Mean compressive stress constitutive equation and crashworthiness optimization design of three novel honeycombs under axial compression

• The simplified super folding element (SSFE) theory is applied.
• The mean crushing stresses of three types of novel honeycombs are deduced.
• Numerical simulation of honeycomb under axial impact.
• The multi-objective crashworthiness optimization of novel honeycomb structure.
• The theoretical solutions and design optimization are feasible and efficient.

Taking typical type of honeycomb as research object, three types of novel honeycombs are studied on the aspects of theoretical prediction under axial crushing. The simplified super folding element (SSFE) theory is applied to estimate the energy dissipation of the typical elements. Taking the inertia effects into account, dynamic mean compressive stress calculating equation is further deduced by utilizing the dynamic enhancement coefficient. In order to validate these theoretical solutions, LS-DYNA is used to simulate the axial loading of three novel honeycombs. The analytical results correlate with these simulation results in an ideal manner. During the multi-objective optimization deign, optimal Latin hypercube design (OLHD) method is used to select sampling points in the design space. Meanwhile, the response surface method (RSM), as an accurate surrogate modeling method, is adopted to obtain a maximum specific energy absorption per mass (SEAm) capacity and minimum peak crushing stress (σpeak). These results yielded from the optimization indicate that the bending cellular honeycomb (BC-H) has the best energy absorption performance under the same limitation of σpeak. Furthermore, the theoretical equations proposed are utilized to validate the simulation results of three optimal structures. The theoretical predictions show excellent agreement with these simulation values, which hence illustrate the feasibility and efficiency of the crashworthiness optimization method based on surrogate models and finite element analysis techniques.