Modeling and prediction of bulk properties of open-cell carbon foam

The emerging ultralightweight material, carbon foam, was modeled with three-dimensional microstructures to develop a basic understanding in correlating microstructural configuration with bulk performance of open-cell foam materials. Because of the randomness and complexity of the microstructure of the carbon foam, representative cell ligaments were first characterized in detail at the microstructural level. The salient microstructural characteristics (or properties) were then correlated with the bulk properties through the present model. In order to implement the varying anisotropic nature of material properties in the foam ligaments, we made an attempt to use a finite element method to implement such variation along the ligaments as well as at a nodal point where the ligaments meet. The model was expected to provide a basis for establishing a process-property relationship and optimizing foam properties.The present model yielded a fairly reasonable prediction of the effective bulk properties of the foams. We observed that the effective elastic properties of the foams were dominated by the bending mode associated with shear deformation. The effective Young's modulus of the foam was strongly influenced by the ligament moduli, but was not influenced by the ligament Poisson's ratio. The effective Poisson's ratio of the foam was practically independent of the ligament Young's modulus, but dependent on the ligament Poisson's ratio. The effective Young's modulus of the carbon foam was dependent more on the transverse Young's modulus and the shear moduli of the foam ligaments, but less significantly on the ligament longitudinal Young's modulus. A parametric study indicated that the effective Young's modulus was significantly improved by increasing the solid modulus in the middle of the foam ligaments, but nearly invariant with that at the nodal point where the ligaments meet. Therefore, appropriate processing schemes toward improving the transverse and shear properties of the foam ligaments in the middle section of the ligaments rather than at the nodal points are highly desirable for enhancing the bulk moduli of the carbon foam.     

胞体椭球比对泡沫塑料力学性能的影响

本文通过数值法研究了胞体椭球比对材料模量及泊松比的影响；在单向受力情况下，研究了变形对材料孔隙度、椭球比、杨氏模量和泊松比等材料参数的影响。     

复合材料模量细观分析的一般性模型

基于细观力学理论,提出了横观各向异性复合材料弹性常数的分析模型,并给出了纵向(纤维长度方向) 与横向弹性模量、横截面内剪切模量和泊松比等材料性能参数的理论推导和计算公式. 此方法简洁准确地反映了材料横观各向异性性能,改进了常规细观力学模型,也为工程分析提供了理论依据;同时在复合材料力学课程教学中,有助于深化学生对复合材料细观分析的理解,具有一定的启发性.     

Effective elastic properties of porous materials: Homogenization schemes vs experimental data

In this paper, we focus on the prediction of elastic moduli of isotropic porous materials made of a solid matrix having a Poisson's ratio vm of 0.2. We derive simple analytical formulae for these effective moduli based on well-known Mean-Field Eshelby-based Homogenization schemes. For each scheme, we find that the normalized bulk, shear and Young's moduli are given by the same form depending only on the porosity p. The various predictions are then confronted with experimental results for the Young's modulus of expanded polystyrene (EPS) concrete. The latter can be seen as an idealized porous material since it is made of a bulk cement matrix, with Poisson's ratio 0.2, containing spherical mono dispersed EPS beads. The Differential method predictions are found to give a very good agreement with experimental results. Thus, we conclude that when vm=0.2, the normalized effective bulk, shear and Young's modulus of isotropic porous materials can be well predicted by the simple form (1 − p)² for a large range of porosity p ranging between 0 and 0.56.     

功能梯度材料的平面断裂力学分析

针对材料参数在厚度方向可能按任意连续变化的梯度材料，给出了一个新的分层模型，利用该模型求解了面内加载下梯度界面层和涂层中的界面裂纹问题，借助Fburier积分技术和传递矩阵方法，将该问题化为一个Cauchy型奇异积分方程，通过数值求解，得到感兴趣的应力强度因子，对不同形式的杨氏模量和泊松比，计算了界面裂纹应力强度因子，结果表明泊松比的变化形式对应力强度因子影响不大，可当作常数处理，而杨氏模量的影响则很大。     

基于光纤传感器的固体杨氏模量与泊松比测量方法研究

提出了一种基于光纤传感器的测量固体材料杨氏模量与泊松比的方法,给出了Sagnac光纤干涉仪的环形光纤作为点传感器检测声波及用于声速测量的原理,推导出固体中声波速度与材料的杨氏模量及泊松比的关系式.以光纤Sagnac干涉仪作为传感器贴附于三角铸铁导轨表面,分别测出声表面波与纵波的速度,根据理论推导,得到了铸铁的杨氏模量与泊松比.实验结果与理论数值基本吻合,表明了此测量方法的可行性,为固体材料性能评估提供了一种新的方法.     

