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Phase-field approximation for a class of cohesive fracture energies with an activation threshold

  • Antonin Chambolle und Vito Crismale ORCID logo EMAIL logo
Veröffentlicht/Copyright: 8. Januar 2020

Abstract

We study the Γ-limit of Ambrosio–Tortorelli-type functionals D ε ( u , v ) , whose dependence on the symmetrised gradient e ( u ) is different in 𝔸 u and in e ( u ) - 𝔸 u , for a -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, 4, 2936–2955]. In particular, we prove that G(S)BD functions with bounded 𝔸 -variation are (S)BD.


Communicated by Gianni Dal Maso


Award Identifier / Grant number: 793018

Award Identifier / Grant number: ANR-11-LABX-0056-LMH

Funding statement: Vito Crismale has been supported by the Marie Skłodowska-Curie Standard European Fellowship No. 793018 and by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH.

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Received: 2019-03-09
Revised: 2019-10-01
Accepted: 2019-12-10
Published Online: 2020-01-08
Published in Print: 2021-10-01

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