Adaptive phase-field modeling of crack propagation in multidirectional functionally graded materials using an isogeometric framework

Functionally graded materials (FGMs) are advanced engineering materials with a gradual variation in material properties throughout their volume, thereby avoiding sharp bimaterial interfaces. Investigation of their fracture response under different gradation profiles and loading conditions is necessary for their reliable structural performance and efficient material utilization. Phase-field modeling offers an effective approach to tackling complex fracture problems by regularizing sharp crack topologies. The present work introduces an isogeometric analysis-based adaptive phase-field formulation to study the fracture response of multidirectional FGMs under a variety of loading conditions. For both the geometric representation and the field approximation, polynomial splines over hierarchical T-meshes (PHT-splines) are adopted, thereby enabling adaptive mesh refinement guided by the phase-field parameter. Through numerical simulations, we (i) examine the impact of uni-, bi-, and tri-directional gradation, along with varied loading and boundary conditions, on fracture response, (ii) validate the proposed method against alternative numerical models, showing strong agreement in critical parameters, and (iii) simulate fracture response of both two- and three-dimensional cracked FGMs. The numerical results indicate that material gradation variations have a strong influence over the critical fracture load and crack evolution patterns. These observations confirm the effectiveness of the proposed framework in designing the functionally graded structural components.