An XFEM multilayered heaviside enrichment for fracture propagation with reduced enhanced degrees of freedom

Bybordiani, M; Latifaghili, A; Soares, D; Godinho, L; Dias‐da‐Costa, D

An XFEM multilayered heaviside enrichment for fracture propagation with reduced enhanced degrees of freedom

Bybordiani, M Latifaghili, A Soares, D Godinho, L Dias‐da‐Costa, D

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Publisher:: Wiley
Publication Type:: Journal Article
Citation:: International Journal for Numerical Methods in Engineering, 2021, 122, (14), pp. 3425-3447
Issue Date:: 2021-05-05

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Field	Value	Language
dc.contributor.author	Bybordiani, M
dc.contributor.author	Latifaghili, A
dc.contributor.author	Soares, D
dc.contributor.author	Godinho, L
dc.contributor.author	Dias‐da‐Costa, D
dc.date.accessioned	2022-05-01T00:32:06Z
dc.date.available	2022-05-01T00:32:06Z
dc.date.issued	2021-05-05
dc.identifier.citation	International Journal for Numerical Methods in Engineering, 2021, 122, (14), pp. 3425-3447
dc.identifier.issn	0029-5981
dc.identifier.issn	1097-0207
dc.identifier.uri	http://hdl.handle.net/10453/156880
dc.description.abstract	The development of advanced numerical techniques such as eXtended/Generalized Finite Elements Methods (XFEM/GFEM) has provided means for accurate prediction of material failure. However, the present theories mostly rely on a global formulation, where the system of equations is subject to progressive dimension increase with crack evolution. In this regard, an independent multilayered enrichment is proposed for the XFEM/GFEM family of methods where a few elements in close proximity are assigned to an enrichment layer independent of the remaining ones. The enhanced degrees of freedom can be condensed out at the layer level, which leads to system dimensions, sparsity, and bandness identical to those of the underlying finite elements. Nodal and elemental enrichment methods are shown to be particular limit cases of present approach. The robustness of the proposed approach is first demonstrated in element-level examples. The use of only few adjacent elements in a group enrichment is shown to suffice for acceptable results while the order of the condition number of the final stiffness matrix resembles the underlying uncracked finite element counterpart. Finally, using several structural examples, the accuracy and robustness of the method is shown in terms of force–displacement response, stress fields, and traction continuity in nonlinear problems.
dc.language	en
dc.publisher	Wiley
dc.relation.ispartof	International Journal for Numerical Methods in Engineering
dc.relation.isbasedon	10.1002/nme.6669
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	09 Engineering
dc.subject.classification	Applied Mathematics
dc.title	An XFEM multilayered heaviside enrichment for fracture propagation with reduced enhanced degrees of freedom
dc.type	Journal Article
utslib.citation.volume	122
utslib.for	09 Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Civil and Environmental Engineering
utslib.copyright.status	closed_access	*
pubs.consider-herdc	false
dc.date.updated	2022-05-01T00:32:04Z
pubs.issue	14
pubs.publication-status	Published
pubs.volume	122
utslib.citation.issue	14

Abstract:

The development of advanced numerical techniques such as eXtended/Generalized Finite Elements Methods (XFEM/GFEM) has provided means for accurate prediction of material failure. However, the present theories mostly rely on a global formulation, where the system of equations is subject to progressive dimension increase with crack evolution. In this regard, an independent multilayered enrichment is proposed for the XFEM/GFEM family of methods where a few elements in close proximity are assigned to an enrichment layer independent of the remaining ones. The enhanced degrees of freedom can be condensed out at the layer level, which leads to system dimensions, sparsity, and bandness identical to those of the underlying finite elements. Nodal and elemental enrichment methods are shown to be particular limit cases of present approach. The robustness of the proposed approach is first demonstrated in element-level examples. The use of only few adjacent elements in a group enrichment is shown to suffice for acceptable results while the order of the condition number of the final stiffness matrix resembles the underlying uncracked finite element counterpart. Finally, using several structural examples, the accuracy and robustness of the method is shown in terms of force–displacement response, stress fields, and traction continuity in nonlinear problems.

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http://hdl.handle.net/10453/156880