复合材料横向剪切弹性模量的识别与层间剪切强度的实验研究

本文提出一种测试复合材料横向剪切弹性模量的参数识别方法。该方法是将复合材料的横向剪切弹性模量视作横向剪应变的函数，由横向剪应变的测量值反演横向剪切弹性模量。剪应变与剪切弹性模量间的函数关系用有限单元法得到。文中给出了参数识别计算格式和一种玻璃布层压板的识别结果。同时，文中提出了用五点弯曲实验测试层间剪切强度的方法，给出了实验结果。     

Through-thickness strain field measurement in a composite/aluminium adhesive joint

This paper presents an experimental procedure, which enables us to assess the shear strain field in an adhesive joint between composite and aluminium. In practice, this strain field is representative of the progressive stress transfer between a loaded structure and a composite patch used for reinforcement purposes. Digital image correlation (DIC) is used to measure the displacement field through the thickness of a patched specimen subjected to a tensile test. The shear strain field derives from the measured displacement field. The shear strain clearly decreases when the distance from the free edge of the adhesive increases, as predicted by numerical and analytical models of the joint. These measurements are used to estimate the in situ shear modulus of the adhesive. It is observed that the shear modulus decreases when the shear stress increases, thereby illustrating the non-linear response of the adhesive.     

Dynamic effective models of two-dimensional acoustic metamaterials with cylindrical inclusions

Based on analytical solutions of elastic waves scattered by a coated cylinder in an infinite elastic matrix, we construct the localization relations for averaged displacement and stress fields in each phase. Dynamic effective mass, in-plane bulk modulus and shear modulus are defined, respectively, as the ratio between the force and acceleration, bulk stress and bulk strain, maximum shear stress and maximum shear strain. Analytic expressions for dynamic effective parameters of two-dimensional acoustic metamaterials are derived. Numerical examples are given to analyze dynamic effective properties of composites with coated inclusions. It is demonstrated that the proposed model can predict negative values of effective mass and effective bulk and shear modulus, and discover the underlying mechanisms of negative effective material parameters. The proposed model will be helpful in designing new acoustic metamaterials.     

含孔隙混凝土复合材料有效力学性能研究

混凝土、岩石等工程材料是典型的多孔介质材料,孔隙或微裂纹的存在对材料的弹性模量及强度等力学参数产生很大影响。该文基于三相球模型确定了含孔隙复合材料的有效体积模量,提出采用空心圆柱形杆模型推导得到了含孔隙复合材料有效剪切模量的理论公式,并在各向同性材料的假设条件下确定了材料的有效弹性模量及泊松比;推导并得到了含孔隙材料的有效抗拉、抗压强度及有效抗剪强度与孔隙率之间的定量关系公式,并进一步得到了含孔基质在达到有效强度时的临界应变与孔隙率之间的定量关系。结果表明该文方法能较好的预测含孔混凝土材料的有效力学性能,且公式简单,易于应用。     

Fourier‐series‐based virtual fields method combining with moiré interferometry for characterising elastic modulus distribution of laser repaired GH4169

Laser cladding is an effective technology for repairing damaged components with high efficiency and low cost. Characterisation for the mechanical properties of the repaired structure is of great importance to evaluate its reliability. In this study, the mechanical properties of laser repaired GH4169 are investigated by Fourier‐series‐based virtual fields method and moiré interferometry. The elastic modulus distribution of the whole structure is identified to understand the mechanical performance of the repaired zone and base material. A uniaxial tensile test is performed and the full‐field deformation is measured by moiré interferometry. With the measured strain field, the distribution of modulus in repaired structures can be calculated. In addition, simulation experiments of moiré interferometry are conducted to optimise the parameters of Fourier‐series‐based virtual fields method to improve the accuracy of the proposed method. On the basis of these results, experiments on the repaired GH4169 material are performed and the variation of modulus in the whole structure is identified. The results verify that the proposed method is effective for characterising modulus distribution of the laser repaired structures, and will have a good prospect for further application.     

Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp

This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson’s ratio is taken as a constant. Coulomb’s dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity problem is formulated utilizing Fourier transforms, and the resulting Cauchy-type singular integral equation of the second type is solved by applying an expansion–collocation technique. The finite element method is used in the computational analysis of the contact problem. In the finite element model, continuous variation of the shear modulus is taken into account by specifying this property at the centroid of each finite element. The finite element-based solution procedure is verified by making comparisons to the results obtained through the analytical method. Numerical results generated for the laterally graded medium with an exponential variation in the shear modulus illustrate the influences of lateral gradation and coefficient of friction upon the contact stress distributions. The capability of the proposed finite element method is further demonstrated by providing numerical results for a laterally graded medium whose shear modulus is represented by a power function.     

A pseudo-elastic local meshless method for analysis of material nonlinear problems in solids

This paper aims to develop an effective meshless technique for the analysis of elasto-plastic problems. The material nonlinearity will be studied by a new pseudo-elastic local radial point interpolation formulation which is based on the local Petrov–Galerkin form and the radial basis function (RBF) interpolation. Hencky's total deformation theory is used to define the effective Young's modulus and Poisson's ratio, which are treated as spatial field variables, and considered as functions of the final stress state and material properties. These effective material parameters are obtained in an iterative manner using the strain controlled projection method. Several numerical examples are presented to illustrate the effectivity of the newly developed formulation, and the numerical results obtained by the present method closely agree with the results obtained by other methods. It has proven that the present pseudo-elastic local meshless method is effective and easy to apply to the analysis of elasto-plastic materials subjected to proportional loading.     

On Eshelby''s inclusion problem in a three-phase spherically concentric solid, and a modification of Mori-Tanaka''s method

The elastic field in the three-phase, spherically concentric solid due to a stress-free transformation strain in the inclusion is obtained. This analysis considers both homogeneous and a polynomial-type, nonlinear transformations. In the former case, the strain field in the inclusion is found to be also homogeneous under a hydrostatic transformation, but becomes heterogeneous under a deviatoric one. The mean fields are uncoupled between a hydrostatic and a deviatoric case, and even between one shear and the other. The elastic energies of the solid under these transformations are also derived. In light of this new development, a modification is suggested for the Mori-Tanaka method. The resulting effective shear modulus of a two-phase composite lies between the Hashin-Shtrikman bounds, and the predicted Young's modulus also compares well with the experimental data.     

Regularization of tissue shear modulus reconstruction using strain variance

An effective setting method (that is, a method using the variances of strain tensor component measurements) is described for the properly spatially varied regularization parameters for our shear modulus reconstruction. At each position, the respective strain variances can be experimentally evaluated using plural field measurements or single field measurement, for example, when using all crosscorrelation- based methods, by using the Ziv-Zakai Lower Bound (ZZLB). The demonstrated regularization by the single field measurement using the cross-spectrum phase gradient method (MCSPGM) in experiments confirms that the use of the axial strain variance estimated by the echo signal-to-noise ratio and correlations (the combined SNRc) effectively stabilizes the 1-D reconstruction on an agar phantom and a human in vivo liver carcinoma during interstitial microwave thermal treatment. The regularization yields a spatially uniform stability in reconstruction.     

Elastic Wave Propagation in a Class of Cracked,Functionally Graded Materials by BIEM

Elastic wave propagation in cracked, functionally graded materials (FGM) with elastic parameters that are exponential functions of a single spatial co-ordinate is studied in this work. Conditions of plane strain are assumed to hold as the material is swept by time-harmonic, incident waves. The FGM has a fixed Poisson’s ratio of 0.25, while both shear modulus and density profiles vary proportionally to each other. More specifically, the shear modulus of the FGM is given as μ (x)=μ ₀ exp (2ax ₂), where μ ₀ is a reference value for what is considered to be the isotropic, homogeneous material background. The method of solution is the boundary integral equation method (BIEM), an essential component of which is the Green’s function for the infinite inhomogeneous plane. This solution is derived here in closed-form, along with its spatial derivatives and the asymptotic form for small argument, using functional transformation methods. Finally, a non-hypersingular, traction-type BIEM is developed employing quadratic boundary elements, supplemented with special edge-type elements for handling crack tips. The proposed methodology is first validated against benchmark problems and then used to study wave scattering around a crack in an infinitely extending FGM under incident, time-harmonic pressure (P) and vertically polarized shear (SV) waves. The parametric study demonstrates that both far field displacements and near field stress intensity factors at the crack-tips are sensitive to this type of inhomogeneity, as gauged against results obtained for the reference homogeneous material case     

