A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials

Bird, R.E.; Coombs, W.M.; Giani, S.

doi:10.1002/nme.5699

A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials

Bird, R.E.; Coombs, W.M.; Giani, S.

Authors

Dr Robert Bird robert.e.bird@durham.ac.uk
PDRA in Computational Solid Mechanics

Professor William Coombs w.m.coombs@durham.ac.uk
Professor

Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor

Abstract

This paper presents a framework for r-adaptive quasi-static configurational force (CF) brittle crack propagation, cast within a discontinuous Galerkin (DG) symmetric interior penalty (SIPG) finite element scheme. Cracks are propagated in discrete steps, with a staggered algorithm, along element interfaces which align themselves with the predicted crack propagation direction. The key novelty of the work is the exploitation of the DG face stiffness terms existing along element interfaces to propagate a crack in a mesh independent r-adaptive quasi-static fashion, driven by the CF at the crack tip. This adds no new degrees of freedom to the data structure. Additionally as DG methods have element specific degrees of freedom, a geometry driven p-adaptive algorithm is also easily included allowing for more accurate solutions of the CF on a moving crack front. Further, for non-determinant systems, we introduce an average boundary condition that restrains rigid body motion leading to a determinant system. To the authors' knowledge this is first time such a boundary condition has been described. The proposed formulation is validated against, single and multiple crack problems with single-and mixed-mode cracks, demonstrating the predictive capabilities of the method.

Citation

Bird, R., Coombs, W., & Giani, S. (2018). A quasi-static discontinuous Galerkin configurational force crack propagation method for brittle materials. International Journal for Numerical Methods in Engineering, 113(7), 1061-1080. https://doi.org/10.1002/nme.5699

Journal Article Type	Article
Acceptance Date	Sep 4, 2017
Online Publication Date	Oct 16, 2017
Publication Date	Feb 17, 2018
Deposit Date	Sep 11, 2017
Publicly Available Date	Sep 14, 2017
Journal	International Journal for Numerical Methods in Engineering
Print ISSN	0029-5981
Electronic ISSN	1097-0207
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	113
Issue	7
Pages	1061-1080
DOI	https://doi.org/10.1002/nme.5699
Keywords	Configurational force, Crack propagation, Discontinuous Galerkin, rp-adaptivity

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Copyright Statement
© 2017 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.