Since Isogeometric Analysis enables higher-order modeling 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 AT1 and AT2 regularizations to model the crack transition region in the context of higher-order formulations [2, 3]. However, several open questions regarding simulations in higher-dimensions, the potential of mesh adaptivity as well as damage initialization using adaptive splines in 3D remain unanswered. In this talk, we present an adaptive isogeometric analysis model for the simulation of brittle fracture in two and three dimensions using phase-field methods. The model employs Truncated Hierarchical B-splines (THB-splines) [4] and algorithms for admissible meshing [5, 6], since the hierarchical framework provides easy extension to higher dimensions. In addition, the model employs either the AT1 or AT2 regularizations to model the crack transition region in the context of higher-order formulations [2, 3]. Through a series of numerical experiments, we elaborate on the influence of different choices for the adaptive meshing algorithm (e.g., marking tolerances or refinement iterations) and the regularization and order of the phase-field model on the total computational costs of the simulation. In addition, we elaborate on the robustness of the proposed framework for the simulation of volumetric phase-field fracture. 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 Adapt