High-order Phase-Field Models for accurate and efficient fracture simulations via Isogeometric discretizations
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The study of fracture mechanics is one of the most contemporary topics in engineering. Accurate prediction of the fracture phenomenon enables improvements in the design of structural elements, significantly impacting society through economic savings. Preventing fractures reduces repair costs, material loss, pollution from spills of environmentally impactful substances, and loss of life. The development of computational technologies has directed the attention towards numerical models for the study of fracture. Among these, the phase-field model has gained prominence. This mathematical model allows to capture interface phenomena by approximating a discontinuous interface in a continuous manner. In the fracture context, a crucial aspect of this method is the accurate representation of how the fracture surface energy is dissipated, process mimicked through appropriate dissipation functionals. Among these functionals, high-order functionals offer significant computational advantages [1]. However, solving high-order partial differential equations is required, where, for example, Isogeometric Analysis [2] offers a natural modeling framework. This contribution highlights the advantages that high-order models bring to fracture mechanics in static and dynamic frameworks, reducing computational costs and providing highly accurate solutions. 1] L. Greco, A. Patton, M. Negri, A. Marengo, U. Perego, and A. Reali, “Higher order phase-field modeling of brittle fracture via isogeometric analysis,” Engineering with Computers, pp. 1–20, 2024. [2] T. Hughes, J. Cottrell, and Y. Bazilevs, “Isogeometric analysis: Cad, finite elements, nurbs, exact geometry and mesh refinement,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 39, pp. 4135–4195, 2005.