硅橡胶基磁流变弹性体的研制

磁流变弹性体是一种新型的智能材料,它的力学性能可以受磁场控制,在需要变刚度的器件等方面有着广泛的应用前景.本文总结了一些制备高性能磁流变弹性体的基本方法,尝试采用不同的组份制备了以硅橡胶为基体的高性能磁流变弹性体.并使用改进的动态机械分析仪来测试分析所制样品的磁致剪切储能模量和损耗因子等性能.结果表明,所制备的磁流变弹性体在600mT磁感应强度下的剪切储能模量相对变化可达到501%.     

Constitutive equation for rubber-like solids

Summary It has been found convenient to refer the deformation to the reference configuration of the body, the resulting constitutive equation being expressed in terms of the right Cauchy-Green deformation tensor, and a stress tensor which is also concerned solely with the reference configuration of the body. This particular measure of stress is referred to as the second referential stress tensor. The ratio, principal Cauchy stresses/principal stretches, identifies the proper numbers of the second referential stress tensor as the components of the force per unit underformed area. Using the Cayley-Hamilton theorem, the proposed constitutive equation is rearranged and expressed in terms of a quantity which is defined to be one quarter of the difference between the right Cauchy-Green deformation tensor and its inverse. In this way the (effective) strain properties of the proposed constitutive equation are formulated by way of the concept of a strain response function. The three response coefficients associated with the strain response function are assumed to be derivable from a strain intensity function. Two types of strain intensity function are considered. One type is characterised by being continuously differentiable, the other being characterised by the existence of vertices, but is piece-wise linear and continuous. The proposed constitutive equation is used to formulate an effective stress-effective strain relation. This effective stress-effective strain relation is used to correlate the individual stress-strain relations characteristic of various simple modes of deformation to give a single stress-strain relation. Correlation between the predictions of the proposed constitutive equation and the results of experiment proceeds by way of the concept of a generalised shear modulus.With 3 Figures     

考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。     

Thermal expansion of composites

A theory is developed for the overall thermal expansion of a composite consisting of either spherical or long cylindrical inclusions of one material in a matrix of another. The strain field of a single inclusion consists of a uniform expansion and a short-range strain field. These two components are related by minimizing the elastic strain energy. To account for a dense array of inclusions, average properties of the mixture are used for the long-range field, but those of the matrix alone for the short-range field. The net dilatation is thus found for inclusions of mismatching volume; hence one finds a differential expression for the thermal expansion in terms of the volume fraction of inclusions, the individual thermal expansivities, the bulk moduli of inclusion and matrix, the shear modulus of the matrix, and, in the case of cylinders, the shear modulus of the inclusions. This expression is integrated over temperature; one accounts for plasticity by letting the shear modulus depend on the temperature and on the accumulated shear strain. A representative numerical example is given.Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

采用数字图像相关方法的莫来石纤维增强气凝胶复合材料力学试验

基于V型缺口试样双轨剪切法设计了面内剪切试验方案,开展了莫来石纤维增强气凝胶复合材料的室温面内剪切和弯曲性能试验,采用数字图像相关方法对试样表面的位移场和应变场进行测量,并分析了力学行为和破坏模式。结果表明:设计的试验方案可以在测试区域获得均匀的剪切应变场,适用于莫来石纤维增强气凝胶复合材料的面内剪切性能测试。试验获得的面内剪切模量和强度分别为248 MPa和0.95 MPa,弯曲模量和强度分别为294 MPa和2.08 MPa。面内剪切载荷下,试样的裂纹萌生于缺口尖端附近,并沿两缺口连线方向扩展。根据弯曲正应变场的分布特点,发现试样中性层与几何对称面不重合,验证了该材料拉压模量不同的性质。采用数字图像相关方法获得的中性层位置和理论计算值比较接近,相对误差在10%左右。     

