Peridynamics (PD) is a relatively new nonlocal method for modeling continua that inherently captures damage evolution, making it an attractive tool for modern engineering applications. Although significant research has focused on isotropic materials since its inception, this review article aims to synthesize studies on modeling material anisotropy within PD. To identify common patterns and approaches to the challenges encountered, key publications from the method's derivation onward have been thoroughly analyzed and categorized. The reviewed papers demonstrate an evolution from simple formulations to more comprehensive models capable of capturing a wide variety of anisotropic phenomena. Fiber composites and general anisotropic models have received the most attention, whereas applications in biomechanics, fluid dynamics, and multiphysics problems remain less explored. This review not only highlights the progress made in modeling anisotropic materials using PD but also identifies gaps in the current literature. This extensive categorization provides a roadmap for addressing the limitations of current models and advancing the practical implementation of PD in various engineering disciplines.
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