Analytical relationships for the mechanical properties of additively manufactured porous biomaterials based on octahedral unit cells

Additively manufacturing (AM) techniques make it possible to fabricate open-cell interconnected structures with precisely controllable micro-architectures. It has been shown that the morphology, pore size, and relative density of a porous structure determine its macro-scale homogenized mechanical properties and, thus, its biological performance as a biomaterial. In this study, we used analytical, numerical, and experimental techniques to study the elastic modulus, Poisson`s ratio, and yield stress of AM porous biomaterials made by repeating the same octahedral unit cell in all spatial directions. Analytical relationships were obtained based on both Euler-Bernoulli and Timoshenko beam theories by studying a single unit cell experiencing the loads and boundary conditions sensed in an infinite lattice structure. Both single unit cells and corresponding lattice structures were manufactured using AM and mechanically tested under compression to determine the experimental values of mechanical properties. Finite element models of both single unit cell and lattice structure were also built to estimate their mechanical properties numerically. Differences in the bulk mechanical properties of struts built in different directions were observed experimentally and were taken into account in derivation of the analytical solutions. Although the analytical and numerical results were generally in good agreement, the mechanical properties obtained by the Timoshenko beam theory were closer to numerical results. The maximum difference between analytical and numerical results for elastic modulus and Poisson's ratio was below 6%, while for yield stress it was about 13%, both occurring at the relative density of 50%. The maximum difference between the analytical and experimental values of the elastic modulus was <15% (relative density = 50%).     

A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites

A literature review on the prediction of Young’s modulus for carbon nanotubes, from both theoretical and experimental aspects, is presented. The discrepancies between the values of Young’s modulus reported in the literature are analyzed, and different trends of the results are discussed. The available analytical and numerical simulations for predicting the mechanical properties of carbon nanotube composites are also reviewed. A gap analysis is performed to highlight the obstacles and drawbacks of the modeling techniques and fundamental assumptions employed which should be overcome in further studies. The aspects which should be studied more accurately in modeling carbon nanotube composites are identified.     

A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects

In conventional continuum mechanics, the surface energy is usually small and negligible. But at nano-length scale, it becomes a significant part of the total elastic energy due to the high specific surface area of nanomaterials. A geometrically nonlinear finite element (FE) model of nanomaterials with considering surface effects is developed in this paper. The aim is to extend the conventional finite element method (FEM) to analyze the size-dependent mechanical properties of nanomaterials. A numerical example, analysis of InAs quantum dot (QD) on GaAs (0 0 1) substrate, is given in this paper to verify the validity of the method and demonstrate surface effects on the stress fields of QDs.     

Suction energy and offset configuration for double-walled carbon nanotubes

Nanostructures such as carbon nanotubes and fullerenes offer the means to create new mechanical devices operating at the nanoscale. Such devices include oscillators constructed from an inner carbon nanotube sliding inside another carbon nanotube. The resultant oscillatory frequency is found to be in the gigahertz range and they have applications in the computing industry for signalling devices, such as an ultra-fast optical filter. While most research in the area is dominated by molecular dynamics simulations, our approach here is to use elementary mechanical principles and classical applied mathematical modelling techniques to formulate explicit analytical criteria and ideal model behaviour. In this paper, we first investigate the suction force experienced by a single-walled carbon nanotube located near an open end of a semi-infinite single-walled carbon nanotube, using the Lennard–Jones potential and the continuum approximation. Second the equilibrium position of an offset inner tube with reference to the cross-section of the outer tube is determined.     

Demand-driven energy requirement of world economy 2007: A multi-region input–output network simulation

This study presents a network simulation of the global embodied energy flows in 2007 based on a multi-region input–output model. The world economy is portrayed as a 6384-node network and the energy interactions between any two nodes are calculated and analyzed. According to the results, about 70% of the world’s direct energy input is invested in resource, heavy manufacture, and transportation sectors which provide only 30% of the embodied energy to satisfy final demand. By contrast, non-transportation services sectors contribute to 24% of the world’s demand-driven energy requirement with only 6% of the direct energy input. Commodity trade is shown to be an important alternative to fuel trade in redistributing energy, as international commodity flows embody 1.74E + 20 J of energy in magnitude up to 89% of the traded fuels. China is the largest embodied energy exporter with a net export of 3.26E + 19 J, in contrast to the United States as the largest importer with a net import of 2.50E + 19 J. The recent economic fluctuations following the financial crisis accelerate the relative expansions of energy requirement by developing countries, as a consequence China will take over the place of the United States as the world’s top demand-driven energy consumer in 2022 and India will become the third largest in 2015.     

