A three dimensional augmented finite element for modeling arbitrary cracking in solids

Abstract

This paper presents a new three dimensional (3D) augmented finite element method (A-FEM) that can account for arbitrary crack initiation and propagation in 3D solids without the need of additional DoF or phantom nodes. The method permits the derivation of explicit, fully condensed elemental equilibrium equations which are of mathematical exactness in the piece-wise linear sense. The method has been implemented with a 4-node tetrahedron element and a simple local tracking algorithm has been employed for calculating and recording the evolving planar or non-planar crack surface. It has been demonstrated through ample numerical examples that the new 3D A-FEM can provide significantly improved numerical accuracy and efficiency when dealing with crack propagation problems in 3D solids with planar or non-planar crack surfaces.