基于三相球模型确定泡沫塑料有效模量

通过复合材料三相球模型确定泡沫塑料的体积模量、剪切模量、杨氏模量和泊松比等材料等参数与材料孔隙比的关系，并将该文结果同微分法得到的结果进行了对比；结果表明：三相球模型确定的材料参数在相同孔隙比情况下，一般都高于微分法确定的结果，两种方法得到的有效剪切模量和杨氏模量差异较小，而体积模量和泊松比则差异较大，然而，由三相球模型确定的泡沫塑料杨氏模量仍可与实验较好地符合。此外，该文结果也同现有的理论及实验     

脆性材料的扩展裂纹前缘形态与三维J积分

本文利用超声波断口图技术对不同类型的PMMA试件进行了测试。这些试件为承受均匀拉伸或三点弯曲变形的带单侧贯穿裂纹的PMMA板，其中拉伸试件又分为光面和带表面沟槽的两种。得到了这些试件断口上的超声波线。发现它们为平面线．其凸凹方向与试件的表面状态有关。基于有限元法，计算了试件的三维J积分，考察了杨氏模量和泊松比对其的影响．结果发现泊松比影响J积分曲线形状，而杨氏模量只影响其绝对数值，不影响其曲线形状。得到的试件在不同裂纹长度下的三维J积分与它们断口图上的超声波线的形状和凸凹方向相似。说明在脆性材料中，扩展裂纹前缘曲线形态是三维J积分的作用的结果。     

砂岩岩石力学参数各向异性研究

对胜利油田不同深度的四口井的砂岩岩芯进行了三轴压缩试验和动态岩石力学参数试验。根据获得的垂直地层方向和平行地层方向的试验数据,计算了各岩石力学参数的各向异性系数。通过分析围压以及深度对各向异性系数的影响,给出了砂岩峰值强度各项异性系数、静泊松比各向异性系数、纵波波速各向异性系数、纵横波速比和动泊松比各向异性系数与深度的拟合公式。发现峰值强度、纵波波速和纵横波速比的各向异性系数都随着深度的增加而减小,而泊松比各向异性系数随着深度的增加而增大。动、静弹性模量各向异性系数与深度相关性都很差,动弹性模量各向异性较弱,静弹性模量相对较强。     

Elastic constant measurement by using line-focus-beam acoustic microscope

The purpose of this study is to develop a method for measuring elastic constants using a LFB acoustic microscope. For this purpose, a theoretical procedure for the estimation of Young's modulus and Poisson's ratio is introduced based on elastic theory. According to this procedure, experimental velocity measurement and elastic constants estimation are made by use of a LFB acoustic microscope. For the confirmation of the availability of this method, the estimated elastic constant is compared to measurements of elastic constants by other methods. The resulting estimated values of Young's modulus and Poisson's ratio obtained by the LFB acoustic microscope are highly accurate which confirms the usefulness of the elastic constant measurement system. T. Mihara is Research Associate, and M. Obata (former SEM Member), deceased, was Professor, Department of Materials Processing, Faculty of Engineering, Tohoku University, Aramaki Aoba, Sendai, 980, Japan.     

