This paper presents the results of the elastic and geometrical properties of four types of nanostructured hierarchical and self-similar honeycombs. It is shown that at the nanometer scale, the elastic properties are size-dependent; the thinner the first order cell walls, the stiffer the hierarchical honeycombs. As an initial strain can be applied and controlled to the first order cell walls by ...

Earlier discovery and presentation of an inherent order of the regular and semiregular polyhedra that displays three interrelated classes, together with consideration of the honeycombs, has led me to posit the existence of a coherent and integral metapattern that should relate the various all-space-filling periodical honeycombs, which I advance in an earlier paper that should be read in conjunc...

Lung parenchyma surrounding an atelectatic region is thought to be subjected to increased stress compared with the rest of the lung. Using 37 hexagonal cells made of linear springs, Mead et al. (1970) measured a stress concentration greater than 30% in the springs surrounding a stiffer central cell. We re-examine the problem using a 2D finite element model of 500 cells made of thin filaments wi...

We review the regular tilings of d-sphere, Euclidean d-space, hyperbolic d-space and Coxeter’s regular hyperbolic honeycombs (with infinite or star-shaped cells or vertex figures) with respect of possible embedding, isometric up to a scale, of their skeletons into a m-cube or m-dimensional cubic lattice. In section 2 the last remaining 2-dimensional case is decided: for any odd m ≥ 7, star-hone...

Small and large deformation in-plane elastic response of a new class of hierarchical fractal-like honeycombs inspired by the topology of the ''spiderweb'' were investigated through analytical modeling, detailed numerical simulations, and mechanical testing. Small deformation elasticity results show that the isotropic in-plane elastic moduli (Young's modulus and Poisson's ratio) of the structure...

A new class of hierarchical fractal-like honeycombs inspired by the topology of the “spiderweb” were introduced and their small and large deformations were investigated analytically, numerically, and experimentally. Small deformation elasticity results show that the isotropic in-plane elastic moduli (Young’s modulus and Poisson’s ratio) of the structures can be controlled over several orders of...

Hierarchical cellular structures are ubiquitous in nature because of their low-density, high-specific properties, and multifunctionality. Inspired by these systems, we created lightweight ceramic architectures composed of closed-cell porous struts patterned in the form of hexagonal and triangular honeycombs by direct foam writing. The foam ink contains bubbles stabilized by attractive colloidal...

We present the possibility that the gravitational growth of primordial density fluctuations leads to what can be considered a week version of the cosmological principle. The large scale mass distribution associated with this principle must have the geometrical structures known as a regular honeycombs. We give the most important parameters that characterize the honeycombs associated with the clo...