Homogenization Techniques for Nanocomposites: A Comprehensive Review

The study analyzes the development of analytical models for the reinforcement of structures using nanomaterials. Initially, it introduces the "Surface stress" phenomenon within the context of composite materials. In fact, nanocomposites show distinct characteristics compared to traditional composites due to the high surface-to-volume ratio at the nanoscale, which significantly influences the mechanical properties. Secondly, the research explores the Eshelby Tensor for a homogeneous solid with inclusions. Thirdly, various homogenization methods are compared, such as the Mori-Tanaka method, the self-consistent method with Eshelby Tensor and the refined Mori-Tanaka method for determining the effective stiffness tensor of nanocomposites. Fourthly, the introduction of "interface stress" between matrix and nanomaterials is analyzed. All the models are compared based on values of experimental results; moreover, a comparison with traditional composite techniques is performed. Overall, this work provides a detailed analytical framework for understanding and predicting the behavior of nanocomposites, integrating advanced mathematical models to account for the unique effects observed at the nanoscale.