We provide a variational approximation by finite-difference energies of functionals of the type \[ \mu\int_{\Omega}|{\cal E}u|^2\,dx+{\lambda\over 2}\int_{\Omega} |{\rm div} u(x)|^2\,dx+\int_{J_u}\Phi\left([u],\nu_u\right)\,d{\cal H}^{n-1}, \] defined for $u\in SBD(\Omega)$, which are related to variational models in fracture mechanics for linearly-elastic materials. We perform this approximation in dimension 2 via both discrete and continuous functionals. In the discrete scheme we treat also boundary value problems and we give an extension of the approximation result to dimension 3.

Finite-difference approximation of energies in fracture mechanics / R. Alicandro; M. Focardi; M.S. Gelli. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - 29:(2000), pp. 671-709.

Finite-difference approximation of energies in fracture mechanics

FOCARDI, MATTEO;
2000

Abstract

We provide a variational approximation by finite-difference energies of functionals of the type \[ \mu\int_{\Omega}|{\cal E}u|^2\,dx+{\lambda\over 2}\int_{\Omega} |{\rm div} u(x)|^2\,dx+\int_{J_u}\Phi\left([u],\nu_u\right)\,d{\cal H}^{n-1}, \] defined for $u\in SBD(\Omega)$, which are related to variational models in fracture mechanics for linearly-elastic materials. We perform this approximation in dimension 2 via both discrete and continuous functionals. In the discrete scheme we treat also boundary value problems and we give an extension of the approximation result to dimension 3.
2000
29
671
709
R. Alicandro; M. Focardi; M.S. Gelli
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/334859
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