A lower semicontinuity result in SBD for surface integral functionals of Fracture Mechanics

Article type: Research Article

Authors: Gargiulo, Giuliano | Zappale, Elvira

Affiliations: Dipartimento di Scienze Biologiche ed Ambientali, Universitá degli Studi del Sannio, via Port'Arsa, 82100, Benevento, Italy. E-mail: giuliano.gargiulo@unisannio.it | DIEII, Università degli Studi di Salerno, via Ponte Don Melillo, 84084 Fisciano (SA), Italy. E-mail: ezappale@unisa.it

Abstract: A lower semicontinuity result is proved in the space of special vector fields with bounded deformation for a fracture energetic model of the type ∫JuΨ([u], νu) dℋN−1,  [u]·νu≥0, ℋN−1 -a.e. on Ju. A representation of the energy density Ψ, which ensures lower semicontinuity, is also given.

Keywords: lower semicontinuity, fracture, special functions of bounded deformation

DOI: 10.3233/ASY-2011-1032

Journal: Asymptotic Analysis, vol. 72, no. 3-4, pp. 231-249, 2011