In the setting of finite elasticity we study the asymptotic behaviour of a crack that propagates quasi-statically in a brittle material. With a natural scaling of size and boundary conditions we prove that for large domains the evolution with finite elasticity converges to the evolution with linearized elasticity. In the proof the crucial step is the (locally uniform) convergence of the non-linear to the linear energy release rate, which follows from the combination of several ingredients: the $\Gamma$-convergence of re-scaled energies, the strong convergence of minimizers, the Euler-Lagrange equation for non-linear elasticity and the volume integral representation of the energy release.

From Finite to Linear Elastic Fracture Mechanics by Scaling / M., Negri; Zanini, Chiara. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 50:(2014), pp. 525-548. [10.1007/s00526-013-0645-1]

From Finite to Linear Elastic Fracture Mechanics by Scaling

ZANINI, CHIARA
2014

Abstract

In the setting of finite elasticity we study the asymptotic behaviour of a crack that propagates quasi-statically in a brittle material. With a natural scaling of size and boundary conditions we prove that for large domains the evolution with finite elasticity converges to the evolution with linearized elasticity. In the proof the crucial step is the (locally uniform) convergence of the non-linear to the linear energy release rate, which follows from the combination of several ingredients: the $\Gamma$-convergence of re-scaled energies, the strong convergence of minimizers, the Euler-Lagrange equation for non-linear elasticity and the volume integral representation of the energy release.
File in questo prodotto:
File Dimensione Formato  
nonlinear-2014.pdf

accesso aperto

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 361.7 kB
Formato Adobe PDF
361.7 kB Adobe PDF Visualizza/Apri
N_Zanini_CVPDE14.pdf

non disponibili

Descrizione: Articolo principale
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 333.86 kB
Formato Adobe PDF
333.86 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2508681
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo