Adaptive multi-patch isogeometric phase-field method for quasi-static brittle fracture based on Nitsche’s method

Abstract

This paper addresses the computational burden typically associated with the phase-field method. Specifically, a multi-patch modeling approach is proposed based on isogeometric analysis, which simulates crack growth in quasi-brittle materials using the phase-field method. The compatibility of the physical quantities, viz., displacements and phase-field variables between the patches, is enforced through Nitsche’s method. Additionally, the spatial discretization relies on locally refined non-uniform rational B-splines (LR NURBS) with a local refinement scheme, which utilizes a prescribed threshold of the phase-field variable as an error indicator. The accuracy, reliability, and robustness of the proposed adaptive approach are verified by several problems involving compressive–shear crack growth and fracture propagation in complex geometries under tension.