Multiple-objective optimization design of triangular-hexagonal gradient honeycombs for balancing initial peak force and specific energy absorption capacity

Abstract

For energy-absorbing honeycomb structures, uniform configurations generally exhibit an inherent trade-off between reducing the initial peak force (IPF) and enhancing the specific energy absorption (SEA) capacity. To overcome this limitation, the multi-objective optimization framework for triangular–hexagonal gradient honeycomb structures is presented. The wall thickness (t) and gradient coefficient (n) were selected as design variables, and a multi-objective optimization model was formulated to minimize IPF while maximizing SEA. An adaptive Kriging surrogate model was constructed using a dataset of 39 quasi-static compression tests, and the Pareto-optimal solution set was obtained using the NSGA-II algorithm. Among these solutions, OPT-1 (t=1.16, n=0.70) was identified as the representative compromise solution using the minimum-distance criterion. Compared with the 1.0-mm-thick uniform triangular honeycomb THS-2, OPT-1 increased SEA by 11.56% while reducing IPF by 19.61%. Moreover, relative to the 1.2-mm-thick uniform honeycomb THS-3, OPT-1 reduced IPF by 44.98% with only a marginal 4.93% decrease in SEA, demonstrating a more favorable compromise between load attenuation and energy absorption. In addition, OPT-1 exhibited a stable progressive layer-by-layer collapse mode, indicating enhanced deformation stability. These findings provide a theoretical basis and methodological guidance for the synergistic optimization of lightweight protective honeycomb structures.