Relaxation of elastic energies with free discontinuities and constraint on the strain
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, p. 275-317
As a model for the energy of a brittle elastic body we consider an integral functional consisting of two parts: a volume one (the usual linearly elastic energy) which is quadratic in the strain, and a surface part, which is concentrated along the fractures (i.e. on the discontinuities of the displacement function) and whose density depends on the jump part of the strain. We study the problem of the lower semicontinuous envelope of such a functional under the assumptions that the surface energy density is positively homogeneous of degree one and that additional geometrical constraints, such as a shearing condition or a normal detachement condition, are imposed on the fractures.
Classification:  49J45,  74R10
@article{ASNSP_2002_5_1_2_275_0,
     author = {Braides, Andrea and Defranceschi, Anneliese and Vitali, Enrico},
     title = {Relaxation of elastic energies with free discontinuities and constraint on the strain},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {2},
     year = {2002},
     pages = {275-317},
     zbl = {1170.49306},
     mrnumber = {1991141},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_2_275_0}
}
Braides, Andrea; Defranceschi, Anneliese; Vitali, Enrico. Relaxation of elastic energies with free discontinuities and constraint on the strain. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 275-317. http://www.numdam.org/item/ASNSP_2002_5_1_2_275_0/

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