Some recent results on the convergence of damage to fracture | Zendy

Sergio Conti | Zendy; Matteo Focardi | Zendy; Flaviana Iurlano | Zendy

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Some recent results on the convergence of damage to fracture

Author(s) -

Sergio Conti,

Matteo Focardi,

Flaviana Iurlano

Publication year - 2016

Publication title -

rendiconti lincei matematica e applicazioni

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.824

H-Index - 28

eISSN - 1720-0768

pISSN - 1120-6330

DOI - 10.4171/rlm/722

Subject(s) - mathematics , convergence (economics) , fracture (geology) , geology , geotechnical engineering , economics , economic growth

— We discuss a recent approximation result for Barenblatt’s cohesive fracture energies in the case of antiplane shear. The regularized functionals are damage energies of Ambrosio– Tortorelli type and the approximation is obtained in the sense of G-convergence. The extension to the general case of linearized elasticity in dimension n is still an open problem. To prepare for this extension we study the structure of a subclass of functions of bounded deformation.

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