A novel augmented finite element method for modeling arbitrary cracking in solids

摘要: of a dissertation at the University Miami. Dissertation supervised by Associate Professor Qingda Yang. No. pages in text. (213) Advanced composite materials are known as important engineering industry. Unlike structural metals which homogeneous and isotropic, composites inherently inhomogeneous anisotropic leads to further difficulty damage tolerance design. The predictive capabilities existing models have met with limited success because they typically cannot account for multiple evolution their coupling. Consequently, current design is heavily dependent upon lengthy costly test programs empirical methods. There an urgent need efficient numerical tools that capable analyzing progressive failure caused nonlinearly coupled, materials. This thesis presents new augmented finite element method (A-FEM) can multiple, intra-elemental discontinuities demonstrated improvement efficiency when compared extended (X-FEM). It has been shown formulation enables derivation explicit, fullycondensed elemental equilibrium equations mathematically exact within context. More importantly, it allows repeated augmentation include interactive cracks single without additional external nodes or degrees freedom (DoFs). A novel algorithm rapidly accurately solve nonlinear level also developed cohesive cracks. solving algorithm, coupled equations, dramatic accuracy, efficiency, stability. AFEM’s excellent capability high-fidelity simulation solids through several examples.