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.

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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