A New Elasticity and Finite Element Formulation for Different Young's Modulus When Tension and Compression Loadings

This paper presents a new elasticity and finite element formulation for different Young's modulus when tension and compression loadings in anisotropy media. The case studies, such as anisotropy and isotropy, were investigated. A numerical example was shown to find out the changes of neutral axis at the pure bending beams.

NANOINDENTATION OF THIN-FILM-SUBSTRATE SYSTEM DETERMINATION OF FILM HARDNESS AND YOUNG'S MODULUS

In the present paper,the hardness and Young's modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models.Aluminum film and two kinds of substrates,i.e.glass and silicon,are studied.Nanoindentation XP Ⅱ and continuous stiffness mode are used during the experiments.In order to avoid the influence of the Oliver and Pharr method used in the experiments,the experiment data are analyzed with the constant Young's modulus assumption and the equal hardness assumption.The volume fraction model(CZ model)proposed by Fabes et al.(1992)is used and modified to analyze the measured hardness.The method proposed by Doerner and Nix(DN formula)(1986)is modified to analyze the measured Young's modulus.Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature,which include the results of two kinds of systems,i.e.,a soft film on a hard substrate and a hard film on a soft substrate.In the modified CZ model,the indentation influence angle,(?), is considered as a relevant physical parameter,which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.

An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach.The confining stress,whose effect on the equivalent elastic modulus is of great importance,is the fundamental stress environment of natural rock masses.This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures(RDFs)or regular fracture sets(RFSs)while considering the confining stress.The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures,but also the geometrical structure of the fractures and the confining stress.The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code(3DEC),leading to a reasonably good agreement.The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress,i.e.it is characterized by stress-dependency.Further,a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach,i.e.the extended Fourier amplitude sensitivity test(EFAST).The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated.The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

EXPERIMENTAL EVALUATION ON MODULUS OF EQUIVALENT HOMOGENEOUS ETTRINGITE

In the present study, the average modulus of delayed ettringite is evaluated by an experimental method combined with theoretical analysis. Firstly, the delayed ettringite crystal is synthesized by chemical reaction of Aluminum sulfate and calcium hydroxide. Secondly, specimens are obtained by compressing the delayed ettringite crystal under different pre-loads. Thirdly, the variation of the modulus of the specimen with different pre-loads is tested using Instron material test machine and the SHPB technique, respectively. It is found that the experimental data may be suitably fitted by Boltzmann Function. Finally, the porosity of the specimen is detected using the saturation method, and the effect of the porosity on the modulus is analyzed by the Eshelby＇s equivalent inclusion method and the Mori-Tanaka＇s scheme. The static and dynamic modulli of the equivalent homogeneous ettringite obtained in present study are approximately 10.64 GPa and 24.61 GPa, respectively.

Influence of random shrinkage porosity on equivalent elastic modulus of casting： A statistical and numerical approach

Shrinkage porosity is a type of random distribution defects and exists in most large castings. Different from the periodic symmetry defects or certain distribution defects, shrinkage porosity presents a random "cloud-like" configuration, which brings difficulties in quantifying the effective performance of defected casting. In this paper, the influences of random shrinkage porosity on the equivalent elastic modulus of QT400-18 casting were studied by a numerical statistics approach. An improved random algorithm was applied into the lattice model to simulate the "cloud-like" morphology of shrinkage porosity. Then, a large number of numerical samples containing random levels of shrinkage were generated by the proposed algorithm. The stress concentration factor and equivalent elastic modulus of these numerical samples were calculated. Based on a statistical approach, the effects of shrinkage porosity's distribution characteristics, such as area fraction, shape, and relative location on the casting's equivalent mechanical properties were discussed respectively. It is shown that the approach with randomly distributed defects has better predictive capabilities than traditional methods. The following conclusions can be drawn from the statistical simulations:(1) the effective modulus decreases remarkably if the shrinkage porosity percent is greater than 1.5%;(2) the average Stress Concentration Factor(SCF) produced by shrinkage porosity is about 2.0;(3) the defect's length across the loading direction plays a more important role in the effective modulus than the length along the loading direction;(4) the surface defect perpendicular to loading direction reduces the mean modulus about 1.5% more than a defect of other position.

