Hydrogen assisted cracking using an efficient virtual element scheme

Abstract

In this paper, a novel virtual element formulation is proposed for phase field modeling of hydrogen assisted cracking (HAC). The multiphysics variational framework is decoupled into three parts which can be solved in a staggered manner, namely, the mechanical, diffusion, and damage sub-problems. The damage and diffusion sub-problems are treated as reaction–diffusion types of equations. The former is subjected to irreversibility constraints while the latter incorporates a transport term to represent the effect of mechanical loading. An efficient super-convergent patch recovery (SPR) scheme is utilized to determine the coefficient of transport term in the hydrogen diffusion equation. Several qualitative and quantitative benchmark problems are considered to validate the proposed framework’s performance. The results show excellent agreement with the corresponding FEM and experimental studies. Meanwhile, without loss of numerical accuracy, the VEM outperforms the FEM with regards to CPU time & memory efficiency and exhibits remarkable versatility in the selection of different element types for simulation. Moreover, this work demonstrates the potential of facilitating the VEM to solve real-scale fracture mechanics problems with multi-physics coupling.