 4(4): 1-22. https://doi.org/10.3934/mine.2022031

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Received: 13 May 2021
Accepted: 31 August 2021
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)