A new augmented finite element method (A-FEM) for progressive failure analysis of advanced composite materials

This paper presents a new augmented finite element method (A-FEM) that enables efficient and accurate treatment of arbitrary, multiple intra-elemental discontinuities in composite materials with complex microstructures. The new A-FEM employs four internal nodes to account for the crack displacements due to an intra-elemental weak or strong discontinuity, and it permits repeated elemental augmentation to include multiple interactive cracks. It thus enables a unified treatment of damage evolution from a weak discontinuity to a strong discontinuity, and to multiple interactive cohesive cracks, all within a single element that employs standard external nodal degree of freedoms (DoFs) only. A novel elemental condensation procedure has been developed to solve the internal nodal DoFs as functions of the external nodal DoFs for any irreversible, piecewise linear cohesive laws. It leads to a fully condensed elemental equilibrium equation with mathematical exactness, eliminating the need for nonlinear equilibrium iterations at elemental level. The new A-FEM's high-fidelity simulation capabilities to interactive cohesive crack formation and propagation in homogeneous and heterogeneous solids have been demonstrated through several challenging numerical examples. It has shown that the new A-FEM, empowered by the novel elemental condensation procedure, is numerically very efficient, accurate, and robust.