Since Isogeometric Analysis enables higher-order modelling of phase-field models, it consequently provides computational advantages for the simulation of fracture [1]. In the context of phase-field fracture, several formulations have been proposed in the recent years, including the AT-1 and AT-2 regularizations to model the crack transition region in the context of higher-order formulations [2, 3]. However, these novel models have been demonstrated solely in two dimensions on fixed meshes, leaving the potential of these formulations in higher dimensions with adaptive meshes unknown. In this talk, we present an adaptive isogeometric model for volumetric phase-field simulations, with application to brittle fracture. Truncated Hierarchical B-splines (THB-splines) [4] form the basis for adaptivity, together with algorithms for admissible meshing [5, 6], since the hierarchical framework provides easy extension to higher dimensions. Using the admissible refinement strategies for THB-splines, we assess different refinement strategies (e.g., mesh projections, marking strategies) and evaluate their performance for volumetric phase-field modelling. Ultimately, we apply this framework to the simulation of brittle fracture in volumetric domains, based on the models presented in [2, 3]. REFERENCES [1] Borden, Michael J., Thomas J.R. Hughes, Chad M. Landis, and Clemens V. Verhoosel. 2014. “A Higher-Order Phase-Field Model for Brittle Fracture: Formulation and Analysis within the Isogeometric Analysis Framework.” Computer Methods in Applied Mechanics and Engineering 273: 100–118. [2] Greco, Luigi, Alessia Patton, Matteo Negri, Alessandro Marengo, Umberto Perego, and Alessandro Reali. 2024. “Higher Order Phase-Field Modeling of Brittle Fracture via Isogeometric Analysis.” Engineering with Computers: 1–20. [3] Greco, Luigi, Eleonora Maggiorelli, Matteo Negri, Alessia Patton, and Alessandro Reali. 2025. “AT1 Fourth-Order Isogeometric Phase-Field Modeling of Brittle Fracture.” [4] Giannelli, Carlotta, Bert Jüttler, and Hendrik Speleers. 2012. “THB-Splines: The Truncated Basis for Hierarchical Splines.” Computer Aided Geometric Design 29(7): 485–98. [5] Bracco, Cesare, Carlotta Giannelli, and Rafael Vázquez. 2018. “Refinement Algorithms for Adaptive Isogeometric Methods with Hierarchical Splines.” Axioms 7(3): 43. [6] Carraturo, Massimo, Carlotta Giannelli, Alessandro Reali, and Rafael Vázquez. 2019. “Suitably Graded THB-Spline Refinement and Coarsening: Towards an Adapti