Designing lightweight nanolattices: multiscale optimization of geometry and size effects

Abstract

Lattice–truss structures have emerged as lightweight architected materials capable of achieving exceptional stiffness-to-weight ratios through geometry-driven design. Nanolattice architectures—composed of periodic networks of nanoscale beams—offer an opportunity to realize lightweight yet mechanically robust materials, whose properties can surpass those of bulk alternatives. However, the mechanical behavior of nanolattices remains difficult to predict accurately, as intrinsic size effects due to surface stresses can substantially alter nanolattice properties. Although multiscale approaches coupling atomistic simulations with continuum models have been employed, the individual contributions of surface-induced stresses and geometric design to nanolattice stiffness have not been clearly distinguished. To address this issue, this study introduces a unified multiscale framework that explicitly separates and quantifies surface-stress effects and beam geometry effects in nanolattice structures. By coupling molecular statics (MS) simulations with finite element analysis (FEA), the mechanical behaviors of body-centered (BC) and octet-truss (OT) lattices are evaluated under controlled beam geometries and lattice size variations. The results demonstrate that the optimal geometries identified at the continuum scale remain valid at the nanoscale when surface effects are incorporated. Surface-stress-corrected MS results exhibit strong agreement with FEA predictions, confirming that geometry-driven stress redistribution, rather than intrinsic surface tension, governs the effective stiffness response. Both BC and OT lattices exhibit a size-dependent stiffening trend, originating from the increase in the axial stiffness of individual nanobeams as their diameter decreases. These findings elucidate how geometry, scale, and surface energy collectively govern mechanical stiffness in nanolattices, providing fundamental design guidelines for lightweight and high-stiffness nanoscale architectures.