Prediction of structures and mechanical properties of composites using a genetic algorithm and finite element method

A combined method of a genetic algorithm and finite element stress analysis has been developed to design the structure of materials. The genetic algorithm is applied to searching structures that have a desired property by combining it with the finite element analysis, which is used to predict the elastic modulus and Poisson's ratio. The calculation of the stress analysis is validated from the comparison with the theory on parallel, series, and random structures. The combined method was applied to two searches of structures. One was to find structures that have a desired elastic modulus, respectively. The calculation successfully found a proper structure for each desired elastic modulus. The other was the search of the structure that shows a negative Poisson's ratio. A structure having the negative Poisson's ratio was generated by the calculation. Although this original structure would appear to have no features, it gave us a good idea for the design of materials by investigating the stress distribution in the original structure. A new structure that consists of a unique and continuous pattern of the higher elastic component was designed from the calculation. The reason for the negative Poisson's ratio is explained by mechanical linkage.     

面外波纹对复合材料层合板弹性性能的影响

基于经典层合板理论（CLT）,提出一个多参数解析模型,定量研究了面外波纹缺陷对含波纹缺陷的复合材料层合板弹性模量、剪切模量和泊松比等弹性性能的影响。 结果表明:面外波纹对主弹性模量、Z向弹性模量、X - Z平面剪切模量和面内泊松比都产生了显著影响;对于碳纤维/环氧树脂材料体系算例,在特定波纹比和波纹区域范围内,面内泊松比出现了负值。该建模方法为研究波纹缺陷对复合材料层合板弹性性能影响提供了参考。      

Elasto-optics in double-coated optical fibers induced by axial strain and hydrostatic pressure

Stresses, microbending loss, and refractive-index changes induced simultaneously by axial strain and hydrostatic pressure in double-coated optical fibers are analyzed. The lateral pressure and normal stresses in the optical fiber, primary coating, and secondary coating are derived. Also presented are the microbending loss and refractive-index changes in the glass fiber. The normal stresses are affected by axial strain, hydrostatic pressure, material properties, and thickness of the primary and secondary coatings. It is found that microbending loss decreases with increasing thickness, the Young's modulus, and the Poisson's ratio of the secondary coating but increases with the increasing Young's modulus and Poisson's ratio of the primary coating. Similarly, changes in refractive index in the glass fiber decrease with the increasing Young's modulus and Poisson's ratio of the secondary coating but increase with the increasing Young's modulus and Poisson's ratio of the primary coating. Therefore, to minimize microbending loss induced simultaneously by axial strain and hydrostatic pressure in the glass fiber, the polymeric coatings should be suitably selected. An optimal design procedure is also indicated.     

Effects of elasticity differences between substrate and coating on the state of stress and strain in a composite. Part 2. Coating tensile stress distribution

An expression is given for the tensile stress in the coating in uniaxial stretching of the substrate, which incorporates the differences in Poisson's ratio for the substrate and coating. The tensile stress is dependent on the substrate strain, the elastic characteristics of substrate and coating, and also on the geometric parameters. A graph is given for the stress distribution for a gas-thermal coating in the plane of adhesive contact. Translated from Problemy Prochnosti, No. 5, pp. 63–67, May, 1996.     

高频热压杨木单板层积材纵向弹性模量和泊松比的测定与分析

基于四点弯曲法,对一种基于高频热压技术的厚型杨木单板层积材的纵向弹性模量和纵横向泊松比进行了试验测定。其中纵向弹性模量的测定,分别采用了挠度法和应变片法。实验结果表明,2种测量方法所得纵向弹性模量数值比较接近,但又存在一定的差异,并对其差异的影响因素进行了探讨。基于高频热压技术的杨木单板层积材纵向弹性模量的测定结果表明,其纵向弹性模量接近甚至超过杨木单板,为该材料引入重型产品包装箱领域甚至结构用材料,从而替代原木,提供了一定的参考价值。     

Elastic properties measurement of glass layers fabricated onsilicon wafers for microelectronics and micromachines

Elastic properties such as the Young's modulus, the Poisson's ratio and the density of Si-B-O glass layers fabricated on (100) silicon substrates by the flame hydrolysis deposition method were measured. Thicknesses of the layers were about 20 μm. It was found that the Young's modulus decreased with the boron dopant concentration. The Poisson's ratio was about 0.26 regardless of the boron dopant concentration. The measured elastic properties will be used in the design of micromachines fabricated with silicon substrates and glass layers     

