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Phase‐field approach to fracture for finite‐deformation contact problems
Author(s) -
Franke Marlon,
Hesch Christian,
Dittmann Maik
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610050
Subject(s) - regularization (linguistics) , fracture (geology) , mortar , phase (matter) , field (mathematics) , phase field models , transient (computer programming) , finite element method , computer science , mechanics , mathematics , materials science , geology , physics , engineering , structural engineering , geotechnical engineering , artificial intelligence , quantum mechanics , pure mathematics , composite material , operating system
The present contribution deals with a variationally consistent Mortar contact algorithm applied to a phase‐field fracture approach for finite deformations, see [4]. A phase‐field approach to fracture allows for the numerical simulation of complex fracture patterns for three dimensional problems, extended recently to finite deformations (see [2] for more details). In a nutshell, the phase‐field approach relies on a regularization of the sharp (fracture‐) interface. In order to improve the accuracy, a fourth‐order Cahn‐Hilliard phase‐field equation is considered, requiring global C 1 continuity (see [1]), which will be dealt with using an isogeometrical analysis (IGA) framework. Additionally, a newly developed hierarchical refinement scheme is applied to resolve for local physical phenomena e.g. the contact zone (see [3] for more details). The Mortar method is a modern and very accurate numerical method to implement contact boundaries. This approach can be extended in a straightforward manner to transient phase‐field fracture problems. The performance of the proposed methods will be examined in a representative numerical example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)