Numerical recipes of virtual element method for phase field modeling of brittle fracture

Abstract

In this work, a new and efficient virtual element formulation for non-standard phase field model of brittle fracture is presented. A multi-pass alternative minimization solution scheme based on algorithm operator splitting is utilized, which decouples the whole problem into two parts, namely, mechanical and damage sub-problems. The former is treated as elasto-static problem, while the latter one is treated as Poisson-type of reaction-diffusion equation subjected to bounded and irreversibility constraint. To demonstrate the performance of proposed formulation, several benchmark problems are studied and results are in good agreement with corresponding finite element calculations and experimental studies.