Analyses on the dynamic strength of honeycombs under the y-directional crushing

• The expression of the honeycombs’ y-directional crushing strength is deduced.
• The optimal cell-wall angle of the honeycomb is analytically obtained.
• A dynamic sensitivity index is proposed.
• The honeycomb’s dynamic sensitivity is reversely proportional to the relative density.
• The crushing strength of the honeycomb with β = 45° is the least sensitive to the impact velocity.

Based on the cells’ collapse mechanisms revealed from the numerical simulations, analytical models are established to deduce the crushing strength of the honeycombs along the y  -direction with wide range of impact velocity, which express crushing strength as a function of the impact velocity, the cell size, the cell-wall angle, and the mechanical properties of the base material. The analytical predictions are in good agreement with the numerical simulation results. The optimal cell-wall angle of the honeycomb is analytically obtained as about 45°, which provides a theoretical confirmation on the finding from the numerical simulations. Moreover, a dynamic sensitivity index is proposed to quantitatively evaluate the sensitivity of the honeycombs’ crushing strength to the impact velocity, which is expressed as a function of the cell-wall angle and the honeycomb’s relative density. It is shown that the dynamic sensitivity of the honeycomb is reversely proportional to the honeycomb’s relative density, while the crushing strength of the honeycomb with β=45°β=45° is the least sensitive to the impact velocity.