Analytical review of nanocomposites: integrating multiscale modeling, micromechanics, and kinetics of nanoparticle synthesis with investigation of matrix effects on mechanical performance in advanced applications

Nanomaterials have gained a special place in materials science and advanced industrial applications due to their unique mechanical, electrical and thermal properties. In this review article, nanomaterials are classified into four categories based on structural dimensions: zero, one, two and three dimensions, and their mechanical behavior in the form of nanocomposites is investigated. The main focus is on carbon nanomaterials, including graphene and single-walled and multi-walled carbon nanotubes, as well as ceramic and magnetic nanomaterials such as TiO₂, Al₂O₃, SiO₂, Fe₃O₄ and Fe₂O₃. The mechanical properties, including Young's modulus, shear modulus and Poisson's ratio, along with the components of the elastic stiffness matrix, are analyzed within the framework of analytical and micromechanical models. In particular, the mixing law and the Halpin-Say model are used to predict the elastic behavior of nanocomposites, and the effects of parameters such as volume fraction, orientation, aspect ratio, and dispersion quality of nanoparticles are evaluated. Also, synthesis methods including sol-gel, co-precipitation, and chemical vapor deposition (CVD) are investigated for their effects on particle size, morphology, and uniformity. The results of the studies show that optimizing the interfacial structure and uniform distribution of nanophases increases the Young's modulus, tensile strength, and stiffness of the composite. In addition, considering nanoscale effects and modifying classical models with multiscale approaches significantly increases the accuracy of predicting elastic behavior. Finally, industrial applications in wear-resistant coatings, magnetic sensors, electromechanical systems, and aerospace industries are reviewed, and the challenges in dispersion and multiscale modeling are analyzed.