Rate-dependent mechanical properties of hierarchical body-centered cubic lattices: Experiments, FE simulation and analytical modeling

Hierarchical lattice structures offer a promising strategy to overcome the stiffness and load-bearing limitations of conventional lattice architectures. In this work, IN625 hierarchical body-centered-cubic (HBCC) lattice structures with different relative densities were fabricated by laser powder bed fusion (LPBF) and systematically investigated under quasi-static and dynamic compression. An analytical model based on Euler-Bernoulli beam theory and the displacement method was developed to predict the yield stress of HBCC lattices, and strain-rate effects were incorporated through the Johnson-Cook formulation. Finite element simulations and compression experiments validate the analytical predictions, with a maximum deviation of 16.1% across different relative density and less than 11.5% discrepancy under varying strain rates. The results demonstrate that the proposed analytical framework can reliably predict the yield stress of HBCC lattices over a wide range of densities and loading rates, providing an efficient theoretical tool for the design and dynamic performance prediction of hierarchical lattice structures. Quasi-static compression results reveal a distinct two-stage deformation mechanism across all densities, characterized by an initial bending-dominated stage followed by a stretching-dominated load-bearing stage. Under dynamic loading, pronounced strain-rate strengthening is observed at low strains; however, increasing strain rates progressively suppress the second deformation stage and lead to a marked reduction in high-strain load-carrying capacity due to premature instability of vertical struts. The analytical modeling proposed in this study can effectively support investigations of the dynamic response of lattice structures, providing a new methodological basis for characterizing and evaluating their dynamic behavior.