EFFECT OF DISPERSION OF MICA IN MATRIX ON YOUNG'S MODULUS OF MICA FILLED POLYETHYLENE

The correlation between Young's modulus of mica-filled high density polyethylene (HDPE), low density polyethylene(LDPE) and the state of dispersion of plasma-treated mica in the polymer matrices was studied. The modulus and the number average diameter of mica aggregates in matrix were determined with tensile testing and image analysis respectively. The interface structure of the filler/matrix and the bulk structure of matrix were examined through the dielectric spectrometry, differential scanning calorimetry (DSC) and dynamic viscoelastic spectrometry. The results show that the Young's modulus of the filial polyethylene depends to a great extent upon the state of dispersion of filler in matrix, but it is independent of the interface structure and bulk structure. The better the dispersion, the higher the Young's modulus.

THE DETERMINATION OF AN EQUIVALENT ELASTIC MODULUS FOR BODIES WITH CRACKS BY BOUNDARY ELEMENT METHOD

The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The Influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.

Anomalies in Young's modulus behavior after annealing in polycrystalline SmS

In this paper,the dependencies of Young's modulus and attenuation decrement on samarium sulfide polycrystals(SmS)under various annealing temperatures are studied by the piezoelectric ultrasonic composite oscillator technique at a frequency of 100 kHz in the temperature range of 80-300 K.A decrease in Young's modulus with an increase of the annealing temperature due to the texturing of the material was revealed.At the same time,attenuation peaks were observed at temperatures about 90 and 125 K,presumably due to Niblett-Wilks and Bordoni relaxations.

Method to analyze wrinkled membranes with zero shear modulus and equivalent stiffness

To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to the previous method (Method I) of local coordinate transposition and stiffness equivalence.The new method is derived and the feasibility is theoretically proved.A small-scale membrane structure is analyzed by the two methods,and the results show that the computational efficiency of the new method (Method II) is approximately 23 times that of Method I.When Method II is applied to a large-scale membrane stadium structure,it is found that this new method can quickly make the second principal stress of one way wrinkled elements zero,and make the two principal stresses of two-way wrinkled elements zero as well.It could attain the correct load responses right after the appearance of wrinkled elements,which indicates that Method II can be applied to wrinkling analysis of large-scale membrane structures.

不同弹性模量计算机辅助设计和计算机辅助制造桩核材料的应力分析

背景:桩核修复是牙体缺损修复的一种常规选择,然而不同桩核材料的修复效果存在差异。目的:利用有限元方法评估不同弹性模量桩核修复模型中桩核与牙根黏结剂部位的应力分布情况。方法:在三维建模软件中构建一个三维根管治疗过的上颌中切牙模型,进行全瓷冠修复,修复中的桩核材料分别使用纳米陶瓷树脂(弹性模量12.8 GPa)、复合树脂(弹性模量16 GPa)、混合陶瓷(弹性模量34.7 GPa)、玻璃陶瓷(弹性模量95 GPa)、钛合金(弹性模量112 GPa)和氧化锆(弹性模量209.3 GPa),将模型约束在皮质骨中,在中切牙牙冠舌侧1/3处加载与牙体长轴呈45°的100 N集中力,通过最大主应力分析修复模型中桩核、牙本质及桩与牙根黏结剂的应力分布。结果与结论:(1)当使用弹性模量较高的桩核材料时,修复模型中的桩核应力较集中;当使用弹性模量接近牙本质的桩核材料(纳米陶瓷树脂和复合树脂)时,桩核的应力分布较均匀;无论桩核材料如何,各修复模型中牙本质上的应力分布相似;使用弹性模量更高的桩核时,修复模型中桩与牙根黏结剂处显示出更多的应力集中。(2)纳米陶瓷树脂模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为31.00,33.21,0.51 MPa,复合树脂模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为36.84,33.14,0.59 MPa,混合陶瓷模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为64.05,32.83,1.00 MPa,玻璃陶瓷模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为112.30,32.69,1.73 MPa,钛合金模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为120.00,32.17,1.86 MPa,氧化锆模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为148.80,31.85,2.28 MPa。(3)桩核材料的弹性模量越高,进行桩核修复时桩核处的最大应力值越大,桩核材料弹性模量对修复模型中桩与牙根黏结剂处与牙本质的最大应力值无明显影响。

Equivalence between Modulus of Smoothness and K-Functional on Rotation Group SO(3)

In this paper we obtain the equivalence between modulus of smoothness and K-functional on rotation group SO(3).

