The in-plane, elastic-plastic response of a filled hexagonal honeycomb at finite strain

Finite strain numerical solutions are derived for the in-plane, elastic-plastic response of a filled hexagonal honeycomb in uniaxial compression and in uniaxial tension. The cell walls and core are treated as elastic, ideally plastic von Mises solids, but the uniaxial strength of the core material is much less than that of the cell walls. The honeycomb has sides of equal length, and its inclined (but non-vertical) cell walls subtend an angle with respect to the transverse direction that can deviate from the usual value of +/-30 degrees which is characteristic of a regular honeycomb. Two responses of the core are assumed: the fully bonded, 'non-cavitating core' (in the presence of a sufficiently high macroscopic pressure) and a 'cavitating core' that can cavitate or debond freely from the cell walls. When the honeycomb has cell walls that are inclined at 30 degrees or less, the unitcell response in uniaxial compression is stable and displays macroscopic hardening, regardless of whether the core can cavitate or not. In contrast, when the inclination of the cell walls exceeds 30 degrees, the honeycomb with a cavitating core displays mild softening in uniaxial compression while the honeycomb with a non-cavitating core has a high initial yield strength, followed immediately by a strongly softening response. The strongly softening, isochoric mode occurs in an inclined shear band by the rotation of inextensional plastic hinges in the cell walls over a wavelength of two cells. A Maxwell construction is adequate for prediction of the propagation stress of the shear band in a finite specimen from a starter defect. Additional insight into the collapse mechanisms of the filled honeycomb (with a cavitating or non-cavitating core) is obtained via analytical solutions for a rigid, ideally plastic honeycomb, whereby the cell walls are treated as slender beams and the core has vanishing deviatoric strength. The full numerical solutions reveal that the filled honeycomb exhibits strong tension-compression asymmetry for both a cavitating core and a noncavitating core.

Automated summary

Finite strain numerical solutions were used to study the elastic-plastic behavior of a hexagonal honeycomb under uniaxial compression and tension. The study found that the inclination angle of the cell walls and the characteristics of the core material significantly affect the response of the honeycomb.