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==Abstract==
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The phase-field approach to predicting crack initiation and propagation relies on a damage accumulation function to describe the phase, or state, of fracturing material. The material is in some phase between either completely undamaged or completely cracked. A continuous transition between the two extremes of undamaged and completely fractured material allows cracks to be modeled without explicit tracking of discontinuities in the geometry or displacement fields. A significant feature of these models is that the behavior of the crack is completely determined by a coupled system of partial differential equations. There are no additional calculations needed to determine crack nucleation, bifurcation, and merging.
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In this presentation, we will review our current work on applying second-order and fourth-order phase-field models to quasi-static and dynamic fracture of brittle and ductile materials, within the framework of isogeometric analysis. We will present results for several two- and three-dimensional problems to demonstrate the ability of the phase-field models to capture complex crack propagation patterns. 
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For background describing our work on brittle fracture, the reader is urged to consult references [<span id='cite-1'></span>[[#1|1]]] and [<span id='cite-2'></span>[[#2|2]]].
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== Recording of the presentation ==
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{| style="font-size:120%; color: #222222; border: 1px solid darkgray; background: #f3f3f3; table-layout: fixed; width:100%;"
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|- 
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| {{#evt:service=youtube|id=https://www.youtube.com/watch?v=JwaH1QDJs68|alignment=center}}
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|- style="text-align: center;" 
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| Location: Technical University of Catalonia (UPC), Vertex Building. 
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|- style="text-align: center;"
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| Date: 1 - 3 September 2015, Barcelona, Spain.
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|}
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== General Information ==
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* Location: Technical University of Catalonia (UPC), Barcelona, Spain.
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* Date: 1 - 3 September 2015
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* Secretariat: [//www.cimne.com/ International Center for Numerical Methods in Engineering (CIMNE)].
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== External Links ==
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* [//congress.cimne.com/complas2015/frontal/default.asp Complas XIII] Official Website of the Conference.
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* [//www.cimnemultimediachannel.com/ CIMNE Multimedia Channel]
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==References==
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<div id="1"></div>
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[[#cite-1|[1]]] M.J. Borden, C.V. Verhoosel, M.A. Scott, T.J.R. Hughes, and C.M. Landis, A phase-field
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description of dynamic brittle fracture, Computer Methods in Applied Mechanics and
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Engineering, Vol’s. 217-220, (1 April 2012) 77-95. 
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<div id="2"></div>
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[[#cite-2|[2]]] M.J. Borden, T.J.R. Hughes, C.M. Landis, and C.V. Verhoosel, A higher-order phase-field
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model for brittle fracture: Formulation and analysis within the isogeometric analysis
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framework, Computer Methods in Applied Mechanics and Engineering, Vol. 273, (1 May 2014)
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100-118.
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