Arbitrary-order virtual element methods for high-order phase-field modeling of ductile fracture

Ductile fracture in metallic materials involves substantial plastic deformation, shear localization, damage accumulation, and eventual crack propagation—phenomena that pose significant computational challenges when combined. We present an arbitrary-order virtual element method (VEM) for ductile fracture using a fourth-order phase-field formulation coupled with rate-dependent plasticity. The fourth-order phase-field regularization provides sharper crack representation and improved accuracy compared to standard second-order models, but requires 𝐶 1 -continuous elements that complicate numerical implementation. We address this challenge by employing 𝐻 2 -conforming VEM for the fourth-order phase-field equation and 𝐻 1 -conforming VEM for the momentum balance equation. The plastic response is modeled using the Bodner–Partom viscoplastic constitutive model with a plastic degradation function that couples damage evolution to plastic deformation. Numerical examples demonstrate the capability to simulate complex ductile fracture phenomena including shear band formation, crack nucleation from plastically deformed regions, and dynamic crack propagation. The results demonstrate this framework as a powerful computational tool for modeling ductile fracture processes using polygonal elements.