A method to determine Young's modulus of soft gels for cell adhesion

A convenient technique is reported in this note for measuring elastic modulus of extremely soft material for cellular adhesion. Specimens of bending cylinder under gravity are used to avoid contact problem between testing device and sample, and a beam model is presented for evaluating the curvatures of gel beams with large elastic deformation. A self-adaptive algorithm is also proposed to search for the best estimation of gels＇ elastic moduli by comparing the experimental bending curvatures with those computed from the beam model with preestimated moduli. Application to the measurement of the property of polyacrylamide gels indi- cates that the material compliance varies with the concentrations of bis-acrylamide, and the gels become softer after being immersed in a culture medium for a period of time, no matter to what extent they are polymerized.

ELECTRIC FIELD EFFECTS ON YOUNG'S MOLULUS OF NANOWIRES

As an important component of nanodevices and nanomachine constructions, the mechanical performance of nanowires （NWs） has been a subject of intense research efforts due to gaining relevance in controlling functionality of nanoelectromechanical systems （NEMS）; meanwhile, one of the characteristics of the NEMS is the dependence of the functionality of the systems upon the applied electric field. The study of the electric effects on the Young＇s modulus of nanostructures is of certain usefulness in the design of NEMS and the precise measurement of mechanical properties of one-dimensional nanostructures. This paper reviews the origin of the size-dependence of the elastic property of NWs and the factors influencing the discrepancies and inconsistencies in the measured values of the Young＇s modulus for the NW, besides the surface effects, nonlinear effects, the electromechanical coupling effects as a possible effect responsible for the differences in quantitative and qualitative performance of the measured Young＇s modulus for the NWs versus the diameter are clarified.

CALCULATION OF THE YOUNG'S MODULUS OF AN ADSORBED POLYMER LAYER

Polymer layers adsorbed to a surface or in a confined environment often change their mechanical properties. There is even the possibility of solidification of the confined layer. To judge the stiffness of such a layer, we used the Hertz model to calculate the Young＇s modulus of the polymer layer in the confinement of AFM experiments with silicon nitride tip with a radius of curvature ofR ≈ 50 nm and a glass sphere attached to the cantilever R =5 μm. Since there is no visible indentation of the layer in the AFM experiments, the layer is either penetrated very easily, or the indentation is too small to be seen in a force curve. The latter would be the case for a polymer layer with a Young＇s modulus above 4 × 10^8 Pa in case of an experiment with a silicon nitride tip and 4×10^5 Pa in case of a glass sphere.

Determination of reduced Young s modulus of thin films using indentation test

The flat cylindrical indentation tests with different sizes of punch radius were investigated using finite element method （FEM） aimed to reveal the effect of punch size on the indentation behavior of the film/substrate system. Based on the FEM results analysis, two methods was proposed to separate film＇s reduced Young＇s modulus from a film/substrate system. The first method was based on a new weight function that quantifies film＇s and substrate＇s contributions to the overall mechanical properties of the film/substrate system in the flat cylindrical indentation test. The second method, a numerical approach, including fitting and extrapolation procedures was put forward. Both of the results from the two methods showed a reasonable agreement with the one input FE model. At last, the effect of maximum indentation depth and the surface micro-roughness of the thin film on the reduced Young＇s modulus of the film/substrate system were discussed. The methods proposed in the present study provide some new conceptions on evaluating other properties of thin films, e.g. creep, for which a flat-ended punch is also employed.

The influence of nonparaxiality on the spectral behavior in Young's experiment illuminated by partially coherent light

Starting from the Rayleigh-Sommerfeld diffraction integral, this paper studies the spectral behavior in Young＇s experiment illuminated by nonparaxial partially coherent light and compares with the paraxial case, where the influence of nonparaxiality of partially coherent light on the spectral shifts and spectral switches is stressed. It is shown that there is a spectral shift in the nonparaxial case relative to the paraxial one and the critical position changes, at which the spectral switch occurs. The ratio of the waist width to the central wavelength ω0/λ0 and relative spatial correlation length △ affect the spectral difference. The smaller ω0/λ0 is, the larger the difference between the nonparaxial and paraxial results appears. The effect of relative spatial correlation length △ is relatively small.