(<i>f</i>, <i>p</i>)-Asymptotically Lacunary Equivalent Sequences with Respect to the Ideal <i>I</i>

In this study, we define (f, p)-Asymptotically Lacunary Equivalent Sequences with respect to the ideal I using a non-trivial ideal , a lacunary sequence , a strictly positive sequence , and a modulus function f, and obtain some revelent connections between these notions.

基于SLM成型钛合金多孔结构的设计分析

针对目前市场上广泛应用的钛合金(TC4)植入假体多为实心假体,其重量过大,同时弹性模量较高容易引起应力遮挡及应力集中等问题,设计了六面体、正八面体、棱形十二面体及衍生十二面体4种变参数钛合金多孔结构,通过SLM技术成型多孔结构验证其力学性能。结果表明,孔隙率对结构力学性能影响较大,孔隙率越低,其结构整体更趋近于各向同性,越接近仿真所得结果。结合断口观察,4种结构都近似呈45°剪切破坏,属于塑性断裂。

不同增强方向的带支柱体心立方点阵及其填充结构的压缩力学性能分析

为研究不同增强方向的带支柱体心立方点阵及其填充结构的压缩力学性能,制备了硅橡胶填充点阵结构试验件。通过试验和仿真方法研究了硅橡胶填充BCC1或BCC2(加载方向分别与带支柱体心立方点阵的支柱杆方向相同或垂直)两种点阵结构的压缩力学性能,并采用铁摩辛柯梁理论和极限载荷法分析了两种点阵结构的等效弹性模量和压缩平台应力。结果表明:提出的理论模型能够很好地预测两种点阵结构的等效弹性模量和压缩平台应力。经过填充后两种点阵结构的压缩强度和吸能性能均会得到增强,BCC2结构的增强效果更加显著。对于BCC1点阵结构,填充提高了其内部杆件的承载力;而对于BCC2点阵结构,填充减小了其“V”形剪切带附近的杆件弯曲变形。随着点阵结构半径的增大,两种结构的吸能耦合因子均先增大后减小,而BCC1型结构的吸能耦合因子变化更明显。

循环剪切作用下土工袋组合体动力特性试验研究

土工袋具有承载力高、阻尼大、造价低等诸多优点,是一种适用于村镇地区中、低层房屋的减/隔震材料。通过开展室内循环剪切试验对土工袋组合体的剪切应力⁃剪切应变关系、动力特性参数以及抗剪强度进行分析讨论,探究不同竖向应力与剪切应变幅值条件下土工袋组合体动剪切模量与等效阻尼比的变化规律,同时研究了循环次数对土工袋组合体动力特性参数以及抗剪强度参数的影响。试验结果表明:在小变形情况下,土工袋组合体的峰值剪切应力和动剪切模量随着循环次数的增加而逐渐增大,等效阻尼比则随着循环次数的增加而逐渐减小;在大变形情况下,土工袋组合体发生层间滑移并出现界面软化现象,此时的峰值剪切应力(抗剪强度)随着循环次数的增加而逐渐减小,动力特性参数随循环次数的变化与小变形情况下完全相反。随着循环次数的增加,土工袋组合体的抗剪强度参数似摩擦角逐渐减小,似黏聚力逐渐增大并趋于稳定。在剪切应变幅值较大的情况下,土工袋组合体通过袋内土体的剪切变形以及土工袋层间滑移产生摩擦耗能,具有较好的减振消能效果。

滨海砂路基结构强度控制研究

为实现滨海砂利用率最大化,针对路基结构强度设计指标要求,采用层状弹性体系理论对两侧包边、上覆改良层的滨海砂填芯路基结构强度进行了研究。明确了砂芯模量、改良层模量及改良层厚度对路基结构顶面回弹模量的影响;提出了路基结构强度控制设计理念和技术。室内外试验结果显示,滨海砂材料的CBR强度随着压实度的提高而增长;经压实后的滨海砂满足公路路基对路基填料CBR值的要求,但滨海砂级配不良、黏聚力低,其单纯滨海砂结构表层无法满足路基结构回弹弯沉指标的要求,因此采取双侧包边和上覆改良层结构可充分发挥滨海砂芯的材料强度性能并满足路基结构回弹模量的强度要求。结果表明:路基顶面当量回弹模量分别与滨海砂自身回弹模量、改良层回弹模量及改善层厚度显著相关,由此建立了多元非线性回归经验公式,获取的路基顶当量回弹模量经验解与层状体系结构的理论解相近;经验公式的提出为改良层的材料选择和厚度优化提供了精准、便捷的计算工具,从而有效实现了对路基结构强度的合理控制,为滨海砂在滨海公路建设中的大量利用、降低建设成本、保护生态环境奠定了可靠的理论支撑。

