An overview of implicit and explicit phase field models for quasi-static failure processes, implementation and computational efficiency

Phase field models have become a promising tool in modelling failure processes for various engineering appli-cations. However, their computational inefficiency has posed challenges for a wider application which is desired in engineering. While most papers present implicit phase field models, only a few studies devoted to explicit phase field models have been reported in recent years and most papers report their high computational efficiency compared to implicit phase field models. The purpose of this contribution is to present an overview of the im-plicit and explicit phase field models for quasi-static failure processes, detailing about their theories and implementation in the commercial software ABAQUS. The provided ABAQUS implementation programs can serve as a numerical tool for modelling engineering problems. Several numerical examples are then presented and a comparison of their computational efficiency is subsequently provided. Moreover, a mass/viscosity scaling scheme for the explicit phase field model and a non-iteration scheme for the implicit phase field model are introduced both improve their efficiency. The comparison results clearly reveal that the computational efficiency can be improved significant by using the explicit phase field model, and more attention should be paid to it.

Automated summary

Phase field models are a useful tool for modelling failure processes in engineering applications, but their computational inefficiency hinders wider adoption. While most studies focus on implicit models, recent studies have shown the higher computational efficiency of explicit models. This contribution provides an overview of both implicit and explicit phase field models for quasi-static failure processes, discussing their theories and implementation in ABAQUS software. Several numerical examples are presented, demonstrating the improved efficiency of the explicit model compared to the implicit model.