On Anisotropic Elastic Materials for which Young''s Modulus E ( n ) is Independent of n or the Shear Modulus G ( n , m ) is Independent of n and m

It is shown that, among anisotropic elastic materials, only certain orthotropic and hexagonal materials can have Young modulus E(n) independent of the direction n or the shear modulus G(n,m) independent of n and m. Thus the direction surface for E(n) can be a sphere for certain orthotropic and hexagonal materials. The structure of the elastic compliance for these materials is presented, and condition for identifying if the material is orthotropic or hexagonal is given. We also study the case in which n of E(n) and n, m of G(n,m) are restricted to a plane. When E(n) is a constant on a plane so are G(n,m) and Poisson's ratio ν(n,m). The converse, however, does not necessarily hold. A plane on which E(n) is a constant can exist for all anisotropic elastic materials. In particular, existence of such a plane is assured for trigonal, hexagonal and cubic materials. In fact there are four such planes for a cubic material. For these materials, not only E(n) is a constant, two other Young's moduli, the three shear moduli and the six Poisson's ratio on the plane are also constant.     

DETERMINATION OF EFFECTIVE MODULI FOR FOAM PLASTICS BASED ON THREE PHASE SPHEROIDAL MODEL

The relations of bulk modulus,shear modulus,Young's modulus and the Poisson's ra-tio with porosity of foam plastics are determined by a three phase spheroidal model commonly used inComposite Mechanics.The results are compared with those using differential scheme.It is shownthat the material properties derived from the present model normally are larger than those obtained bydifferential scheme for foam plastics with identical porosity.The differences in shear moduli andYoung's moduli obtained by the two methods are small,but they are larger for bulk moduli of incom-pressible matrix and Poisson's ratios.The Young's moduli of high density foam plastics derived by thepresent model agree better with experimental ones.     

Macroscopic elastic properties of regular lattices

In this paper we study analytically the elastic properties of the 2-D and 3-D regular lattices consisting of bonded particles. The particle-scale stiffnesses are derived from the given macroscopic elastic constants (i.e. Young's modulus and Poisson's ratio). Firstly a bonded lattice model is presented. This model permits six kinds of relative motion and corresponding forces between each bonded particle pair. By comparing the strain energy distributions between the discrete lattices and the continuum, the explicit relationship between the microscopic and macroscopic elastic parameters can be obtained for the 2-D hexagonal lattice and the 3-D hexagonal close-packed and face-centered cubic structures. The results suggest that the normal stiffness is determined by Young's modulus and the particle size (in 3-D), and that the ratio of the shear to normal stiffness is related to Poisson's ratio. Rotational stiffness depends on the normal stiffness, shear stiffness and particle sizes. Numerical tests are carried out to validate the analytical results. The results in this paper have theoretical implications for the calibration of the spring stiffnesses in the Discrete Element Method.     

具有梯度界面层的双材料悬臂梁解析解

采用应力函数法,求得了具有弹性模量沿高度线性变化的梯度界面层的双材料悬臂梁在均布载荷作用下的应力和位移解析解。该解可退化为双材料梁、弹性模量沿整个梁高线性变化的梯度梁以及均质材料梁的情况,退化为均质材料梁时与已有结果一致。通过一具体算例将得到的解析解与有限元解进行了比较,两者吻合较好。并讨论了梯度界面层的高度变化对梁中的应力和梁端挠度的影响。结果表明,在梁的总高度不变的情况下,增加梯度界面层的高度可减小弯曲应力和梁端挠度,而对挤压应力和切应力的影响很小。     

A molecular mechanics study on size-dependent elastic properties of single-walled boron nitride nanotubes

We present an analytical study for the elastic properties of single-walled boron nitride nanotubes via a molecular mechanics model. Closed-form expressions for Young's modulus, Poisson's ratio and surface shear modulus are derived as functions of the nanotube diameter. The results are helix angle sensitive and comparable to those from ab initio calculations. This work is a first effort to establish analytical model of molecular mechanics for composite nanotubes and reveals the dissimilarities between size-dependent elastic properties of carbon and boron nitride nanotubes.     

Evaluation of rigid rotations in flexural loading tests by holographic interferometry

The authors develop a simple method based on holographic interferometry for determining the Poisson's ratio and the Young's modulus for a specimen subjected to four-point flexural testing that evaluates and eliminates the effects of the unwanted rigid-body rotations. In the experimental setup, they use an additional mirror to record the underside and the front surface of the specimen simultaneously. The theoretical analysis shows that it is possible to correlate the holographic fringe pattern of the underside and front surface of the sample. Each rotation angle can be evaluated by counting the fringe orders between two points chosen on the two fringe patterns.     