Dynamic stability of carbon nanotubes reinforced composites

Based on an effective model of multi-walled carbon nanotubes and Donnell-shell theory, an analytical method is presented to study dynamic stability characteristics of multi-walled carbon nanotubes reinforced composites considering the surface effect of carbon nanotubes. From obtained results it is seen that carbon nanotubes composites, under combined static and periodic axial loads, may occur in a parametric resonance, the parametric resonance frequency of dynamic instability regions of CNTs reinforced composites under axially oscillation loading enhances as the stiffness of matrix surrounding CNTs increases, and the surface effective modulus and residue stress of carbon nanotubes make the parametric resonance frequency and the region breadth of dynamic instability of carbon nanotubes reinforced composites increase.     

Smoke flow phenomena and turbulence characteristics of tunnel fires

Gravity currents are similar in behavior with smoke flows. This work aims to provide evidence justifying the use of gravity current approach to model smoke flows downstream of the fire source. The turbulence solver available in almost all commercial CFD codes solves RANS for the flow field. To find out how well the nature of smoke flow be accurately modeled using RANS that is widely used for incompressible flows. The feasibility of using both Reynolds- and Favre-averaging schemes was numerically compared and examined in this paper. In this work, numerical simulations of a fire occurred in a 400-m longitudinally ventilated tunnel have been successfully performed using FDS version 4. Large eddy simulation is employed in this study. Although the ranges of fire size and ventilation velocity vary respectively from 0 MW to 100 MW and 0 m/s to 10 m/s, this paper focuses on the general flow and temperature fields and the turbulence characteristics. Furthermore, the turbulence kinetic energy levels of the flow in the tunnel at several locations were investigated. Since the flow field is generally induced by mechanical ventilation and combustion, the main contribution to the turbulence kinetic energy comes from its longitudinal, vertical, or their combination.     

Methods of analysing ropes. The extension–torsion method

Two new approaches are used for calculating the stress–strain state of a rope and its stiffnesses. The first approach relies on the theory of fibrous composites and Saint-Venant's solution for a cylinder with helical anisotropy. The second approach is based on the solution by the finite element method of the three-dimensional problem of elasticity theory for a solid inhomogeneous cylinder formed by a finite number of elastic fibres arranged in helical lines and connected by a weak filler (in the sense that its Young's modulus is several orders of magnitude less than the Young's modulus of the fibre). The behaviour of the stiffness when the modulus of elasticity of the filler tends to zero is analysed, and the results of the limiting transition are discussed. The numerical results obtained are compared with calculations by other well-known applied theories.     

Development of a Neuro-Fuzzy approach for treating multimodal distributions and spurious clusters

In this paper, we introduce a developed approach of neuro-fuzzy model free estimators to treat decision problems, where presence of highly multimodal distribution and spurious clusters in decision space causes problems in estimation. After critical analysis of Bart Kosko's DCL–AVQ + FAM neuro-fuzzy system, we developed our Straitjacket + F-wing system. Straitjacket neural system is an improved version of Kohonen's feature mapping according to convergence and termination conditions. F-wing fuzzy system bases on the feature map produced by Straitjacket and provides faster and more exact estimator interface than Bart Kosko's FAM, using fuzzy wing functions instead of fuzzy hyperpyramids. At the end of the paper we perform a test on artificial database comparing the efficiency of our approach with Kosko's system, discriminant analysis, hierarchic and K-mean clustering.     

Developing interaction potential for H (2H) → Cu(1 1 1) interaction system: A numerical study

In this study, we have used London–Eyring–Polanyi–Sato (LEPS) functional form as an interaction potential energy function to simulate H (2H) → Cu(1 1 1) interaction system. The parameters of the LEPS function are determined in order to analyze reaction dynamics via molecular dynamics computer simulations of the Cu(1 1 1) surface and H/(2H) system. Nonlinear least-squares method is used to find the LEPS parameters. For this purpose, we use the energy points which were calculated by a density-functional theory method with the generalized gradient approximation including exchange-correlation energy for various configurations of one and two hydrogen atoms on the Cu(1 1 1) surface. After the fitting procedures, two different parameters sets are obtained that the calculated root-mean-square values are close to each other. Using these sets, contour plots of the potential energy surfaces are analyzed for H → Cu(1 1 1) and 2H → Cu(1 1 1) interactions systems. In addition, sticking, penetration, and scattering sites on the surface are analyzed by using these sets.     

