Access the full text.
Sign up today, get DeepDyve free for 14 days.
References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.
AbstractWe study the Γ-limit of Ambrosio–Tortorelli-type functionals Dε(u,v){D_{\varepsilon}(u,v)}, whose dependence on the symmetrised gradient e(u){e(u)}is different in 𝔸u{\mathbb{A}u}and in e(u)-𝔸u{e(u)-\mathbb{A}u}, for a ℂ{\mathbb{C}}-elliptic symmetric operator 𝔸{\mathbb{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{\mathbb{A}}-variation are (S)BD.
Advances in Calculus of Variations – de Gruyter
Published: Oct 1, 2021
Keywords: Free discontinuity problems; special functions of bounded deformation; cohesive fracture; 49J45; 26A45; 49Q20; 74R99; 35Q74
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.