Numerical computation of effective elastic constants of the honeycomb sandwich panel with the 3-D multi-step homogenization

Using the 3-D homogenization method and the finite element technique, we evaluate the effective elastic constants of the 3-D honeycomb sandwich panel. Like Hassani^[4], we consider the 3-D honeycomb core as a two-phase composite and model it with the finite element technique; we take Hassani's 2-D homogenization method and extend it to become a 3-D one. We validate our 3-D homogenization method through comparing the results obtained with 3-D homogenization method with those obtained with the methods of Fu et al^[3] and Hassani^[4]; the comparison can be seen in Table 2 of the full paper. We use three variations of our 3-D homogenization method to evaluate the overall effective elastic constants of the 3-D honeycomb sandwich with upper and lower skins; the evaluation results are given. We use one-step, two-step, multi-step homogenization methods and the engineering empirical method to calculate three kinds of effective elastic moduli of 3-D honeycomb sandwich panel. The computed results of the one-step, two-step, and multi-step homogenization methods are in fairly good agreement with those of the engineering empirical method.