3D modeling of arbitrary cracking in solids using augmented finite element method

A three dimensional (3D) augmented finite element method (AFEM) for modeling arbitrary cracking without the need of additional degree of freedom (DoFs) or phantom nodes is presented. Four or three internal nodes are employed to explain displacement jump due to the weak and strong discontinuity. In this method, damage and discontinuity are treated from a weak discontinuity to a strong one without additional degree of freedom and without explicit representation of the crack. A fully condensed elemental equilibrium equations as mathematical exactness in the piece-wise linear sense is explicitly derived within AFEM formulation. The method is implemented in ABAQUS 4-node tetrahedron user element with a local crack tracking method for crack path detection. Through some numerical examples, it is shown that the 3D AFEM can accurately and efficiently crack initiation and propagation.