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.

orthotropic composites, crack-tip fields, Stroh formalism, interaction integral, phase-field fracture, peridynamics, XFEM, isogeometric analysis, T-stress, mode mixity, aerospace materials, composite airframe structures

Berrada Gouzi, M., El Khalfi, A., Vlase, S., & Scutaru, M. L. (2024). X-IGA is used for orthotropic material crack growth. Materials, 17(15), 3830. https://doi.org/10.3390/ma17153830

Ebrahimi, M., & Fakoor, M. (2025). Design-oriented fracture criteria for orthotropic composites based on minimum strain energy density theory. Theoretical and Applied Fracture Mechanics, 140, 105182. https://doi.org/10.1016/j.tafmec.2025.105182

Jain, I., Muixí, A., Annavarapu, C., Mulay, S. S., & Rodriguez-Ferran, A. (2023). Adaptive phase–field modeling of fracture in orthotropic composites. Engineering Fracture Mechanics, 292, 109673. https://doi.org/10.1016/j.engfracmech.2023.109673

Nobili, A., & Radi, E. (2022). Hamiltonian/Stroh formalism for anisotropic media with microstructure. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380(2231), 20210374. https://doi.org/10.1098/rsta.2021.0374

Vellwock, A. E., & Libonati, F. (2024). XFEM for composites, biological, and bioinspired materials: A review. Materials, 17(3), 745. https://doi.org/10.3390/ma17030745

Tafreshi, A. (2024). Analytical expressions for Jk-integrals of orthotropic/isotropic interface cracks. Theoretical and Applied Fracture Mechanics, 129, 104643. https://doi.org/10.1016/j.tafmec.2024.104643

Wang, H., Tanaka, S., Oterkus, S., & Oterkus, E. (2024). Fracture mechanics investigation for 2D orthotropic materials by using ordinary state-based peridynamics. Composite Structures, 329, 117757. https://doi.org/10.1016/j.compstruct.2023.117757

Oterkus, E., & Oterkus, S. (2024). Recent advances in peridynamic theory: A review. AIMS Materials Science, 11(3), 515–546. https://doi.org/10.3934/matersci.2024026

Tian, H., Shao, J., Liu, C., Liu, S., & Guo, X. (2025). Tensor-involved peridynamics: A unified framework for isotropic and anisotropic materials. Engineering Fracture Mechanics, 290, 111294. https://doi.org/10.1016/j.engfracmech.2024.111294

Zhuang, X., Zhou, S., Huynh, G. D., Areias, P., & Rabczuk, T. (2022). Phase field modeling and computer implementation: A review. Engineering Fracture Mechanics, 262, 108234. https://doi.org/10.1016/j.engfracmech.2021.108234