Young＇s Modulus Enhancement and Measurement in CNT/Al Nanocomposites

Young＇s modulus is a critical parameter for designing lightweight structure, but Al and its alloys only demonstrate alimited value of 70-72 GPa. The introduction of carbon nanotubes （CNTs） is an effective way to make Al and its alloysstiffer. However, little research attention has been paid to Young＇s modulus of CNT/Al nanocomposites attributed to theuncertain measurement and unconvincing stiffening effect of CNTs. In this work, improved Young＇s modulus of 82.4 ± 0.4 GPa has been achieved in 1.5 wt% CNT/Al nanocomposite fabricated by flake powder metallurgy, which wasdetermined by resonance test and 13.5% higher than 72.6 ± 0.64 GPa of Al matrix. A comparative study and statisticalanalysis further revealed that Young＇s modulus determined by tensile test was relatively imprecise （83.1 ± 4.0 GPa） dueto the low-stress microplasficity or interface decohesion during tensile deformation of CNT/Al nanocomposite, while thevalue （98-100 GPa） was highly overestimated by nanoindentation due to the ＂pile-up＂ effect. This work shows an in-depthdiscussion on studying Young＇s modulus of CNT/Al nanocomposites.

An improved model for predicting effective Young's modulus of the twisted structure under cyclic loading:taking into account the untwisting effect

Twist structures have diverse applications, ranging from dragline, electrical cable, and intelligent structure. Among these applications, tension deformation can＇t be avoided during the fabrication and working processes, which often leads to the twist structure rotation （called untwisting effect） and twist pitch increasing. As a consequence, this untwisting behavior has a large effect on the effective Young＇s modulus. In this paper, we present an improved model based on the classical Costello＇s theory to predict the effective Young＇s modulus of the basic structure, twisted by three same copper strands under cyclic loading. Series of experiments were carried out to verify the present model taking into account the untwisting effect. The experimental results have better agreements with the presented model than the common Costello＇s model.

EXPERIMENTAL RESEARCHES ON MAGNETO-THERMO-MECHANICAL CHARACTERIZATION OF TERFENOL-D

The coupling effects of axial pre-stress, temperature and magnetic field on magne- tostrictive strain and magnetization as well as Young＇s modulus ofa Terfenol-D （Tbo.3Dyo.rFei.93） rod are tested to give a good understanding of magneto-thermal-mecha- nical characteristics of giant magnetostrictive materials. Results show that magneto-thermo-mechanical coupling of giant magnetostrictive materials is very strong; and the influences of pre-stress and temperature on magnetostrictive strain and Young＇s modulus vary with the intensity of magnetic field.

Design of a Biomimetic Skin for an Octopus-Inspired Robot - Part I： Characterising Octopus Skin

Octopus skin samples were tested under quasi-static and scissor cutting conditions to measure the in-plane material prop- erties and fracture toughness. Samples from all eight arms of one octopus were tested statically to investigate how properties vary from arm to arm. Another nine octopus skins were measured to study the influence of body mass on skin properties. In- fluence of specimen location on skin mechanical properties was also studied. Material properties of skin, i.e. the Young＇s modulus, ultimate stress, failure strain and fracture toughness have been plotted against the position of skin along the length of arm or body. Statistical studies were carried out to help analyzing experimental data obtained. Results of this work will be used as guidelines for the design and development of artificial skins for an octopus-inspired robot.

Compressive and energy absorption properties of closed-cell magnesium foams

The quasi-static compressive mechanical behavior and deformation mechanism of closed-cell magnesium foams were studied, and the ef- fects of the density of magnesium foams on the compressive and energy absorption properties were also discussed. The results show that the compressive process of closed-cell magnesium foams is characterized by three deformation stages： linear elastic stage, collapsing stage and densification stage. At the linear elastic stage, the peak compressive strength （t70） and Young＇s modulus （E0） increase as the density increases Magnesium foams can absorb energy at the collapsing stage. In a certain strain range, the energy absorption capacity also increases as the density of magnesium foams increases.

