An extended isogeometric collocation method for fracture analysis

A collocation method is developed for discrete fracture models in the context of the partition-of-unity method. Spline technologies used in isogeometric analysis are exploited to provide a smooth inter-element transition of gradients, thus allowing to get rid of extra flux terms at element boundaries which are generated by Lagrange polynomials. Bézier extraction is utilised to formulate isogeometric analysis commensurate with a standard finite element data-structure. The efficacy of the proposed approach is examined through different numerical examples and is compared with other discrete methods for fracture analysis. The proposed approach is competitive in terms of accuracy with the least computational cost, rendering it a suitable candidate for superseding available collocation approaches for fracture simulation. Moreover, the approach naturally assesses the possibility of Physics Informed Neural Networks (PINNs) for fracture simulation, to which collocation is central.