负泊松比微结构拓扑优化设计

在构建负泊松比结构拓扑优化模型时,直接用负泊松比的数学表达式构造目标函数,将使得目标函数高度非线性,迭代过程敏度分析困难。采用线性拟合法,构建了具有线性特征的负泊松比微结构拓扑优化目标函数,基于能量法和均匀化方法,结合拓扑优化理论,构建了一种可以快速准确求解负泊松比的拓扑优化设计模型,求解该模型得到了一种优化的拓扑构型及相应的负泊松比值。根据优化求解得到的结构模型,参考国家标准GB/T 22315-2008《金属材料弹性模量和泊松比试验方法》,利用有限元软件对其泊松比进行仿真计算,然后采用激光加工方式制造试样,并测试其泊松比,经过与优化模型求解得到的泊松比值对比分析,验证了所构建优化模型的正确性。本文方法既避免了以负泊松比表达式为优化函数时会出现的高度非线性问题,也降低了求解的复杂程度,为负泊松比微结构的设计提供了一种参考方法。     

含周期性索-杆胞元的二维网格结构拟膜分析

利用拟膜法分析含周期性索-杆胞元的二维网格结构的面内有效弹性性能。拟膜法是将具有周期性微结构的平面网格结构在力学性能上比拟成均匀的连续体。根据两者在面内力学行为上的等效性,网格结构的拟膜的弹性本构参数可由网格结构中单胞的材料和几何参数解析表示。分析表明索-杆胞元存在拉压性能差异现象。这导致拟膜表现出双模量特点,即材料沿某一方向的拉伸弹性模量与压缩模量不同。采用悬臂梁算例考察这些参数的正确性:利用网格结构和其拟膜分别构造同尺寸和工况的两个悬臂梁;利用有限元方法分析两个梁;比较得出两个梁的中性层位置与解析解均吻合,且两个梁中性层挠度之间的相对误差极小。     

Fracture mechanisms of ceramic coating during wear

A typical buckling phenomenon of the coating on the wear groove caused by the residual compressed stress was analyzed by the interface fracture mechanics and the buckling theory. It has been found that there is a critical thickness of coating on the wear groove for the buckling. The critical thickness can be calculated by t_b/c_d = [12(1 − v²_f)σ_R/π²E_f]1/2 (here t_b is the coating thickness, c_d the length of the interfacial crack, v_f the Poisson's ratio of the coating, σ_R the residual compressed stress in the coating, and E_f the elastic modulus of the coating).     

岩石可释放应变能及耗散能的实验研究

地下岩石结构的变形破坏是能量耗散与能量释放的综合结果.岩石结构内部储藏的可释放应变能和己耗散能的计算,涉及到在当时工况下岩石的卸荷弹性模量和泊松比,并与加载速度与载荷水平有关.该文在不同加载速度及不同载荷水平下,对岩石试件进行了单压加卸载实验,得到了卸荷弹性模量与泊松比、可释放应变能与耗散能的变化规律;进行了SHPB动...     

Elastic moduli of Al-Si and Al-Ge solid solutions

The elastic moduli of Al-Si and Al-Ge alloys obtained by solid-solution under pressure are investigated theoretically using a previous treatment based on the microscopic electronic theory. The obtained results for elastic coefficients such as bulk modulus, shear modulus, Young's modulus and Poisson's ratio for matrix Al are in good agreement with temperature-dependent experimental data. These moduli of Al-Si and Al-Ge alloys are calculated, and the concentration dependence of the elastic data is presented quantitatively.     

温克勒地基上结合式双层板中性面分析

温克勒地基上结合式双层板问题分析的关键在于中性面的求解,但目前对于两层板泊松比不同时的情况仍没有理想的理论公式和求解方法。根据薄板假设,推导了该问题的中性面方程,并提出一种数值法来求解此方程,得到了中性面曲线;最后分析了地基反应模量、两层板泊松比比值、模量比和厚度比对中性面位置的影响,发现地基反应模量、泊松比仅在荷载附近的影响较为明显,模量比对中性面影响较大,中性面明显向模量较大的板方向偏移,而厚度比对中性面影响不大。     

Some Further Considerations about the Theory of Elastic Stress Transfer from Partially Embedded Axially Loaded Fiber to Matrix

In this paper the elastic stress transfer from the fiber to the matrix is analysed for fiber-reinforcedcomposites when the fiber is loaded axially.The dependence of the elastic stress transfer on the as-pect ratio of the fiber,the volume fraction of the fiber,the fiber-to-matrix elastic modulus ratio andthe Poisson's ratio of the fiber and the matrix has been shown in detail.     

The Young's modulus and Poisson's ratio of arsenic,antimony and bismuth

The orientational dependences of the Young's modulus and Poisson's ratio of the A7 structure elements arsenic, antimony, and bismuth are investigated, using available experimental data of the six elastic compliance constants. The behaviour of these technical elastic constants in antimony and bismuth is shown to differ not only in degree but also in kind from that of arsenic, which exhibits the characteristics expected of a layer-like crystal; arsenic is elastically a very anisotropic material, its Young's modulus varies by a factor as large as 11.3: the largest anisotropy ratio reported for a metallic element.     

