Nonlinear mechanical response of lightweight non-self-similar hierarchical metamaterials subjected to quasi-static and dynamic loadings

• The junctions between first-order and second-order unit cells in non-self-similar hierarchical topology (NSSHT) reach yield stress first. • The NSSHT presents negative Poisson’s ratio behavior due to the lateral shrinking of unit cells before stress enhancement stage. • The in-plane geometric parameters significantly affect the deformation mode and failure mechanism of NSSHT. • The specific peak stress, specific plateau stress and specific energy absorption of NSSHT under dynamic loading are all improved. Light-weight hierarchical honeycomb is a sort of high-potential multifunctional micro topology structure in aviation and automotive industries attributed to its excellent impact resistance and specific strength/stiffness. The present research investigates a new non-self-similar hierarchical topology (NSSHT) with coupled bending-stretching, and gives an insight into the quasi-static and dynamic mechanical responses. Results demonstrate the numerically predicted mechanical behaviors are consistent with the experiments. The stress at the junctions between first-order and second-order unit cell is higher than those at the other locations before stress enhancement stage, and these positions achieve yield stress first. The NSSHT exhibits NPR behavior ascribed to the lateral shrinking of unit cells before stress enhancement stage, whereas presents a PPR (positive Poisson’s ratio) behavior afterwards. The NSSHT is compressed layer by layer during dynamic impact, the propagation speed of stress wave is about 2679 m/s in NSSHT. As γ or η increases, the failure of NSSHT is progressively transformed from elastic-plastic bending to fracture of cell walls. The specific peak/plateau stress and SEA of NSSHT under dynamic loading are significantly improved compared with the quasi-static, and they are all enhanced with the rise in relative density