Modeling the Stress–Strain State near Crack Tips in Orthotropic Composite Materials: A Review of Analytical and Numerical Approaches

This paper surveys analytical and computational techniques for evaluating crack-tip fields in orthotropic composites, emphasizing stress-intensity factors, mode mixity, and T-stress. The review consolidates Stroh-type anisotropic elasticity and interaction-integral formulations for benchmark extraction of K and T, and compares extended finite element and isogeometric enrichments with phase-field and peridynamic schemes that capture fiber-guided path deviation and branching. Particular attention is paid to interface cracks and calibration of anisotropy-aware phase-field surface densities and nonlocal peridynamic kernels. In addition to synthesizing recent methods, the article highlights the relevance of orthotropic crack modeling to high-performance aerospace composite structures, where accurate crack-tip prediction directly supports durability, certification, and safety of aircraft components. This connection strengthens the applicability of the proposed workflow to national priority areas involving advanced composite structures and reliability-critical industries such as aviation. The objective is to synthesize a reproducible workflow that links analytical eigensolutions, robust mode-decomposition tools, and mesh-objective crack-evolution solvers. Methods include comparative analysis and structured evidence mapping across ten recent sources. The conclusion outlines when each framework is preferable, validation with Stroh/Jk, discovery with phase-field, CAD-centric accuracy with X-IGA/XFEM, and length-scale-sensitive evolution with peridynamics, together with guidance on uncertainty control and cross-validation.