锌漆薄膜/钢基底系统界面断裂韧性的试验与模拟

以锌漆薄膜与304不锈钢基底之间的界面裂纹为研究对象,采用声发射与显微镜实时检测技术与三点弯曲试验相结合的方法,测量了锌漆涂层的界面断裂韧性。同时将界面裂纹长度的有限元模拟结果和实验结果相比较,结果较为吻合。通过ABAQUS有限元模拟发现,界面断裂韧性与多种影响因素有关,界面裂纹扩展长度随薄膜厚度和外荷载的增加而增加,随界面断裂韧性和薄膜弹性模量的增大而减小,而泊松比对其影响不大。     

Anelastic behaviour of materials under multiaxial strains

Data on Young's modulus and Poisson's ratio obtained in AISI-1080 steel, in the temperature region between about 300 and 600 K, are presented. The measurements have been performed in longitudinal excitation and several harmonics were used, to obtain Poisson's ratio from the measured resonant frequencies. The maximum observed in the temperature dependence of Young's modulus, for the fundamental resonant frequency, is attributed to a stress-induced disordering of carbon atoms in the octahedral interstices of the martensitic matrix. The increases of Young's modulus with temperature are described in terms of expressions deduced in the paper, which are based on Landau theory of second-order phase transitions. The critical temperature is related to theM _s temperature which characterizes the martensitic phase transition. Finally, the temperature dependence of Poisson's ratio is described in terms of a theory of anelastic behaviour under multiaxial strains, based on the standard anelastic solid model.     

Statistical spherical cell model for the elastic properties of particulate-filled composite materials

The single spherical cell model of F. J. Guild et al. (J. Mater. Sci. Lett. 13 (1994) 10) is extended to take into account the statistical spatial distribution of the inclusions in particulate-filled composite materials. Using this model, the elastic properties of a glass-bead filled epoxy composite material were calculated. When compared with the single spherical cell model, we found that the statistical spherical cell model gave predictions consistently closer to the experimental values for both the Young's modulus and the Poisson's ratio.     

Analysis of the single-fiber fragmentation test

An analysis of the single-fiber fragmentation test was investigated.An approximate solution for the stress fields of a fiber embedded in a polymer matrix of different elastic moduli was obtained by the Eshelby method. The fiber was modeled as a prolate spheroid. The axial stress of the fiber increases with increasing aspect ratio and fiber-matrix shear modulus ratio and decreases with increasing matrix and fiber Poisson's ratios. Using this analysis, the fracture stress of a single-fiber fragmentation specimen was derived. The applied stress at fiber fracture decreases monotonically with increasing aspect ratio of the fragmented fiber and increases with increasing fiber and matrix Poisson's ratios. This model is in qualitative agreement with published experimental data.     

Application of homogenization FEM analysis to regular and re-entrant honeycomb structures

Honeycomb structures are widely used in structural applications because of their high strength per density. Re-entrant honeycomb structures with negative Poisson's ratios may be envisaged to have many potential applications. In this study, an homogenization finite element method (FEM) technique developed for the analysis of spatially periodic materials is applied for the analysis of linear elastic responses of the regular and re-entrant honeycomb structures. Young's modulus of the regular honeycomb increased with volume fraction. Poisson's ratio of the regular honeycomb structure decreased from unity as volume fraction increased. The re-entrant honeycomb structure had a negative Poisson's ratio, its value dependent upon the inverted angle of cell ribs. Young's modulus of the re-entrant honeycomb structure decreased as the inverted angle of cell ribs increased. The results are in good agreement with previous analytical results. This homogenization theory is also applicable to three-dimensional foam materials — conventional and re-entrant.Nomenclature b _i Body force - E, E _ijkl Young's modulus, elasticity tensor - E _e Effective Young's modulus - E _ijkl ^H Homogenized elasticity tensor - t _i Traction - u _i , u Displacement - v _i , v Virtual displacement - x _i , x Macroscale coordinate - y _i , y microscale coordinate - Microscopic/macroscopic ratio - Volume fraction - v Poisson's ratio - v_e Effective Poisson's ratio - _ij Stress - _P ^KL Microscale parameter of separation of variables     

Effect of Poisson's Ratio on the Limiting Stressed State of a Coating

We present relations for the calculation of equivalent stresses in a coating. Plots of equivalent stresses against the difference in Poisson's ratio between the substrate and the coating have been constructed. It has been shown that the calculated curves give a good fit to the magnitudes of the maximum normal and equivalent stresses for different coatings. Analysis of the results obtained shows that it is necessary to take into account the effect of Poisson's ratio of the coating on the equivalent stresses and, accordingly, on the limiting stressed state of the coating in the strength analysis of coated structural elements and in the experimental determination of cohesive strength in laboratory tests. When designing coated structural elements, one should seek the combination of the elastic properties of the substrate and coating at which the magnitude of the equivalent stresses in the coating achieves its minimum value.