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size effects of effective young's modulus for periodic cellular materials

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science China(Physics,Mechanics & Astronomy) 2009年第8期52卷 1262-1270页

作者： DAI GaoMing ZHANG WeiHong Engineering simulation and Aerospace Computing Key Laboratory of Contemporary Design&Integrated Manufacturing TechnologyNorthwestern Polytechnical UniversityXi’an 710072China

With the wide demands of cellular materials applications in aerospace and civil engineering,research effort sacrificed for this type of materials attains nowadays a higher level than ever *** paper is focused on the prediction methods of effective young's modulus for periodical cellular *** on comprehensive studies of the existing homogenization method(HM),the G-A meso-mechanics method(G-A MMM) and the stretching energy method(sEM) that are unable to reflect the size effect,we propose the bending energy method(BEM) for the first time,and a comparative study of these four methods is further made to show the generality and the capability of capturing the size effect of the BEM ***,the underlying characteristics of each method and their relations are *** do this,the detailed finite element computing and existing experimental results of hexagonal honeycombs from the literature are adopted as the standard of comparison for the above four *** and bending models of periodical cellular materials are taken into account,respectively for the comparison of stretch and flexural displacements resulting from the above *** conclude that the BEM has the strong ability of both predicting the effective young's modulus and revealing the size *** a method is also able to predict well the variations of structural displacements in terms of the cell size under stretching and bending loads including the non-monotonous variations for the hexagonal *** the contrary,other three methods can only predict the limited results whenever the cell size tends to be infinitely small.

关键词： periodic cellular materials effective young’s modulus size effect bending energy method homogenization method G-A mesomechanics method stretching energy method

Is a nanorod (or nanotube) with a lower young’s modulus stiffer? Is not young’s modulus a stiffness indicator?

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science China(Physics,Mechanics & Astronomy) 2010年第4期53卷 712-724页

作者： Lim C. W. Department of Building and Construction City University of Hong Kong

It has been a known fact in classical mechanics of materials that young’s modulus is an indicator of material stiffness and materials with a higher young’s modulus are stiffer. At the nanoscale, within the scope and under specific circumstances described in this paper, however, a nanorod (or a nanotube) with a smaller young’s modulus (smaller stress-strain rate) is stiffer. In such a scenario, young’s modulus is not a stiffness indicator for nanostructures. Furthermore, the nonlocal stress-strain rate is dependent on types of load, boundary conditions and location. This is likely to be one of the many possible reasons why numerous experiments in the past obtained significantly varying values of young’s modulus for a seemingly identical nanotube, i.e. because the types of loading and/or boundary conditions in the experiments were different, as well as at which point the property was measured. Based on the nonlocal elasticity theory and within the scope of material and geometric linearity, this paper reports the strange and hitherto unrealized effect that a nanorod (or a nanotube) with a lower young’s modulus (smaller stress-strain rate) indicates smaller extension in tensile analysis. similarly, it is also predicted that a nanorod (or a nanotube) with a lower young’s modulus results in smaller bending deflection, higher critical buckling load, higher free vibration frequency and higher wave propagation velocity, which are at all consequences of a stiffer nanostructure.

关键词： nanorod nanotube nonlocal stress nonlocal elasticity stiffness tensile young’s modulus

The young's moduli prediction of random distributed short-fiber-reinforced polypropylene foams using finite element method

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science China(Technological sciences) 2009年第1期52卷 72-78页

作者： WANG Bo1, WANG RongXiu2 & WU Yong1 1 school of Mathematic science, Chongqing Institute of Technology, Chongqing 400050, China 2 Department of Computer science and Information Engineering, Chongqing Technology and Business University, Chongqing 400067, China school of Mathematic science Chongqing Institute of Technology Chongqing China Department of Computer science and Information Engineering Chongqing Technology and Business University Chongqing China

The elastic moduli of short-fiber-reinforced foams depend critically on the fiber content and fiber length, as well as on the fiber orientation distribution. Based on periodic tetrakaidecahedrons, the finite element models with short-fiber reinforcement were proposed in this paper to examine the effects of the fiber content and fiber length on young's modulus. The fiber length distribution and fiber orientation distribution were also considered. The proposed models featured in a three-dimensional diorama with random short-fiber distribution within or on the surfaces of the walls and edges of the closed-cells of polypropylene (PP) foams. The fiber length/orientation distributions were modeled by Gaussian prob-ability density functions. Different fiber volume fractions, different lengths, and different distributions were investigated. The predicted young's moduli of the PP foams with short-glass-fiber or short-carbon-fiber reinforcement were compared with other theoretic and experimental results, and the agreement was found to be satisfactory. The proposed finite element models were proved to be acceptable to predict the young's moduli of the grafted closed-cell PP foams with short-fiber reinforcement.

