Virtual Element Formulation for Phase-Field Modeling of Ductile Fracture

An efficient low-order virtual element method (VEM) for the phase-field modeling of ductile fracture is outlined within this work. The recently developed VEM is a competitive discretization scheme for meshes with highly irregular shaped elements. The phase-field approach is a very powerful technique to simulate complex crack phenomena in multi-physical environments. The formulation in this contribution is based on a minimization of a pseudo-potential density functional for the coupled problem undergoing large strains. The main aspect of development is the extension toward the virtual element formulation due to its flexibility in dealing with complex shapes and arbitrary number of nodes. Two numerical examples illustrate the efficiency, accuracy, and convergence properties of the proposed method.