Mechanical Modeling of Short Fiber Reinforced Composites Using the Extended Finite Element Method
Pike, Matthew Gregory
This dissertation presents a computational framework for the formulation and implementation of an Extended Finite Element Method (XFEM) for random short fiber reinforced composite materials. XFEM is used to eliminate the need to resolve random fiber inclusions and the need to conform the mesh of the domain to the fibers. The mechanical response of the composite is obtained in two dimensions for rigid fibers embedded in a matrix, elastic fibers with cohesive interfaces and for interactions between fibers as well as in three dimensions for random fibers. First, a fiber enrichment function is incorporated to model the effect of random fiber inclusions within XFEM along with fiber motion modeled by constraining the deformation field along the domain of the fiber inclusions. The elastic response of rigid short fiber reinforced composites is formulated by coupling the XFEM with the enrichment function and constraint equations. Second, a debonding enrichment function is developed to idealize the progressive debonding between the fiber-matrix interfaces. The fiber deformation is approximated as axial and directly incorporated into the Lagrangian. The progressive failure within the matrix material is idealized using an integral-type nonlocal damage model. Third, to account for neighboring fibers, multiple fiber and debonding enrichments lie within a single element. Enrichment coupling with XFEM is used to capture the fiber interactions. Lastly, the short fiber reinforced composites are modeled in XFEM for three dimensions to demonstrate the elastic and progressive debonding response. Composites are assessed for individual fibers as well as multiple fibers. Numerical examples are presented to verify the XFEM model with the direct finite element method.