As the honeycomb yields in the plateau region, the regular hexagonal cell with a height (l + 2l sin θ) changes shape with the protruding apices being pressed toward one another to give cells with the shape of a bow-tie and a height l.
If the cells deform uniformly then the strain at which this occurs, εD, is given by
Note true strain is used because the strains are large and compressive. As θ = 30°, εD, is predicted to have a magnitude of 0.7. Further increases in strain cause opposing cell walls to be pressed against one another and the stress required for further deformation increases rapidly. As can be seen in the stress strain curve below this prediction gives good agreement with the observed stress-strain curve.
Note: This animation requires Adobe Flash Player 8 and later, which can be downloaded here.
It can be seen that this collapse does not occur uniformly throughout the whole structure, but layer by layer of cells. This behaviour is rather dependent on the size of the cell compared to that of the sample. Increasing the number of cells in a cross-section causes the behaviour to become more uniform as might be expected.
It is now possible to quantitatively understand the entire stress-strain behaviour of a simple honeycomb. The next step is to extend these ideas to less regular structures, such as foams and fibrous structures.
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