Description of the Behavior of a Polymer Hybrid-A Mathematical and Numerical Review.

Polymer hybrid materials have attracted considerable interest because combining different reinforcing constituents can provide improved mechanical performance, durability, lightweight characteristics, and structural efficiency. However, designing their behaviour remains challenging due to heterogeneous microstructures, constituent interactions, interfacial behaviour, reinforcement architecture, and manufacturing conditions. This review critically examines analytical, micromechanical, numerical, and reliability-based modelling approaches for polymer hybrid materials, covering their classification, mechanical characteristics, and predictive frameworks. Their applications in predicting tensile, flexural, and impact behaviour, damage, failure, and material degradation are discussed. The role of experimental characterization in determining material properties, model calibration, and numerical validation is also considered. Machine learning is emerging as a complementary tool for surrogate modelling within multiscale frameworks. The reviewed studies demonstrate variations between theoretical, numerical, and experimental results due to differences in material systems, fibre architecture, manufacturing and testing conditions, and modelling assumptions. This review highlights the need for reliable material datasets and unified modelling frameworks to improve predictive accuracy and support the design and optimization of polymer hybrid materials.