关键词： short-fiber reinforcement young’s modulus finite element Gaussian distribution

Biodegradation of Polymethylmethacrylate Bone Cement May Not Be a serious Issue in Total Hip Arthroplasty—Retrieval study for Knoop Hardness and young’s Modulus

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Open Journal of Orthopedics 2013年第6期3卷 269-277页

作者： Masaaki Maruyama William N. Capello Department of Orthopaedic surgery Indiana University Medical Center Clinical Building Suite Indianapolis USA Department of Orthopaedic surgery Shinonoi General Hospital Nagano Japan Department of Orthopaedic surgery Shinonoi General Hospital Nagano Japan.

Introduction: To investigate a long-term in vivo deterioration of polymethylmethacrylate (PMMA) bone cement over time, we evaluated retrieved PMMA cement in terms of chemical elements presenting in the cement using energy dispersive analysis of X-rays;Knoop hardness;and the young’s modulus using scanning acoustic microscopy. Materials and Methods: For mechanical evaluation, we could neglect the influences of entrapped air bubbles or blood by the use of small specimens. The study was based on thirteen cement samples (six used in the acetabulum and seven in the femur) derived from eight patients (age at revision surgery: mean 72.5, range 68 to 79). All of these samples were simplex-P?cement. They were functioning well at least ten years after the previous surgery. Duration until revision surgery was ranged 12 to 25 years (average, 17.4 years). The reason for revision was aseptic mechanical loosening. Twenty samples of simplex-Preg;cement were served by manually mixing as a control. Results: The average of the hardness of the cement was 17.0 ± 1.2 (range, 13.4-20.6). In the control, the hardness was 17.8 ± 1.5 (range, 14.0-24.6). There was no significant difference between these values. The mean of young’s modulus of the cement was 5.61 ± 0.19 GPa (range, 5.09-6.10). In the control, the modulus was 6.04 ± 0.13 GPa (range, 5.68-6.45). Although the modulus was significantly less than that of the control, there was only 7% decrease in average between twelve and twenty-five years in vivo. Conclusions: Our results suggest that long-term implantation and functional loading in vivo may not be the limiting factor in the mechanical integrity of the bone cement.

关键词： Polymethylmethacrylate Bone Cement Biodegradation Total Hip Arthroplasty Retrieval study Knoop Hardness young’s Modulus

Vibration of Gold Nano-Beam with Variable young’s Modulus Due to Thermal shock

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World Journal of Nano science and Engineering 2015年第4期5卷 194-203页

作者： Eman A. N. Al-Lehaibi Hamdy M. Youssef Mathematics Department College of Science and Arts-Sharoura Najran University Najran KSA Mechanics Department Faculty of Engineering Umm Al-Qura University Makkah KSA

In this paper, we will study the most important effects in the nano-scale resonator: the coupling effect of temperature and strain rate, and the non-Fourier effect in heat conduction. A solution for the generalized thermoelastic vibration of nano-resonator induced by thermal loading has been developed. The young’s modulus is taken as a linear function of the reference temperature. The effects of the thermal loading and the reference temperature in all the studied fields have been studied and represented in graphs with some comparisons. The young’s modulus makes significant effects on all the studied fields where the values of the temperature, the vibration of the deflection, stress, displacement, strain, stress-strain energy increase when the young’s modulus has taken to be variable.

关键词： Thermoelasticity Euler-Bernoulli Equation Goldnano-Beam young’s Modulus

Macroscopic young’s Elastic Modulus Model of Particle Packing Rock Layers

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Open Journal of Geology 2012年第3期2卷 198-202页

作者： Cheng-Yao Guan Jia-Fu Qi Nan-sheng Qiu Guo-Chun Zhao Qiao Yang Xiang-Dong Bai Chao Wang Institute of Disaster Prevention Sanhe China state Key Laboratory of Petroleum Resources and Prospecting China University of Petroleum Beijing China The College of Geosciences and Resources China University of Geosciences Beijing China

Based on the Hertzian granular contact mechanics model, the paper built up a Macroscopic young’s Elastic Modulus of particle/granular packing rock layers, and built up a ties to connecting young’s Elastic Modulus of sand particle in Meso and the Macroscopic young’s Modulus of granular packing rock layers. The Macroscopic young’s Modulus of granular packing rock layers is far less than the young’s Modulus of sand particle. The Macroscopic young’s Modulus of granular packing rock layers is proportioned to the powers of 1/3 of the vertical contact force of sand particles. The Macroscopic young’s Modulus is inversely proportional to particle diameter. The paper calculated the vertical contact force of five types aligning mode of the particles. When equal stress, the increased of the coordination number lead to the decrease of the contact force fn, this lead to the coordination number is an inverse proportion to Macroscopic young’s Modulus. But the larger coordination number change only means very little Macroscopic young’s Modulus change.

