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BibTeX
A phase-field model for cohesive fracture
International journal for numerical methods in engineering, 2013-10, Vol.96 (1), p.43-62
Verhoosel, Clemens V.
de Borst, René
2013
Details
Autor(en) / Beteiligte
Verhoosel, Clemens V.
de Borst, René
Titel
A phase-field model for cohesive fracture
Ist Teil von
International journal for numerical methods in engineering, 2013-10, Vol.96 (1), p.43-62
Ort / Verlag
Chichester: Blackwell Publishing Ltd
Erscheinungsjahr
2013
Link zum Volltext
Quelle
Wiley Blackwell Single Titles
Beschreibungen/Notizen
SUMMARYIn this paper, a phase‐field model for cohesive fracture is developed. After casting the cohesive zone approach in an energetic framework, which is suitable for incorporation in phase‐field approaches, the phase‐field approach to brittle fracture is recapitulated. The approximation to the Dirac function is discussed with particular emphasis on the Dirichlet boundary conditions that arise in the phase‐field approximation. The accuracy of the discretisation of the phase field, including the sensitivity to the parameter that balances the field and the boundary contributions, is assessed at the hand of a simple example. The relation to gradient‐enhanced damage models is highlighted, and some comments on the similarities and the differences between phase‐field approaches to fracture and gradient‐damage models are made. A phase‐field representation for cohesive fracture is elaborated, starting from the aforementioned energetic framework. The strong as well as the weak formats are presented, the latter being the starting point for the ensuing finite element discretisation, which involves three fields: the displacement field, an auxiliary field that represents the jump in the displacement across the crack, and the phase field. Compared to phase‐field approaches for brittle fracture, the modelling of the jump of the displacement across the crack is a complication, and the current work provides evidence that an additional constraint has to be provided in the sense that the auxiliary field must be constant in the direction orthogonal to the crack. The sensitivity of the results with respect to the numerical parameter needed to enforce this constraint is investigated, as well as how the results depend on the orders of the discretisation of the three fields. Finally, examples are given that demonstrate grid insensitivity for adhesive and for cohesive failure, the latter example being somewhat limited because only straight crack propagation is considered. Copyright © 2013 John Wiley & Sons, Ltd.
Sprache
Englisch
Identifikatoren
ISSN: 0029-5981
eISSN: 1097-0207
DOI: 10.1002/nme.4553
Titel-ID: cdi_proquest_miscellaneous_1448720147
Format
–
Schlagworte
Approximation
,
Brittle fracture
,
Classical and quantum physics: mechanics and fields
,
Classical mechanics of continuous media: general mathematical aspects
,
Cohesion
,
cohesive fracture
,
cracking
,
damage
,
Dirichlet problem
,
Displacement
,
Exact sciences and technology
,
fracture
,
Fracture mechanics
,
Fracture mechanics (crack, fatigue, damage...)
,
Fundamental areas of phenomenology (including applications)
,
gradient models
,
Mathematical analysis
,
Mathematical models
,
Mathematics
,
Methods of scientific computing (including symbolic computation, algebraic computation)
,
Numerical analysis. Scientific computation
,
phase-field models
,
Physics
,
Sciences and techniques of general use
,
Solid mechanics
,
Structural and continuum mechanics
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