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You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!
How does elastic deformation of a honeycomb with hexagonal cells with some faces aligned parallel to the loading axis take place?
What is the criterion for the onset of yielding in a honeycomb?
The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.
How might elongating the cells of a hexagonal honeycomb in the direction of loading change E/ES for a given relative density?
C. Increase it. The length of the beam that must bend is decreased whilst the original length of the cell is increased.
For a highly porous structure E/ES is proportional to (ρ/ρS)n. In which case will the structure show an increased bending stiffness? Hence explain why many porous materials are often used as the core in sandwich structures.
In many open-cell structures n = 2, so that there is no benefit in using the porous structure alone. However advantage can be obtained if the surfaces of the material are covered with a stiff, strong material.
The structure will be stiffer in bending if n < 2. In this case the relative second moment of area will increase as the density is reduced faster than the Young modulus will decrease.
Consider a honeycomb loaded with some faces parallel to the compressive loading direction, in which the shape of the hexagonal cell is such that θ < 0, how would the material deform elastically in the transverse direction?
A. contract inwards, in other words the material has a negative Poisson ratio.