Surface-driven computational homogenization method for metamaterial beams

Metamaterials exhibit extraordinary mechanical properties that surpass those of their constituent materials and conventional constitutive relationships, primarily due to the unique characteristics of their microstructural units and their interactions. However, traditional homogenization methods often fail to capture these remarkable behaviors. This study explores the influence of microstructural units on the size-dependent bending response of metamaterial beams, attributing the observed effects to microstructure-induced surface elasticity. A full-thickness representative volume element (RVE) is constructed, and a surface-driven computational homogenization method (CHM) is developed to accurately characterize the microstructure-induced surface effects. The surface thickness parameters in the homogenized elastic model are calibrated using high-fidelity, high-throughput FEM-based homogenization of the full-thickness RVE. By precomputing a dataset of effective properties and surface thicknesses for various full-thickness RVEs, the developed homogenization model enables efficient and accurate online predictions of metamaterial beam behavior. The results demonstrate that the developed homogenization method, incorporating microstructure-dependent surface thickness, can effectively and accurately capture the mechanical response of metamaterial beams. The proposed model significantly outperforms classical homogenization model that neglect surface effects, particularly in macroscopic bending deformation.