For the topological diversity, in-plane hexagonal honeycombs show some interesting mechanical properties which can be related to Poisson's ratios. This work trying understand how ratios affects crashworthiness of honeycombs. Based on standard beam theory, analytical model that predicting is derived, from crushing strength in terms further proposed by using one-dimensional shock model. Combining...

Rigid honeycombs were introduced by Knutson et al. (J Am Math Soc 17:19–48, 2004), and they shown in Bercovici Funct Anal 258:1579–1627, 2010) to be sums of extreme rigid honeycombs, with uniquely determined summands up permutations. Two are essentially the same if have proportional exit multiplicities and, this identification, there countably many equivalence classes such honeycombs. We descri...

Vascular smooth muscle cells (VSMCs) in the normal aorta are described as having a contractile phenotype because they can contract and do not proliferate. VSMCs in pathological conditions such as atherosclerosis and restenosis can proliferate and migrate, but lose their ability to contract, which is referred to as a synthetic phenotype. VSMCs show plasticity by changing their phenotype accordin...

Let G = (V (G), E(G)) be a planar digraph embedded in the plane in which all inner faces are equilateral triangles (with three edges in each), and let the union R of these faces forms a convex polygon. The question is: given a function σ on the boundary edges of G, does there exist a concave function f on R which is affinely linear within each bounded face and satisfies f(v)− f(u) = σ(e) for ea...

The effective planar elastic moduli and planar conductivity (or dielectric constant) of regular hexagonal and triangular honeycombs were investigated for the entire range of volume fractions. Only the extreme limits of the volume fraction have been studied in the past. We studied the effective properties both numerically, via finite elements, and analytically, via rigorous three-point bounds, t...

This paper highlights the effects of cell wall material strain hardening and density functional gradation (FG) on in-plane constant-velocity dynamic crushing response and impact behavior of hexagonal honeycombs. Results show that cell wall material strain hardening influences the distinct deformation modes induced by crushing velocity generally observed in regular hexagonal honeycombs. This is ...