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A Phase Field Model for Three‐Dimensional Dynamic Fracture and its Efficient Numerical Implementation
Author(s) -
Hofacker Martina,
Miehe Christian
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110068
Subject(s) - classification of discontinuities , complex fracture , fracture (geology) , fracture mechanics , integrator , phase field models , field (mathematics) , representation (politics) , computer science , mechanics , structural engineering , phase (matter) , engineering , mathematics , mathematical analysis , physics , geotechnical engineering , computer network , bandwidth (computing) , quantum mechanics , politics , law , political science , pure mathematics
The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. We focus on the extension of a recently developed phase field model for fracture from the quasi‐static setting towards the dynamic setting. It is obtained by taking into account inertial terms and associated dynamic integrators. The introduction of a history field, containing a maximum fracture‐driving energy, provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of an extremely robust operator split technique. In a subsequent step, the proposed model is extended to three dimensional problems. The dynamic treatment opens the door to the analysis of complex fracture phenomena like multiple crack branching and crack arrest. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)