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Error estimation and adaptivity for discontinuous failure
Author(s) -
Pannachet T.,
Sluys L. J.,
Askes H.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2495
Subject(s) - discontinuity (linguistics) , discretization , partition of unity , finite element method , norm (philosophy) , interpolation (computer graphics) , measure (data warehouse) , mathematics , discontinuous galerkin method , computer science , polygon mesh , mathematical optimization , degree of a polynomial , algorithm , polynomial , geometry , mathematical analysis , structural engineering , engineering , animation , computer graphics (images) , database , political science , law
Abstract Discontinuous failure is simulated via the introduction of a geometrical discontinuity. The cohesive zone is modelled via the use of the partition‐of‐unity property of the finite element interpolation. By this approach, a crack can pass through the elements without any restriction to the underlying mesh. Despite such a feature, it has been confirmed that a sufficiently fine mesh discretization still needs to be ensured in order to obtain a correct crack path and mechanical response. The p ‐adaptive scheme, driven by error in an energy norm measure or a goal‐oriented measure, has been examined due to its implementational simplicity. The results have shown that, if considering only increasing the polynomial degree, the p ‐approach can greatly improve the results. Copyright © 2008 John Wiley & Sons, Ltd.