Mechanical Characterization of Electroplated Ni Films by Micro-tensile Testing

Mechanical properties of structural materials are particularly important for design, performance realization and reliability analysis of microelectromechanical systems （MEMS）. Furthermore, accurate database of mechanical properties at the micro scale can provide indispensable reference for establishing MEMS standard. Electroplated nickel film is one of the most favored structural materials used in MEMS, thus its mechanical properties has been studied for many years. However, the measured values show large scatter in Yotmg＇s modulus of nickel film. Young＇s modulus and yield stress of electroplated nickel film are measured by using a micro-tensile testing instrument. The tensile load applied on the specimen is measured by a load cell with accuracy 0.25 mN directly, without additional friction. Through measuring the axial stiffness coefficient of the tensile instnunent in situ, the tensile strain of the specimen is obtained by using two-serial spring model. The electroplated nickel films were fabricated from sulfarnate baths, and the gauge section is 500μm long and 10μm wide nominally, and thickness range between 25 μm and 50μm. The obtained Young＇s modulus from tensile testing is 83＋6 GPa for nickel specimens electroplated at current density of 20 mA/cm2 and it increases to 124＋5 GPa as current density is decreased to 10 mA/cm2. The phenomena are interpreted in terms of porosity of microstructure. The higher current density produced rnicrostucture with low density and high volume fraction of pores, and the microstructure of high porosity corresponds to a lower modulus. The measured values of Young＇s modulus are consistent with those of calculated from the exponential empirical formula between Young＇s modulus and porosity. The micro-tensile testing instrument can also be used for mechanical measurement of other MEMS films.

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes （SWCNT＇s） is established to describe the nonlinear stress-strain curve of SWCNT＇s and to predict both the elastic properties and breaking strain of SWCNT＇s during tensile deformation. An analysis based on the virtual internal bond （VIB） model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT＇s.

Surface-effects-dominated thermal and mechanical responses of zinc oxide nanobelts

t Molecular dynamics （MD） simulations are carried out to characterize the mechanical and thermal responses of [011^-1]-oriented ZnO nanobelts with lateral dimensions of 21.22A × 18.95 A, 31.02A× 29.42 A, and40.81A ×39.89A over the temperature range of 300-1000 K. The Young＇s modulus and thermal conductivity of the nanobelts are evaluated. Significant surface effects on properties due to the highsurface-to-volume ratios of the nanobelts are observed. For the mechanical response, surface-stress-induced internal stress plays an important role. For the thermal response, surface scattering of phonons dominates. Calculations show that the Young＇s modulus is higher than the corresponding value for bulk ZnO and decreases by -33% as the lateral dimensions increase from 21.22 A × 18.95A to 40.81 A × 39.89A. The thermal conductivity is one order of magnitude lower than the corresponding value for bulk ZnO single crystal and decreases with wire size. Specifically, the conductivity of the 21.22 A × 18.95 A belt is approximately （31-18）% lower than that of the 40.81 A × 39.89 A belt over the temperature range analyzed. A significant dependence of properties on temperature is also observed, with the Young＇s modulus decreasing on average by 12% and the conductivity decreasing by 50% as temperature increases from 300 K to 1000 K.

NANOMECHANICAL MAPPING OF CARBON BLACK REINFORCED NATURAL RUBBER BY ATOMIC FORCE MICROSCOPY

Atomic force microscopy （AFM） has the advantage of obtaining mechanical properties as well as topographic information at the same time. By analyzing force-distance curves measured over two-dimensional area using Hertzian contact mechanics, Young＇s modulus mapping was obtained with nanometer-scale resolution. Furthermore, the sample deformation by the force exerted was also estimated from the force-distance curve analyses. We could thus reconstruct a real topographic image by incorporating apparent topographic image with deformation image. We applied this method to carbon black reinforced natural rubber to obtain Young＇s modulus distribution image together with reconstructed real topographic image. Then we were able to recognize three regions; rubber matrix, carbon black （or bound rubber） and intermediate regions. Though the existence of these regions had been investigated by pulsed nuclear magnetic resonance, this paper would be the first to report on the quantitative evaluation of the interfacial region in real space.

