On the Use of Drilling Degrees of Freedom to Stabilise the Augmented Finite Element Method

Abstract

The augmented finite element method (AFEM) embeds cracks within solid elements. These cracks are modelled without additional degrees of freedom thanks to a dedicated static condensation process. However, static condensation can induce a lack of constraint problem, resulting in singular stiffness matrices. To address this issue, we propose a new method called the stabilised augmented finite element method (SAFEM), which produces non-singular stiffness matrices. We conducted 2D experiments involving stationary traction-free cracks and propagating cohesive discontinuities to compare the performance of the SAFEM with the AFEM. The SAFEM outperforms the AFEM in modelling traction-free cracks.

Keywords

• augmented finite element method
• finite element analysis
• drilling degrees of freedom
• cohesive zone modelling
• crack modelling
• strong discontinuities