Special Functions on the Sphere with Applications to Minimal Surfaces

A function which is homogeneous in x, y, z of degree n and satisfies V_xx + V_yy + V_zz = 0 is called a spherical harmonic. In polar coordinates, the spherical harmonics take the form rⁿf_n, where f_n is a spherical surface harmonic of degree n. On a sphere, f_n satisfies ▵ f_n + n(n + 1)f_n = 0, where ▵ is the spherical Laplacian. Bounded spherical surface harmonics are well studied, but in certain instances, unbounded spherical surface harmonics may be of interest. For example, if X is a parameterization of a minimal surface and n is the corresponding unit normal, it is known that the support function, w = X · n, satisfies ▵w + 2w = 0 on a branched covering of a sphere with some points removed. While simple in form, the boundary value problem for the support function has a very rich solution set. We illustrate this by using spherical harmonics of degree one to construct a number of classical genus-zero minimal surfaces such as the catenoid, the helicoid, Enneper's surface, and Hennenberg's surface, and Riemann's family of singly periodic genus-one minimal surfaces.     

An improved parallel implementation of RainbowCrack using MPI

Nearly three decades ago, Martin Hellman introduced a cryptanalytic time-memory trade-off algorithm which reduced the time of cryptanalysis by using precalculated data. Rivest shortly improved this technique by introducing distinguished points which significantly reduced the frequency of memory lookups during cryptanalysis. In 2003, Philip Oechslin proposed a new and improved algorithm which reduces the number of calculations during cryptanalysis by a factor of two. In this research we present the results of a parallel implementation of Oechslin's faster time-memory trade-off algorithm using MPI on a SHARCNET supercomputer. We use MS-Windows hashes (alphanumeric sequences of length 14 characters or less). We can construct 119 GB of data in 6 days and crack 99.9% of all passwords hashes in 6 s or less. On a standard desktop machine, the same task requires 2354 days (6 years!) to construct the data and 3–15 min to crack the password.     

Molecular dynamics of thermal vibration effects: Ar + Ni(1 0 0) collision system

In this work constant energy molecular dynamics simulations are achieved for investigating sputtering process of Ar + Ni(1 0 0) collision system. The Ni crystal is imitated by an embedded-atom potential, whereas the interaction between the projectile and the surface is modeled by re-parameterized ZBL potential. Seven hundred eighty-four Ar atoms carrying 20–50 eV are sent towards a Ni(1 0 0) surface at normal incidence. Each projectile meets with different initial coordinates (phase) of the nickel atoms because of thermal vibrations in the slab. Effects of the different initial phases of the surface are compared with the available theoretical and experimental data.     

Systems accounting for energy consumption and carbon emission by building

The method of systems accounting for overall energy consumption and carbon emission induced by a building is illustrated in terms of a combination of process and input–output analyses with a concrete procedure to cover various material, equipment, energy and manpower inputs. A detailed case study based on raw project data in the Bill of Quantities (BOQ) is performed for the structure engineering of the landmark buildings in E-town, Beijing (Beijing Economic–Technological Development Area). Based on the embodied energy and carbon emission intensity database for the Chinese economy in 2007, the energy consumption and the carbon emission of the structure engineering of the case buildings are quantified as 4.15E+14 J and 4.83E+04 t CO₂ Eq., corresponding to intensities of 6.91E+09 J/m² and 0.81 t CO₂ Eq./m² floor area. Steel and concrete contribute respectively about 50% and 30% of the energy consumption and the carbon emission, as a result of the reinforced-concrete structure of the case buildings. Materials contribute up to about 90% of the total energy consumption and carbon emission, in contrast to manpower, energy and equipment around 8%, 1% and 0.1%, respectively.     