沥青混合料动态模量预测模型研究

通过室内试验,并结合时温等效原理,预测更大频率(温度)范围的动态模量值.室内试验中,利用动态剪切流变仪(DSR)对90#基质沥青、SBS改性沥青以及EVA改性沥青进行频率扫描试验,得到不同温度和频率下的动态剪切模量值|G\+|.对这三种沥青的不同级配的沥青混合料进行动态模量试验得到|E\+|,并结合Williams-Landel-Ferry(WLF)方程与Sigmoid函数得到其动态模量主曲线.基于试验数据评价Hirsch模型、人工神经网络模型的预测能力,发现Hirsch模型预测能力较低,并对其做出优化,结果表明:修正后的Hirsch模型预测能力进一步提升.相比经验模型,人工神经网络模型的预测精度较高.

索道用钢丝绳轴向弹性模量有限元仿真研究

轴向弹性模量是索道用钢丝绳重要的力学特性,影响着索道设计中对钢丝绳的选用。应用微分几何理论推导每根钢丝的中心线参数方程,通过Creo建立一个捻距长度的钢丝绳三维模型,将三维模型文件导入Hypermesh中划分网格、设置边界条件,最后利用Abaqus计算得到不同轴向拉力下钢丝绳的变形与等效应力云图,得出钢丝绳拉力与等效弹性模量的关系。结果表明,在拉力较小时,钢丝绳等效弹性模量随拉力增大而增大,当拉力到达一定值后,等效弹性模量稳定在钢丝材料弹性模量的0.64倍。

Photoacoustic elastography based on laser-excited shear wave

Elastography can be used as a diagnostic method for quantitative characterization of tissue hardness information and thus,differential changes in pathophysiological states of tissues.In this study,we propose a new method for shear wave elastography(SWE)based on laser-excited shear wave,called photoacoustic shear wave elastography(PASWE),which combines photoacoustic(PA)technology with ultrafast ultrasound imaging.By using a focused laser to excite shear waves and ultrafast ultrasonic imaging for detection,high-frequency excitation of shear waves and noncontact elastic imaging can be realized.The laser can stimulate the tissue with the light absorption characteristic to produce the thermal expansion,thus producing the shear wave.The frequency of shear wave induced by laser is higher and the frequency band is wider.By tracking the propagation of shear wave,Young’s modulus of tissue is reconstructed in the whole shear wave propagation region to further evaluate the elastic information of tissue.The feasibility of the method is verified by experiments.Compared with the experimental results of supersonic shear imaging(SSI),it is proved that the method can be used for quantitative elastic imaging of the phantoms.In addition,compared with the SSI method,this method can realize the noncontact excitation of the shear wave,and the frequency of the shear wave excited by the laser is higher than that of the acoustic radiation force(ARF),so the spatial resolution is higher.Compared to the traditional PA elastic imaging method,this method can obtain a larger imaging depth under the premise of ensuring the imaging resolution,and it has potential application value in the clinical diagnosis of diseases requiring noncontact quantitative elasticity.

共固化穿孔纤维增强阻尼薄膜结构面内力学性能研究

共固化穿孔纤维增强阻尼薄膜结构(CCPFRDFE)是一种大阻尼、高层间结合性能的新型阻尼处理模式,在空天技术、尖端武器、快速交通等领域具有广阔的应用前景。但复杂的结构为其力学性能的研究增加了难度,未知的力学性能限制了该新结构的开发与应用。介绍了CCPFRDFE的制作工艺,建立了CCPFRDFE有限元模型,并搭建实验平台对有限元模型进行了验证。利用有限元模型,分别研究了纤维增强阻尼层穿孔孔径、孔距和阻尼材料厚度对CCPFRDFE面内等效弹性参数的影响规律。结果表明,增加穿孔孔径、减小孔距、增加阻尼层厚度有利于提高CCPFRDFE面内等效剪切模量,但不利于提高面内等效弹性模量。所得结果将为非连续阻尼薄复合材料的振动特性研究与大挠度设计奠定基础。