Journal
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
Volume 33, Issue 4, Pages 1033-1067Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.anihpc.2015.02.001
Keywords
Cohesive fracture; Phase field models; Gamma-convergence; Damage problems
Categories
Funding
- Hausdorff Center for Mathematics
- ERC [290888]
- European Research Council (ERC) [290888] Funding Source: European Research Council (ERC)
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We obtain a cohesive fracture model as Gamma-limit epsilon -> 0, of scalar damage models in which the elastic coefficient is computed from the damage variable v through a function f(epsilon) of the form f(epsilon)(v) = min{1, epsilon(1/2) f(v)}, with f diverging for v close to the value describing undamaged material. The resulting fracture energy can be determined by solving a one-dimensional vectorial optimal profile problem. It is linear in the opening s at small values of s and has a finite limit as s -> infinity. If in addition the function f is allowed to depend on the parameter epsilon, for specific choices we recover in the limit Dugdale's and Griffith's fracture models, and models with surface energy density having a power-law growth at small openings. (C) 2015 Elsevier Masson SAS. All rights reserved.
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