Random Honeycombs Research Articles

Suppressing filamentation instability due to laser beam self-filtering

Abstract The development of small-scale self-focusing in a nonlinear Kerr medium after preliminary self-filtering of a laser beam propagating in free space is studied numerically. It is shown that, under definite conditions, due to self-filtering, filamentation instability (beam splitting into filaments) either occurs at significantly larger values of the B-integral, or does not occur at all. In the latter case, there develops the honeycomb instability revealed in this work. This instability is the formation of a random honeycomb structure in the beam cross-section. It is shown that self-filtering can significantly increase the permissible values of the B-integral, at which the beam quality remains acceptable.

Honeycomb-ring hybrid random mesh design with electromagnetic interference (EMI) shielding for low stray light.

A honeycomb-ring hybrid random mesh structure is designed to achieve low stray light performance. The honeycomb-ring hybrid random mesh comprises the random honeycomb and random ring, achieving two random superpositions in the structure distribution. The stray light distribution is very low by the combination design with different random hybrid structures. In order to illustrate the advantages of the hybrid random structure, we design a random honeycomb network by randomly offsetting vertices. At the same time, for the random honeycomb structure, we replace each vertex with the ring structure with the size of the ring randomly controlled. Thus, the corresponding honeycomb-ring hybrid random structure is obtained. Compared with the random honeycomb, the maximal normalized high-order diffraction energy of the honeycomb-ring hybrid random mesh is about a 62.85% drop, and the shielding performance is increased by about 50%. At the same time, the optical transmittance remains nearly unchanged. Due to the enjoyable property of the designed honeycomb-ring hybrid random mesh, a sample was prepared for performance verification. The measurement results show that it achieves eminent diffraction pattern distribution with the maximal normalized high-order diffraction energy of about -31.8 dB. At the same time, the average optical transmittance exceeds 86%, and the electromagnetic shielding effectiveness (SE) in the Ku band is greater than 26 dB. Based on the fine photoelectric performance of the honeycomb-ring hybrid random mesh structure, it has great application potential for high-quality optical windows.

Investigations on the quasi-static/dynamic mechanical properties of 3D printed random honeycombs under in-plane compression

The aim of this study was to reveal the effects of inertia and base material strain rate on the mechanical properties of 3D-printed random honeycombs. First, random honeycombs were established with various meso-structural parameters based on the Voronoi technique and then manufactured by 3D printing. Quasi-static compression tests were performed using a universal test machine. The results indicated that the random honeycombs exhibited a more uniform deformation mode which led to a gentle stress–strain curve when compared with the regular honeycombs. Furthermore, the strain rate effect of the base material was determined by Split Hopkinson Pressure Bar (SHPB) tests. Finite element models considering the base material strain rate were verified by the quasi-static compression and drop weight impact tests. Dynamic simulations were carried out to determine the critical velocity between the deformation mode and clarify its mechanisms. The second critical velocities increase as the cell size and cell wall thickness increased or as the strain rate effect of the base material is considered. The effects of inertia and base material strain rate on the mechanical properties were discussed. The dynamic stress enhancement is dominated by the strain rate effect of the base material and the inertia effect in the random and shock modes, respectively. Finally, an empirical model that includes the inertia effect and strain rate effect of the base material was proposed based on the 1D shock wave theory and the Johnson–Cook material model.

The role of network topology on the uniaxial tensile behaviour of low density random open cellular structures

The effect of cellular structure on the mechanical properties of cellular solids is included in the prefactors of the relative density term in the Gibson and Ashby scaling laws. The effect of cell shape, cell size distribution, cell shape anisotropy, cell wall curvature and strut cross sectional variation have been known to affect these prefactors. This paper investigates the dependence of these prefactors on the network connectivity in random honeycombs and three-dimensional random open cellular structures. Beginning with intact structures, the network connectivity is reduced by randomly removing struts. A scaled genus density, that remains independent of sample volume, absolute cell size, and the relative density, has been defined and taken as a quantitative measure of the global connectivity. The variation in the overall stiffness and offset yield stress due to loss in connectivity was found to clearly depend on the scaled genus density when the relative density is kept constant, indicating that the geometric prefactors are functions of scaled genus density. The prefactors for intact perturbed cubic voronoi, perturbed BCC voronoi structures, and perturbed cubic body diagonal lattices with widely differing scaled genus density also confirm this strong correlation. We also show that the prefactors can be factored to quantitatively decouple the effects of anisotropy and scaled genus density.

Experimental studies on quasi-static axial crushing of additively-manufactured PLA random honeycomb-filled double circular tubes

The Voronoi-based random honeycomb cylindrical shell with specific mesostructures was constructed programmatically and additively manufactured on material of polylactide (PLA). Then, a new PLA random honeycomb-filled double circular tube (PLA-RHFDCT) was proposed. The mechanical performance of the PLA-RHFDCTs in terms of deformation mode, crushing response and energy absorption was studied experimentally by carrying out the quasi-static axial compression loading. A parametric study was performed to evaluate the influence of tube sizes and the mesostructures of honeycomb cores on the crushing resistance and energy absorption capacity of the PLA-RHFDCTs. Results indicate that the cell configuration dominates the deformation modes of PLA honeycomb cylindrical structure. For the PLA-RHFDCTs, the deformation and the bearing capacity are mainly determined by the wall thicknesses of tubes. The introduction of PLA honeycomb core enhances the mechanical performance and affects the localized buckling of the PLA-RHFDCTs due to both the in-plane and out-of-plane crushing resistance of honeycomb core structures. Compared with the parameter of cell irregularity, the relative density of honeycomb cylindrical cores exhibits a higher influence on the energy absorption performance of the PLA-RHFDCTs, though the relatively low crushing strength of PLA honeycomb cylindrical structures.

