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| − | The phase-field approach to predicting crack initiation and propagation relies on a damage
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| − | accumulation function to describe the phase, or state, of fracturing material. The material is in some
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| − | phase between either completely undamaged or completely cracked. A continuous transition
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| − | between the two extremes of undamaged and completely fractured material allows cracks to be
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| − | modeled without explicit tracking of discontinuities in the geometry or displacement fields. A
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| − | significant feature of these models is that the behavior of the crack is completely determined by a
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| − | coupled system of partial differential equations. There are no additional calculations needed to
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| − | 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
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| − | phase-field models to quasi-static and dynamic fracture of brittle and ductile materials, within the
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| − | framework of isogeometric analysis. We will present results for several two- and three-dimensional
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| − | problems to demonstrate the ability of the phase-field models to capture complex crack propagation
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| − | patterns.
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