The Extended Finite Element Method for crack propagation problems: Theory and implementation details

Bakalakos, Serafeim

dc.contributor.author	Bakalakos, Serafeim	el
dc.date.accessioned	2020-10-13T07:37:41Z
dc.date.available	2020-10-13T07:37:41Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/51406
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.19104
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	*
dc.subject	Εκτεταμένη Μέθοδος Πεπερασμένων Στοιχείων, Διάδοση ρωγμών, Γραμμική Ελαστική Θραυστομηχανική, Υλοποίηση	el
dc.subject	XFEM, Extended Finite Element Method, Crack propagation, Linear Elastic Fracture Mechanics, Implementation	en
dc.title	The Extended Finite Element Method for crack propagation problems: Theory and implementation details	en
dc.contributor.department	Institute Of Structural Analysis and Antiseismic Research	el
heal.type	masterThesis
heal.classification	Structural Engineeirng	el
heal.language	en
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2017-10-25
heal.abstract	In this thesis, the eXtended Finite Element Method (XFEM) is implemented to model crack interfaces. XFEM avoids the need of conforming the finite element mesh to the crack geometry each time the crack propagates. Instead the displacement field is allowed to be discontinuous across the crack interface, by enriching the finite dimensional spaces with appropriate functions. Enrichment functions can be used to locally incorporate known behavior into the polynomial approximation of traditional FEM. For domains containing cracks, fracture mechanics provides analytic expressions of the displacement field near the crack tip, in addition to it being discontinuous across the crack body. Predicting the crack propagation path is based on Linear Elastic Fracture Mechanics. The stress intensity factors (SIFS) are evaluated to describe the singular stress field near the crack tip and estimate the crack growth direction. A versatile and robust technique to calculate the SIFs is the J-integral method, which is suitable for computations over a finite element mesh. This thesis is concerned with crack propagation in brittle, linear elastic materials. XFEM is applied to 2D structures under static loading. Although extending XFEM to 3D is straightforward, an accurate and efficient method to describe 3D crack geometries is the subject of ongoing research. Instead this document delves into the details of crack propagation analysis. Many algorithms and implementation details are presented for XFEM, the J-integral technique and the methods used to represent the crack geometries. Alongside this document, C# code has been developed to implement the described theories and algorithms. This code is freely available as part of the open source software MSolve for structural analysis and design, developed by the Institute of Structural Analysis and Antiseismic Research at the National Technical University of Athens.	en
heal.advisorName	Georgioudakis, Manolis	el
heal.committeeMemberName	Papadrakakis, Manolis	el
heal.committeeMemberName	Papadopoulos, Vissarion	el
heal.committeeMemberName	Spiliopoulos, Konstantinos	el
heal.academicPublisher	Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.numberOfPages	220
heal.fullTextAvailability	true