Elastic properties of three-dimensional cellular lattice structures using asymptotic homogenization method

Abstract

This study presents an innovative application of the asymptotic homogenization method (AHM) for analytically determining the effective elastic properties of lattice structures. In contrast to traditional computational or experimental methods, the AHM provides a robust, efficient, and scalable approach for predicting elastic properties of various lattice topologies. New unit cell designs are proposed and benchmarked against existing configurations, demonstrating enhanced stiffness and strength characteristics. The study examines the impact of relative density and topology on the mechanical behavior of lattice structures, emphasizing the critical distinction between isotropic and orthotropic properties. The results indicate that unit cells exhibiting stretch-dominated behavior significantly outperform those with bending-dominated behavior in terms of stiffness and strength. Moreover, the proposed AHM-based approach demonstrates strong agreement between numerical predictions and experimental results, validating its reliability and accuracy. This research advances the theoretical understanding of lattice mechanics and provides a practical framework for designing lightweight, high-performance cellular materials for various engineering applications. By enabling efficient and precise property predictions, the methodology substantially reduces dependence on computationally expensive simulations and resource-intensive experiments. The novel integration of AHM into lattice structure analysis marks a transformative step forward, paving the way for future innovations in material design and optimization.