关键词： Particle Contact Macroscopic young’s Modulus Arrangements of Particle

Nanoindentation of circular multilayer graphene allotropes

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science China(Technological sciences) 2019年第2期62卷 269-275页

作者： HUO ZhanLei GUO ZhengRong LENG JianTao CHANG TienChong shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai University

Nanoindentaion has been proposed as an efficient technique to measure mechanical single-layer two-dimensional(2D) materials via combining the membrane theory with the indentation data. However, for multilayered structures of 2D materials, significant discrepancy exists between the young's modulus obtained from the existing membrane model and those from other *** we develop a multilayer indentation model by taking the multilayer effect into account in the previous membrane *** show that the present model can accurately predict the young's modulus of multilayered 2D carbon materials. For few layer graphene and twin graphene structures, the deviation of the young's moduli obtained by the present model are both within a reasonable range, while the error caused by the direct use of the previous single-layer membrane model increases with the number of layers. The present model provides an efficient tool to extract the mechanical properties of 2D materials from the nanoindentation data of their multilayered structures.

关键词： nanoindentaion two-dimensional materials young’s modulus molecular dynamics

The properties of N-doped diamond-like carbon films prepared by helicon wave plasma chemical vapor deposition

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Plasma science and Technology 2019年第2期21卷 78-82页

作者：陈佳丽季佩宇金成刚诸葛兰剑吴雪梅 school of Physical science and Technology Soochow University school of Physical science and Technology Jiangsu Key Laboratory of Thin FilmsSoochow University state Key Laboratory for strength and Vibration of Mechanical structures Xi'an Jiaotong University Analysis and Testing Center Soochow University

In this paper, N-doped diamond-like carbon(DLC) films were deposited on silicon substrates by using helicon wave plasma chemical vapor deposition(HWP-CVD) with the Ar/CH_4/N_2 mixed gas. The surface morphology, structural and mechanical properties of the N-doped DLC films were investigated in detail by scanning electron microscopy(sEM), x-ray photoelectron spectroscopy(XPs), Raman spectra, and atomic force microscopy(AFM). It can be observed from sEM images that surface morphology of the films become compact and uniform due to the incorporation of N. The maximum of the deposition rate of the films is 143 nm min^(-1), which is related to the high plasma density. The results of XPs show that the N incorporates in the films and the C-C sp^3 bond content increases firstly up to the maximum(20%) at 10 sccm of N_2 flow rate, and then decreases with further increase in the N_2 flow rate. The maximum young's modulus of the films is obtained by the doping of N and reaches 80 GPa at 10 sccm of N_2 flow rate, which is measured by AFM in the scanning probe microscope mode. Meanwhile, friction characteristic of the N-doped DLC films reaches a minimum value of 0.010.

关键词： N-doped DLC helicon wave plasma young’s modulus friction coefficient

surface segregation of hydrogen in free-standing Pd-H alloy nanofilms

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science China(Technological sciences) 2019年第10期62卷 1735-1746页

作者： CAI Hong MAI JiaWei GAO YingXin HUANG He sUN sheng ZHANG TongYi Materials Genome Institute Shanghai University

The interaction between mechanics and chemistry plays an essential and critical role in the behaviors and properties of materials,especially in nanoscale alloys. Based on the classical Gibbs and Mc Lean adsorption isotherms, the present study takes the freestanding nanometer thick films of Pd-H solid solutions as a typic example to investigate surface segregation of hydrogen. The surface eigenstress model is further developed here to give analytic formulas, which have the capability to quantitatively predict the size-dependent surface segregation. Molecular dynamics(MD) simulations are conducted on free-standing Pd-H *** MD simulations verify the theoretical analytic results and determine the values of parameters involved in the theoretical analysis. The integrated theoretical and numerical study exhibits that both surface excess H concentration and apparent biaxial young’s modulus of Pd-H thin films depend on the nominal H concentration and the film thickness. The MD simulations determine the values of three parameters involved in the theoretical analysis. Especially, the parameter of the differentiation in reference chemical potential behaves like the molar free energy of segregation in the Mc Lean adsorption isotherm.

关键词： palladium-hydrogen nanofilms the biaxial young’s modulus concentration