Phase-field fracture analysis for implicit geometric model via adaptive extended isogeometric analysis

Mechanical parts produced via additive manufacturing method often needs a re-evaluation of their strength due to precision challenges. In this study, we introduce an adaptive extended isogeometric analysis (XIGA) method, grounded in an implicit geometric model, to assess structural strength. This method is seamlessly integrated with the phase field fracture theory to appraise part fracture strength and replicate crack propagation. The investigation encompasses both second-order and fourth-order phase-field models. The fourth-order phase-field model entails the computation of higher-order phase-field derivatives, necessitating the utilization of at least C1 continuous shape functions. This prerequisite is readily met through the application of isogeometric analysis. Moreover, we employ polynomial splines over hierarchical T-meshes (PHTsplines) within this framework to enable localized hierarchical refinement. The adaptive refinement of boundary elements efficiently furnishes precise stress solutions, while substantially enhancing the computational efficiency of phase-field fracture analysis through adaptively refining the element near the crack. Numerical illustrations validate the method's exceptional accuracy in stress field solutions and fracture crack predictions. Experimental outcomes underscore the method's proficiency in faithfully capturing the propagation of cracks within intricate porous structures. Furthermore, we furnish a schematic outlining the process of assessing fracture strength in additively manufactured components, thereby emphasizing the promising utility of the proposed methodology.