Journal
ADVANCES IN CALCULUS OF VARIATIONS
Volume 14, Issue 4, Pages 475-497Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/acv-2019-0018
Keywords
Free discontinuity problems; G-convergence; special functions of bounded deformation; cohesive fracture
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Funding
- Marie Sklodowska-Curie Standard European Fellowship [793018]
- Investissement d'avenir project [ANR-11-LABX0056-LMH]
- LabEx
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The text discusses the Gamma-limit of Ambrosio-Tortorelli-type functionals and their dependence on different factors, as well as the relationship between the limit energy and the crack opening and surface. The limit energy is shown to be intermediate between two different modes of fracture energy, and it is proven that G(S)BD functions with bounded A-variation are (S)BD.
We study the Gamma-limit of Ambrosio-Tortorelli-type functionals D-epsilon(u, v), whose dependence on the symmetrised gradient e(u) is different in. Au and in e(u) - Au, for a C-elliptic symmetric operator A, in terms of the prefactor depending on the phase-field variable v. The limit energy depends both on the opening and on the surface of the crack, and is intermediate between the Griffith brittle fracture energy and the one considered by Focardi and Iurlano [Asymptotic analysis of Ambrosio-Tortorelli energies in linearized elasticity, SIAM J. Math. Anal. 46 (2014), no. 4, 2936-2955]. In particular, we prove that G(S)BD functions with bounded A-variation are (S)BD.
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