Mesoscale Homogenization of Composite Lattice Structures Using the Variational Asymptotic Method

Composite lattice structures, also referred to as grid-stiffened structures, offer superior specific strength, specific stiffness, and damage tolerance compared to conventional composite stringer-stiffened and sandwich designs. However, their design and optimization are inherently complex due to the large number of interacting design variables. Multiscale modeling has emerged as an effective strategy to address this complexity, with its success critically dependent on the accuracy of stiffness homogenization at various scales, particularly at the mesoscale. This study proposes a novel mesoscale homogenization framework for the lattice Representative Volume Element (RVE) based on the Variational Asymptotic Method (VAM). The proposed VAM approach is systematically evaluated over a broad range of lattice structural parameters and is compared against results obtained from three-dimensional finite element (FE)-based homogenization and analytical methods. The VAM model demonstrates excellent agreement with the FE results while achieving significant computational efficiency, making it a highly effective tool for design optimization. In contrast, analytical methods exhibit reduced accuracy owing to inherent simplifying assumptions.