Crack growth in homogeneous media using an adaptive isogeometric fourth-order phase-field model

By using the threshold on the phase-field variable as an error indicator, an adaptive fourth-order phase-field method in the framework of isogeometric analysis is proposed for fracture simulation. The spatial and geometric discretization is based on locally refined non-uniform rational B-splines (LR NURBS), which have the ability for local refinement. The C1 continuous LR NURBS basis function is employed as the fourth-order phase field which requires higher-order derivatives. A hybrid formulation is adopted, and the coupled elasticity and phase-field equations are solved using a staggered method. The simulation starts with a coarse discretization and the spatial discretization is adaptively refined on the fly. The robustness and the reliability of the adaptive fourth-order phase-field model based on isogeometric analysis are demonstrated with a few standard benchmark problems. From the numerical study, it is inferred that the proposed framework yields accurate results without compromising accuracy. Further, the fourth-order phase-field model gives a narrow diffusive region, which reduces the region to be refined that improves the computational efficiency.