Volume 06
Effects of Circular Hierarchy Elements on Effective Elastic Properties of First Order Hierarchical Honeycombs
Authors
Mustafa Yıldız, Fatih Göncü
Abstract
The mechanical behavior of honeycombs with circular hierarchy under in-plane loading was investigated using analytical and numerical methods. To obtain the first-degree hierarchy, the combinations of the cell walls of the hexagonal base structure were replaced with smaller circular elements. Besides, a new parameter was obtained to control the material ability to resist deformations by applying different thickness status (heterogeneity). Effective Young’s module and effective Poisson’s ratio of the hierarchical structure were calculated by applying Castigliano’s theorem. The effective shear modulus was also determined with the help of the equation for isotropic materials based on classical strength of materials. To easily interpret the effects of hierarchy and different thickness status on the non-hierarchical honeycomb, these mechanical properties were normalized with the mechanical properties displayed by the ordinary honeycomb. The effect of the scaling factor which controls the size of the circular geometry, and the heterogeneity factor which controls the wall thickness ratio between ones of base and hierarchical parts on the elastic properties are studied. The findings showed that by changing the scaling and heterogeneity factor, structures with 2 times the stiffness and 0.3 times the effective Poisson’s ratio of an ordinary honeycomb having the same average density is obtained.
Keyword: Circular hierarchy, In-plane effective properties, Castigliano’s second theorem, Finite element method, Periodic boundary conditions.
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