Absorption-desorption of carbon dioxide in carbon honeycombs at elevated temperatures

The recently synthesized honeycomb carbon allotrope has numerous potential applications, in particular for storage of gases inside carbon matrices. In this work this carbon form was experimentally studied in its denser form in order to estimate the upper temperature limit for keeping a gas inside the cellular structure. Along with the previously reported random honeycombs of a zigzag type we have also revealed the densest armchair structure. The mechanism of absorption-desorption of carbon dioxide studied by means of high energy electron diffraction at low temperatures showed the two — stage character of the observed desorption at elevated temperatures. This effect is associated to the weaker or stronger bonding of molecules with pore walls depending on the specific configuration of channels with different sizes. We have found that complete desorption of CO2 does not occur even at the temperatures about three times higher as compared with the sublimation point of carbon dioxide in our vacuum conditions.

Adsorption-induced strain of a nanoscale silicon honeycomb

We report on systematic measurements of both adsorption and anisotropic mechanical deformations of mesoporous silicon, using heptane at room temperature. Porous Si obtained from highly doped (100) Si can be thought of as a nanoscale random honeycomb with pores parallel to the [001] axis. We show that strains and measured along and transversely to the pore axis exhibit a hysteretic behavior as a function of the fluid pressure, which is due to the hysteresis in fluid adsorption. The pressure dependence of the strains together with the independent measurement of the transverse stress, allows us to determine the biaxial transverse modulus and to estimate the longitudinal Young's modulus of porous Si. We argue that the value of these constants implies that Young's modulus of the 6 nm thick walls of the honeycomb is about 5 times smaller than that of bulk silicon, striking evidence of finite-size effects.

Role of cell regularity and relative density on elasto-plastic compression response of random honeycombs generated using Voronoi diagrams

The Voronoi tessellation technique and solid modeling methods are used in this work to create virtual random structures and link cell morphology with the mechanical behavior. Their compression responses are analyzed using the finite element method. First, the effect of loading direction is analyzed for structures with different levels of randomness characterized by a regularity parameter to assess the degree of scatter in the results. Subsequently, morphological characteristics such as arrangement of cells and randomness are analyzed separately. The effect of relative density on structures with different levels of randomness is also studied. Simulations suggest that at low relative densities the arrangement of cells has a negligible effect on the compression response of random honeycombs. On the contrary, the cellular randomness has significant influence on the elastic and plastic characteristics especially when fully random structures are compared with the regular counterparts.

On the distribution of elastic forces in disordered structures and materials. I. Computer simulation

Randomly structured materials and structures develop distributed internal forces when subjected to external loadings. Using granular packings, and random honeycombs and open–cell foams as prototypic examples, computer simulations were carried out to elucidate the statistical distribution of the internal forces in randomly structured materials. It was found that the sharpness of the force distribution depends critically on the degree of randomness of the structure. In general, the force distributions in these exemplary systems are found to range from the Maxwell–Boltzmann form to a sharply peaked Gaussian form. The results presented here form the basis for the development of a statistical mechanics theory to be presented elsewhere as part II.

Modelling fatigue damage accumulation in two-dimensional Voronoi honeycombs

Trabecular bone, a porous, cellular type of bone found at the ends of the long bones and within the vertebrae, is subject to cyclic compressive loading resulting from the activities of daily living. Such fatigue loading can result in fracture, especially in vertebrae of patients with osteoporosis. As an initial step in understanding compressive fatigue of trabecular bone we previously used finite-element analysis to model the progressive damage and failure of a simple, two-dimensional hexagonal honeycomb. In this study, the analysis is extended to a random, Voronoi honeycomb. Bending of the cell walls induces tensile stresses even when the overall loading is compressive. The cell walls are assumed to have a distribution of crack lengths in their tensile zones. The cracks are assumed to grow according to a Paris law and fail when the cracks reach 75% of the cell wall thickness. Failed cell walls are removed from the structure, the stress distribution recalculated and the next increment of fatigue loading are simulated. The Young's modulus of the honeycomb is calculated after each cell wall failure. Overall failure of the Voronoi structure is assumed to occur when the modulus is reduced by 5%; further loading reduces the modulus sharply. The slope of the S–N curve for the Voronoi honeycomb is the same as that for the hexagonal honeycomb. The model suggests that a random honeycomb is more sensitive to fatigue than a regular one.

Effect on the groundstate threshold pc by different boundary conditions in 2 D ± J Ising models

In the so-called uniform classes HC z , SQ z , TR z of random honeycomb, square and triangular ± J Ising models without exterior magnetic field, we investigate the effect of periodic and mixed lattice boundary conditions (b.c.) on the groundstate threshold p c of the spontaneous absolute magnetization per spin; z is a fixed number of PAF-bonds on the plaquette perimeter where these bonds have the same positive probability p to be antiferromagnetic and the probability 1− p to be ferromagnetic, the remaining bonds are ferromagnetic. For the models in the uniform classes it turns out that periodic b.c. ensure the existence of a critical concentration p c, p. b. c. (at zero temperature). Whereas for mixed b.c. (periodic b.c. in one direction, and in the orthogonal direction only couplings +1 on opposite boundaries) there are, in the classes SQ 1 and TR 1, models for which p c, m. b. c. does not exist. The emphasis is on models in classes SQ 1, TR 1, HC 1, as a counterpart to isotropic models. For z=1, by means of simulations of exact groundstates, we have strong support that there is a first-order phase transition in the magnetization, in several models. For p c in the three regular isotropic models we give a simple formula based on the lattice node degree.