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

Fernando Farroni; Giovanni Scilla; Francesco Solombrino; Fernando Farroni; Giovanni Scilla; Francesco Solombrino

doi:10.3934/mine.2022031

Mathematics in Engineering

2022, Volume 4, Issue 4: 1-22. doi: 10.3934/mine.2022031

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

1.
Dipartimento di Matematica ed Applicazioni "R. Caccioppoli", Università di Napoli Federico II, Via Cintia Monte Sant'Angelo, 80126 Napoli, Italy
2.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria (SBAI), Sapienza Università di Roma, Via A. Scarpa 16, 00161 Roma, Italy

Received: 13 May 2021 Accepted: 31 August 2021 Published: 16 September 2021

The approximation in the sense of $ \Gamma $-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.
- non-local approximations,
- $ \Gamma $-convergence,
- Griffith functional,
- brittle fracture
Citation: Fernando Farroni, Giovanni Scilla, Francesco Solombrino. On some non-local approximation of nonisotropic Griffith-type functionals[J]. Mathematics in Engineering, 2022, 4(4): 1-22. doi: 10.3934/mine.2022031

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Abstract

The approximation in the sense of $ \Gamma $-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.

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