Abstract
Advanced composite materials are known as important engineering materials in industry. Unlike structural metals which are homogeneous and isotropic, composites are inherently inhomogeneous and anisotropic which leads to further difficulty in damage tolerance design. The predictive capabilities of existing models have met with limited success because they typically cannot account for multiple damage evolution and their coupling. Consequently, current composite design is heavily dependent upon lengthy and costly test programs and empirical design methods. There is an urgent need for efficient numerical tools that are capable of analyzing the progressive failure caused by nonlinearly coupled, multiple damage evolution in composite materials. This thesis presents a new augmented finite element method (A-FEM) that can account for multiple, intra-elemental discontinuities with a demonstrated improvement in numerical efficiency when compared to the extended finite element method (X-FEM). It has been shown that the new formulation enables the derivation of explicit, fully-condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoFs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks. This new solving algorithm, coupled with mathematically exact elemental equilibrium equations, leads to dramatic improvement in numerical accuracy, efficiency, and stability. The A-FEM’s excellent capability in high-fidelity simulation of interactive cracks in solids has been demonstrated through several numerical examples.