Augmented Finite Element and Binary Model for Structural Applications

Advanced composite materials are known as important engineering materials in industry such as aircraft, automotive and wind turbine. Fracture is most of concern since it limits the performance of above applications. Fracture in a composite structure is the result of the evolution and interactions of discrete damage events such as fiber/matrix debonding, matrix cracking, delamination between plies, and fiber failure. Due to the large number of damage mechanisms that must be considered and their complex interactions, modeling progressive failure in composite materials and structures remains a challenge after years of extensive research. Augmented finite element method (A-FEM) has been demonstrated as an efficient numerical method to account for multiple intra-element cohesive cracks with much improved numerical efficiency. It has been shown that the formulation, which treats arbitrary intra-element cracking without additional nodes or DoFs, enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. Based on this method, this thesis focused on two aspects. In the first part the one dimensional augmented finite element is developed and coupled with binary model for discrete crack modeling of ceramic matrix composites (CMCs). The developed augmented element is used to represent fiber tow in a textile composite to simulate fiber deformation from elastic stage to complete rupture during loading. Elemental validation and verification of the coupled 3D BM-AFEM model has been performed and the BM-AFEM results are in good agreement with analytical estimates. The established BM-AFEM method are then used to simulate the progressive failure of example CMC panels, which shows great potential of this method for 3D textile composites with complex fiber tow architectures. The second part is extending the quasi-static A-FEM to be capable of solving 2-D combined in-plane (membrane) loading and bending problems. In this part, the augmented plate element was developed to calculate deformations of thick plates under combined in-plane loading and out of plane bending. This is followed by an exhaustive element level verification against available analytical result. Finally a bench mark example was simulated, the numerical result was compared with experiment result published in journal. The comparison shows the developed augmented plate element result agrees well with experiment result and can be used to simulate in-plane, out of plane coupled loading problem in the future