To start let us assume that the predominant contribution to the elastic strain comes from the axial compression of the vertical struts, as shown below.
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We can estimate the magnitude of this strain as the cross-sectional area of solid material, AV, in a cut across just the vertical faces is less than that if the material were completely solid by the ratio of the cell wall thickness, t, to the horizontal distance across each cell, 2 l cos θ.
As t << l cos θ, this is given by
Using the measured values of t ( = 0.09 mm) and l ( = 6.30 mm), and taking θ = 30° as the cells are hexagonal gives AV as 0.008. Taking the Young modulus of aluminium as 70 GPa, this predicts the Young modulus of the honeycomb to be 560 MPa. This is greater than the observed value of 435 kPa by more than 3 orders of magnitude and shows that axial compression of the vertical faces makes a negligible contribution to the elastic strain.
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