Singularity modal analysis of frictional interfaces in orthotropic composites

•Crack-tip fields for frictional cracks in orthotropic composites are proposed.•Modes of fracture failure in CNT-based reinforced CFRP composites are assessed.•PUFEM eigen-functions in sliding contact of orthotropic materials are extracted.•Direct-XFEM/PUFEM is proposed to utilize the local singular stress solutions. Shear crack or sliding contact within or between orthotropic composites contains innovative local solutions in terms of stress singularity, which are concentrated in this study. For this purpose, a finite element asymptotic expansion is proposed, which extracts the singular point solution for different frictional crack or contact problems in orthotropic composite design. The investigations illustrate the fact that many situations in orthotropic fracture and contact mechanics deal with stress singularities of order higher than the conventional cracks in isotropic materials and even the free crack conditions in the same orthotropic cases. In this paper, the significance of different situations for shear crack and various configuration of frictional contact between orthotropic composites are discussed in terms of the order of singularity. The consistent singular enrichment function derived may be utilized in numerical simulations of fracture and contact phenomena. Direct eXtended Finite Element Method (Direct-XFEM) proposed facilitates an efficient algorithm for implementation of the singularity modal analysis results.