Closed-form analysis of the size effects in Body-centered cubic micro-/nanolattices

Micro-/nanolattice structures exhibit exceptional mechanical properties, making them highly promising for applications in micro/nano devices and aerospace areas. However, existing research has primarily focused on experimental studies of compression and bending in three-dimensional micro-/nanolattices, resulting in a limited understanding of the size-dependent mechanisms influencing their macroscopic behavior. To address this gap, this study develops a trans-scale analytical model that integrates modified couple stress theory and Timoshenko beam theory, enabling a comprehensive analysis of body-centered cubic(BCC) micro-/nanolattice unit cells. The model is derived using the Hamiltonian principle through variational calculations, taking into account both Poisson’s ratio and size effects. Utilizing Navier’s method, an analytical relationship is established between the length scale parameter and the macroscopic response of the unit cell under quasi-static conditions. The effectiveness of the model in predicting responses is validated against experimental data. Parameter analysis reveals that size effects cannot be neglected when the dimensionless parameter $d/l$ is less than 10 in BCC micro-/nanolattice unit cell response evaluations. Under the combined influence of substrate parameters and size effects, the unit cell exhibits both linear and nonlinear mechanical behaviors, even notable singular features. In particular, strong size effects result in a negative Poisson’s ratio feature of the unit cell. This study not only bridges the theoretical gap in evaluating the response of micro-/nanolattices under size effects but also provides solid theoretical support for the optimized design of micro-/nanolattice devices and aerospace devices area.