Mathematical modelling of energy absorption property for paper honeycomb in various ambient humidities

A mathematical model was developed to describe the relationship between the energy absorption properties of paper honeycombs and ambient humidity, as well as the structural parameters thereof. The model is a piecewise function modelling the energy absorption of four deformation stages of paper honeycomb (linear-elastic stage, yield stage, plateau stage and densification stage) separately. Function of each stage is a simple formula relating the energy absorption capacity to the thickness-to-length ratio of honeycomb cell, the mechanical property of a cell-wall material tested under a controlled atmosphere [23 °C and 50% relative humidity (RH)] and the RH. Energy absorption curves were thereby obtained for paper honeycombs with a wide range of thickness-to-length ratios in arbitrary humidity environments. The created model was then verified by comparing the predicted energy absorption curves with the experimental ones. A good accordance between the predictions and the observations was achieved, indicating that the energy absorption models developed here could be used to practical application for the designing optimisation and material selection of paper honeycombs.