域外奇点法在弹性问题及其物性值反问题中的应用

本文采用域外奇点法中的位移法和应力法求解弹性问题，并对弹性物性值进行反分析，由有限个观测点的位移值。同时反算出材料的纵向弹性模量Ｅ和泊桑比Ｖ。本文方法属于边界型解法，可有效地避免解的奇异性，不需要数值积分，具有输入数据少，精度高，计算时间短和程序编制容易等优点。     

Atomistic simulation of the structure and elastic properties of gold nanowires

We performed atomistic simulations to study the effect of free surfaces on the structure and elastic properties of gold nanowires aligned in the 〈100〉 and 〈111〉 crystallographic directions. Computationally, we formed a nanowire by assembling gold atoms into a long wire with free sides by putting them in their bulk fcc lattice positions. We then performed a static relaxation on the assemblage. The tensile surface stresses on the sides of the wire cause the wire to contract along the length with respect to the original fcc lattice, and we characterize this deformation in terms of an equilibrium strain versus the cross-sectional area. While the surface stress causes wires of both orientations and all sizes to increasingly contract with decreasing cross-sectional area, when the cross-sectional area of a 〈100〉 nanowire is less than , the wire undergoes a phase transformation from fcc to bct, and the equilibrium strain increases by an order of magnitude. We then applied a uniform uniaxial strain incrementally to 1.2% to the relaxed nanowires in a molecular statics framework. From the simulation results we computed the effective axial Young's modulus and Poisson's ratios of the nanowire as a function of cross-sectional area. We used two approaches to compute the effective elastic moduli, one based on a definition in terms of the strain derivative of the total energy and another in terms of the virial stress often used in atomistic simulations. Both give quantitatively similar results, showing an increase in Young's modulus with a decrease of cross-sectional area in the nanowires that do not undergo a phase transformation. Those that undergo a phase transformation experience an increase of about a factor of three of Young's modulus. The Poisson's ratio of the 〈100〉 wires that do not undergo a phase transformation show little change with the cross-sectional area. Those wires that undergo a phase transformation experience an increase of about 10% in Poisson's ratio. The 〈111〉 wires show, with a decrease of cross-sectional area, an increase in one of Poisson's ratios and small change in the other.     

Effect of dentin tubules to the mechanical properties of dentin. Part II: Experimental study

To verify the theoretical models of varying transversely isotropic stress-strain relations of dentin established in the preceding work (Part I), we perform a set of experiments. Because of the very fine tooth size, it usually seems to be difficult to directly measure the inhomogeneous and anisotropic parameters of dentin. In this paper, by the digital speckle correlation method, tensile experiments are made on the small dentin samples either parallel or perpendicular to the dentin tubules. With the theoretically predicted elastic stress-strain relations, an optimization method is proposed to fit the strain curve adapted to the experimental data. The results show that the theoretical elastic stress-strain relations coincides very well with the experimental observations. The determined Young's modulus and Poisson's ratio of dentin matrix are 29.5 GPa and 0.44, respectively, in the optimization sense. The project supported by the National Natural Science Foundation of China (19525207)     

Interpretation of experimental data for Poisson's ratio of highly nonlinear materials

The Poisson's ratio of a material is strictly defined only for small strain linear elastic behavior. In practice, engineering strains are often used to calculate Poisson's ratio in place of the mathematically correct true strains with only very small differences resulting in the case of many engineering amterials. The engineering strain definition is often used even in the inelastic region, for example, in metals during plastic yielding. However, for highly nonlinear elastic materials, such as many biomaterials, smart materials and microstructured materials, this convenient extension may be misleading, and it becomes advantageous to define a strainvarying Poisson's function. This is analogous to the use of a tangent modulus for stiffness. An important recent application of such a Poisson's function is that of auxetic materials that demonstrate a negative Poisson's ratio and are often highly strain dependent. In this paper, the importance of the use of a Poisson's function in appropriate circumstances is demonstrated. Interpretation methods for coping with error-sensitive data or small strains are also described.