Novel approach for measuring the effective shear modulus of porous materials

A new approach is proposed for the experimental study of the effective shear modulus of porous elastic materials using the uniaxial tension test. The idea is to measure strains at a few points surrounding a cluster of holes that represents the structure of the material. The representative cluster is placed in the material with the same elastic properties as those of the matrix. The measured strains lead to the properties of the equivalent circular inhomogeneity, which would produce the same elastic fields as from the cluster. An aluminum plate containing a cluster of seven circular or hexagonal holes was used. The effective shear modulus obtained from the strain data was compared with theoretical predictions and various bounds, and it was shown that the laboratory estimated values are quite accurate. The experimental technique can be used for the determination of the effective Poisson’s ratio of porous media and/or cellular solids if more detailed strain data are obtained.     

Two‐scale shear band evolution by local partition of unity

We introduce a methodology to model shear band evolution in the quasi‐static regime using the extended finite element method. We enrich the finite element polynomial displacement field with a fine scale function, which models the high displacement gradient in the shear band. For this purpose we use a local partition of unity and a parameterized displacement enrichment based on closed form solutions for one‐dimensional shear bands. A stabilized consistent penalty method is used to circumvent locking in the regularized elasto‐viscoplastic plane‐strain regime and to guarantee element stability. The loss of stability of the boundary value problem is used as an indicator of shear band initiation point and direction. Shear band development examples are shown, illustrating the capabilities of the method to track shear band evolution and strains as high as 1000%. Copyright © 2005 John Wiley & Sons, Ltd.     

考虑频率参数协调的频率相关等效线性化方法

基于土动力试验呈现出的土体动参数频率相关特性,结合一维等效线性化理论,建立了能够考虑动三轴或共振柱测试频率Rf和波速测试频率f（v_s）相协调的频率相关等效线性化方法。首先,基于国内外不同学者的试验结果,回归建立了土体剪切模量-频率和阻尼比-频率关系式,推导得到了规准化频率相关土体剪切模量比和阻尼比随剪应变变化关系式;其次,对频率无关等效线性化方法进行了改进,传递函数采用频率相关的剪切模量和阻尼比,建立了频率相关的等效线性化方法;最后,采用频率相关和频率无关等效线性化方法,分别对单层覆盖层均质线性场地和单层覆盖层非线性场地进行了不同工况下的土层地震反应分析计算,计算结果表明:1）试验室土动力性能参数测试频率Rf对地震响应影响较大,波速测试频率f（v_s）影响较小;2）采用动三轴试验给出的土动参数,频率相关方法得到的结果略低于频率无关方法结果。采用共振柱试验给出的土动参数,频率相关方法得到的结果大幅高于频率无关方法结果。     

采用面积坐标的四边形厚薄板通用单元

本文采用四边形面积坐标,利用假设剪切应变场方法和广义协调理论构造出一个具有12个自由度的四边形厚薄板通用弯曲单元TACQ。基本思路如下：首先从Mindlin厚板理论出发,独立假设剪应变场和挠度场,而转角场则由挠度场和剪应变场导出;其次,单元剪应变场是先按Timoshenko厚梁理论确定单元各边剪应变,然后在单元内进行合理插值导出;第三,单元挠度场是根据单元角点处挠度的点协调条件以及单元各边挠度和法向转角的平均协调条件导出。这个方法有两个特点,（1）由于满足点协调和边协调的广义协调条件,故能保证收敛;（2）由于在薄板情况剪应变退化为零,故不出现剪切闭锁现象。数值算例表明：该单元具有精度高,收敛性和可靠性好,对网格畸变不敏感,无剪切闭锁现象等优点;适用于从极薄板到厚板较大的范围。     

含双周期不等长刚性线材料有效反平面剪切模量研究

研究无限介质中含双周期刚性线夹杂复合材料的反平面问题,其基本胞元含有四条不同长度的刚性线夹杂。运用椭圆函数和保角变换理论,获得了该问题严格的闭合解。利用微结构的周期性和平均应力/应变定理得到了复合材料有效反平面剪切模量的精确公式。由结果的特殊情形可以得到一系列有意义的解答。数值结果给出了该类非均匀材料有效反平面剪切模量随微结构参数变化的规律。精确解可以为其它数值和近似方法提供有价值的参考。