COMPLAS 2025

Arbitrary-Order Virtual Element Methods for High-Order Phase-Field Modeling of Ductile Fracture

  • Leng, Yu (Los Alamos National Laboratory)
  • Mourad, Hashem (Los Alamos National Laboratory)

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Accurate modeling of fracture in ductile materials subjected to dynamic loading conditions is important in a wide range of application areas. Second-order phase-field fracture models have gained wide acceptance given their ability to capture the formation of complex fracture patterns, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models introduced in recent years [1] lead to a higher-regularity exact solution, and thus higher spatial convergence rate with mesh refinement. However, they require special numerical techniques, such as the virtual element method (VEM), to preserve the higher regularity of the phase field solution. The VEM, which is a generalization of the finite element method, also allows computations to be conducted on meshes of general polytopal elements. In this work, we adapt a VEM framework that we previously developed for brittle fracture problems [2], and apply it here to problems involving plastic deformation and dynamic ductile fracture. We use H1-conforming virtual elements and generalized-alpha method for the momentum conservation equation, and H2-conforming virtual elements for the fourth-order phase-field equation. The material behavior is represented using an elastic-viscoplastic material model. We first study shear localization problems without fracture and then show numerical examples involving dynamic ductile fracture. References: [1] Borden M.J., Hughes T.J.R., Landis C.M., Verhoosel C.V., A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework. Computer Methods in Applied Mechanics and Engineering, vol. 273, pp. 100–118, 2014. [2] Leng Y., Svolos L., Boureima I., Manzini G., Plohr J.N., Mourad H.M., Arbitrary order virtual element methods for high-order phase-field modeling of dynamic fracture. International Journal for Numerical Methods in Engineering, vol. 126, Art. no. e7605, 2025. LA-UR-25-21851