Necessary and Sufficient Conditions of Doubly Weighted Hardy-Littlewood-Sobolev Inequality

Using product and convolution theorems on Lorentz spaces, we characterize the sufficient and necessary conditions which ensure the validity of the doubly weighted Hardy-Littlewood-Sobolev inequality. It should be pointed out that we con- sider whole ranges of p and q, i.e., 0 〈 p ≤∞ and 0 〈 q ≤∞.

Vibration analysis of foam plates based on cell volume distribution

In this paper, vibration analysis of irregular-closed-cell foam plates is per- formed. A cell volume distribution coefficient is introduced to modify the original Gibson- Ashby equations of effective Young＇s modulus of foam materials. A Burr distribution is imported to describe the cell volume distribution situation. Three Burr distribution pa- rameters are obtained and related to the cell volume range and the diversity. Based on the plate theory and the effective modulus theory, the natural frequency of foam plates is calculated with the change of the cell volume distribution parameters. The relationship between the frequencies and the cell volumes are derived. The scale factor of the average cell size is introduced and proved to be an important factor to the performance of the foam plate. The result is shown by the existing theory of size effects. It is determined that the cell volume distribution has an impact on the natural frequency of the plate structure based on the cell volume range, the diversity, and the average size, and the impact can lead to optimization of the synthesis procedure.

Coronal multi-walled silicon nanotubes

By means of first-principles density functional theory （DFT） calculations and molecular dynamics （MD） simulations, a series of coronal multi- walled silicon nanotubes （MWSiNTs） without or with hydrogen terminations are systematically identified. Notably, coronal MWSiNTs, where the interaction between the walls is preferable through covalent bonds rather than weak interaction, show better stability than CNT-like SiNTs. Moreover, they exhibit good elasticity with small Young＇s modulus. The investigation of the electronic structure demonstrates that they present metallic characteristics, which is in striking contrast to bulk silicon. Thus, the MWSiNTs may find important applications in electronic devices.

(L^p, L^q)-Boundedness of Hausdorff Operators with Power Weight on Euclidean Spaces

In this paper, we prove the （L^p, L^q）-boundedness of （fractional） Hausdorff operators with power weight on Euclidean spaces. As special cases, we can obtain some well known results about Hardy operators.

Characterization of FeCo Nanoparticles Reinforced Natural Rubber using Nanomechanical Mapping

The morphology, nanomechanical properties and interfacial regions of natural rubber（NR） and FeCo nanoparticles composite were determined by AFM nanomechanical mapping. The results showed that the size of FeCo particles was mostly from 40 to 100 nm and the FeCo nanoparticles were homogeneously dispersed in the NR bulk. The strength of NR composite increased with the FeCo nanoparticles loading. Young＇s modulus of NR region, FeCo region and interfacial region was measured by AFM nanomechanical tapping as 1.6 ± 0.6, 16.7 ±4.2 and 5.8 ± 1.5 MPa, respectively. The width of the interface for NR5, NR10 and NR15 was determined to be 15±8.1, 26±14.3 and 32±16.4 nm, respectively.

Young's modulus determination of low-k porous films by wide-band DCC/LD LSAW

Low-k interconnection is one of the key concepts in the development of high-speed ultra-large-scale integrated（ULSI） circuits.To determine the Young＇s modulus of ultra thin,low hardness and fragile low-k porous films more accurately,a wideband differential confocal configured laser detected and laser-generated surface acoustic wave（DCC/LD LSAW） detection system is developed.Based on the light deflection sensitivity detection principle, with a novel differential confocal configuration,this DCC/LD LSAW system extends the traditional laser generated surface acoustic wave（LSAW） detection system＇s working frequency band,making the detected SAW signals less affected by the hard substrate and providing more information about the thin porous low-k film under test.Thus it has the ability to obtain more accurate measurement results.Its detecting principle is explained and a sample of porous silica film on Si（100） is tested.A procedure of fitting an experimental SAW dispersion curve with theoretical dispersion curves was carried out in the high frequency band newly achieved by the DCC/LD LSAW system.A comparison of the measurement results of the DCC/LD LSAW with those from the traditional LSAW shows that this newly developed DCC/LD LSAW can dramatically improve the Young＇s modulus measuring accuracy of such porous low-k films.