Extended Voronoi cell finite element model for damage in brittle matrix composites

In this thesis, the traditional Voronoi cell finite element model(VCFEM) has been improved for studying the interfacial debonding. A new eXtended Voronoi cell finite element model (X-VCFEM) has been developed for modeling interfacial debonding with arbitrary matrix cohesive cracking in fiber-reinforced composites.; To describe the onset and growth of damage along the fiber-matrix interface, normal and tangential cohesive zone models are coupled into VCFEM. It is shown that the initiation and especially propagation of debonding depends not only on the total cohesive energy, but also on the shape of the traction-displacement curve. The model is also used to study the influence of various local morphological parameters on damage evolution by interfacial debonding. A special function of various geometric parameters is developed to predict the location of debonding in microstructures with varying morphology.; Further, this thesis introduces an eXtended Voronoi cell finite element model (X-VCFEM) for modeling multiple cohesive crack propagation in brittle materials. The cracks are modeled by a cohesive zone model and their incremental directions and growth lengths are determined in terms of the cohesive energy near the crack tip. Extension to VCFEM is achieved through enhancements in stress functions in the assumed stress hybrid formulation. In addition to polynomial terms, the stress functions include branch functions in conjunction with level set methods, and multi-resolution wavelet functions in the vicinity of crack tips. Comparison of X-VCFEM simulation results with results in literature for several fracture mechanics problems validates the effectiveness of X-VCFEM. Effect of stereographic features such as size and distribution of heterogeneities on damage evolution in random microstructures are also discussed.; Finally, in order to study the interaction between interface debonding and cohesive matrix cracking; a criterion based on cohesive models is proposed to assess the crack penetrating into matrix from the interface and is validated by numerical examples.