Extended Voronoi cell finite element methods for fracture analysis of composites

The extended Voronoi cell finite element model used to solve the fracture problems of isotropic materials and particle reinforced composites has been proven to be accurate and efficient. In this paper, the extended Voronoi cell finite element method is developed to analyse cracked orthotropic composite structures. The X-VCFEM is enhanced by orthotropic crack-tip enrichment stress functions to accurately capture the crack tip singularity. In addition, the stress functions also include polynomial stress functions. For elliptical internal cracks, reciprocal stress functions associated with polynomial functions is adopted, which are obtained by conformal mapping technique. The traction-free at crack face is introduced into functionals by the Lagrange multiplier method. The proposed method is applied for numerical investigation of fracture mechanics parameters for orthotropic composites, in which the stress intensity factors (SIFs) are calculated using the least square method. The effectiveness of the proposed method is validated by comparing with the results from ABAQUS or reference solutions. This method yields accurate results with fewer elements, which is the advantage of the proposed method.