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.File | Dimensione | Formato | |
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