Exact integration of the stiffness matrix of an 8‐node plane elastic finite element by symbolic computation

Computer algebra systems (CAS) are powerful tools for obtaining analytical expressions for many engineering applications in both academic and industrial environments. CAS have been used in this paper to generate exact expressions for the stiffness matrix of an 8‐node plane elastic finite element. The Maple software system was used to identify six basic formulas from which all the terms of the stiffness matrix could be obtained. The formulas are functions of the Cartesian coordinates of the corner nodes of the element, and elastic parameters Young's modulus and Poisson's ratio. Many algebraic manipulations were performed on the formulas to optimize their efficiency. The redaction in CPU time using the exact expressions as opposed to the classical Gauss–Legendre numerical integration approach was over 50%. In an additional study of accuracy, it was shown that the numerical approach could lead to quite significant errors as compared with the exact approach, especially as element distortion was increased.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007     

The stresses in single lap joints with a functionally graded adhesive bondline: an efficient modelling approach

In this work, an efficient analytical model for the stress analysis of single lap joints with a functionally graded adhesive bondline is proposed which considers peel as well as shear stresses in the adhesive. The model takes into account the nonlinear geometric characteristics of a single lap joint under tensile loading and allows for the analysis of various adhesive Young's modulus variations. The obtained stress distributions are compared to results of detailed Finite Element analyses and show a good agreement for several single lap joint configurations. In addition, different adhesive Young's modulus distributions and their effect on the peel and shear stresses are studied and discussed in detail. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effects of geometrical parameters on force distributions and mechanics of carbon nanotubes: A critical study

In this paper, using the continuum approximation together with Lennard–Jones potential, a new semi-analytical expression is given to evaluate the van der Waals interaction between two single-walled carbon nanotubes. Based on this expression, two new formulations are also proposed to model multi-walled carbon nanotubes. In the first one, the interactions between each pair of shells from the inner and outer tubes are summed up over all of the pairs, whereas in the second formulation, a set of correction factors are applied to convert the results of double-walled carbon nanotubes to the correlated multi-walled ones. With respect to the present formulations, extensive studies on the variations of force distributions are performed by varying nanotube geometries so that the important features of the geometrical parameters are explored. Moreover, an acceptance condition for a nanotube at rest which is to be sucked into a semi-infinite nanotube is obtained. The influence of different geometrical parameters on the acceptance condition and suction energy, two main characteristics of nanotube-based systems for applications such as drug delivery and so on, is fully demonstrated. Lastly, an interesting relation for the maximum value of suction energy in terms of geometrical parameters is also extracted in this study.     

On Pauli’s principles of “Zweiteilung und symmetrie verminderung” in Higgs physics and non-linear dynamics

Pauli’s principle of bi-division and symmetry reduction “Zweiteilung und symmetrie verminderung” is generalized to cover maximally symmetric spaces specified by Killing’s vector fields and its successive symmetry breaking to yield the particles of the standard model of high energy physics.An analogous picture borrowed from non-linear dynamics and complexity theory will be used to illustrate the conceptual aspect of the procedure from which one could infer, the existence not only of one, but several Higgs particles, possibly three neutral and two charged Higgs with masses not that far from the presently accessible electro-weak energy scale. A tree level estimation with one Higgs to approximate the mass was found to give m_H ≃ 162 Gev.     

Simulación numérica del flujo turbulento de aire con gotas dispersas de agua a través de separadores de torres de refrigeración

This work presents a numerical study on the turbulent flow of air with dispersed water droplets in separators of mechanical cooling towers. The averaged Navier-Stokes equations are discretised through a finite volume method, using the Fluent and Phoenics codes, and alternatively employing the turbulence models k ? ?, k ? ω and the Reynolds stress model, with low-Re version and wall enhanced treatment refinements. The results obtained are compared with numerical and experimental results taken from the literature. The degree of accuracy obtained with each of the considered models of turbulence is stated. The influence of considering whether or not the simulation of the turbulent dispersion of droplets is analyzed, as well as the effects of other relevant parameters on the collection efficiency and the coefficient of pressure drop. Focusing on four specific eliminators (‘Belgian wave’, ‘H1-V’, ‘L-shaped’ and ‘Zig-zag’), the following ranges of parameters are outlined: 1 ≤ U_e ≤ 5 m/s for the entrance velocity, 2 ≤ D_p ≤ 50 μm for the droplet diameter, 650 ≤ Re ≤ 8.500 for Reynolds number, and 0.05 ≤ P_i ≤ 5 for the inertial parameter. Results reached alternately with Fluent and Phoenics codes are compared. The best results correspond to the simulations performed with Fluent, using the SST k ? ω turbulence model, with values of the dimensionless scaled distance to wall y⁺ in the range 0.2 to 0.5. Finally, correlations are presented to predict the conditions for maximum collection efficiency (100 %), depending on the geometric parameter of removal efficiency of each of the separators, which is introduced in this work.