APPLICATION OF TOPOLOGICAL OPTIMIZATION TECHNIQUES TO STRUCTURAL CRASHWORTHINESS

The topological optimization of components to maximize crash energy absorption for a given volume is considered. The crash analysis is performed using a DYNA3D finite element analysis. The original solid elements are replaced by ones with holes, the hole size being characterized by a so-called density (measure of the reduced volume). A homogenization method is used to find elastic moduli as a function of this density. Simpler approximations were developed to find plastic moduli and yield stress as functions of density. Optimality criteria were derived from an optimization statement using densities as the design variables. A resizing algorithm was constructed so that the optimality criteria are approximately satisfied. A novel feature is the introduction of an objective function based on strain energies weighted at specified times. Each different choice of weighting factors leads to a different structure, allowing a range of design possibilities to be explored. The method was applied to an automotive body rear rail. The original design and a new design of equal volume with holes were compared for energy absorption.     

纤维束内部孔洞对2.5D-C/SiC复合材料弹性性能的影响研究

采用Mori-Tanaka方法分两步计算了含孔洞C/SiC纤维束的弹性常数,并进一步考虑经向纤维束在空间上的不完全连续,给出了更为准确的2.5D-C/SiC复合材料弹性性能计算模型.分析了纤维束内部孔洞形状及体积含量对2.5D-C/SiC复合材料弹性性能的影响,结果表明纤维束内部孔洞的形状对材料弹性性能影响较小,而纤维...     

In-situ X-ray computed tomography characterisation of 3D fracture evolution and image-based numerical homogenisation of concrete

In-situ micro X-ray Computed Tomography (XCT) tests of concrete cubes under progressive compressive loading were carried out to study 3D fracture evolution. Both direct segmentation of the tomography and digital volume correlation (DVC) mapping of the displacement field were used to characterise the fracture evolution. Realistic XCT-image based finite element (FE) models under periodic boundaries were built for asymptotic homogenisation of elastic properties of the concrete cube with Young's moduli of cement and aggregates measured by micro-indentation tests. It is found that the elastic moduli obtained from the DVC analysis and the FE homogenisation are comparable and both within the Reuss-Voigt theoretical bounds, and these advanced techniques (in-situ XCT, DVC, micro-indentation and image-based simulations) offer highly-accurate, complementary functionalities for both qualitative understanding of complex 3D damage and fracture evolution and quantitative evaluation of key material properties of concrete.     

Simulation of Degraded Properties of 2D plain Woven C/SiC Composites under Preloading Oxidation Atmosphere

In this paper, a numerical model which incorporates the oxidation damage model and the finite element model of 2D plain woven composites is presented for simulation of the oxidation behaviors of 2D plain woven C/SiC composite under preloading oxidation atmosphere. The equal proportional reduction method is firstly proposed to calculate the residual moduli and strength of unidirectional C/SiC composite. The multi-scale method is developed to simulate the residual elastic moduli and strength of 2D plain woven C/SiC composite. The multi-scale method is able to accurately predict the residual elastic modulus and strength of the composite. Besides, the simulated residual elastic moduli and strength of 2D plain woven C/SiC composites under preloading oxidation atmosphere show good agreements with experimental results. Furthermore, the preload, oxidation time, temperature and fiber volume fractions of the composite are investigated to show their influences upon the residual elastic modulus and strength of 2D plain woven C/SiC composites.     

二维二轴1×1编织复合材料细观结构模型及力学性能有限元分析

考虑纤维束相互挤压及横截面形状变化, 采用纤维束截面六边形假设, 建立了二维二轴1×1编织复合材料的参数化单胞结构模型。通过引入周期性位移边界条件, 基于细观有限元方法, 对编织材料的弹性性能进行预测, 讨论了编织角及纤维体积含量对面内弹性常数的影响, 并分析了典型载荷下单胞细观应力场分布。研究表明: 单胞结构模型有效反映了纤维束的空间构型和交织特征, 实现了不同编织工艺参数下模型的快速建立; 基于单胞有限元模型的弹性性能预测结果与试验结果较为吻合; 模型给出了单胞合理的应力场分布, 为二维编织复合材料的结构优化和损伤预测奠定基础。      

Predictions of elastic property on 2.5D C/SiC composites based on numerical modeling and semi-analytical method

In this paper, the predictions of elastic constants of 2.5D (three-dimension angle-interlock woven) continue carbon fiber reinforced silicon carbide (C/SiC) composites are studied by means of theoretical model and numerical simulation. A semi-analytical method expressing elastic constants in terms of microstructure geometrical parameters and constitute properties has been proposed. First, both the geometrical model of the 2.5D composite and the representative volume element (RVE) in both micro- and meso-scale are proposed. Second, the effective elastic properties of the RVE in 2.5D C/SiC composites are obtained using finite element method (FEM) simulation based on energy equivalent principle. Finally, the remedied spatial stiffness average (RSSA) method is proposed to obtain more accurate elastic constants using nine correction factor functions determined by FEM simulations, also the effects of geometrical variables on mechanical properties in 2.5D C/SiC composites are analyzed. These results will play an important role in designing advanced C/SiC composites.     

Numerical Modeling of Oxidized 2D C/SiC Composites in Air Environments Below 900 °C: Microstructure and Elastic Properties

A numerical model is presented for simulation of the oxidation-affected behaviors of two dimensional carbon fiber-reinforced silcon carbide matrix composite (2D C/SiC) exposed to air oxidizing environments below 900 °C, which incorporates the modeling of oxidized microstructure and computing of degraded elastic properties. This model is based upon the analysis of the representative volume cell (RVC) of the composite. The multi-scale model of 2D C/SiC composites is concerned in the present study. Analysis results of such a composite can provide a guideline for the real 2D C/SiC composite. The micro-structure during oxidation process is firstly modeled in the RVC. The elastic moduli of oxidized composite under non-stress oxidation environment is computed by finite element analysis. The elastic properties of 2D-C/SiC composites in air oxidizing environment are evaluated and validated in comparison to experimental data. The oxidation time, temperature and fiber volume fractions of C/SiC composite are investigated to show their influences upon the elastic properties of 2D C/SiC composites.     

2.5D机织复合材料弹性性能的有限元分析

在已有研究的基础上,提出了一个新的2.5D机织复合材料有限元模型,该模型较为真实的模拟了织物内纤维束的轮廓结构和走向,模型中纤维束单元的材料属性根据其所处位置及纱线走向的不同对其分别进行定义。利用该模型,以机织结构和纤维束排列密度为参数,详细研究了其对2.5维机织复合材料弹性性能的影响情况,并对其影响特征进行了分析讨论。将计算结果与实验值和刚度平均法预测结果进行了对比分析。结果表明,有限元法预测结果介于实验值和刚度平均法预测值之间,非常接近于实验值,且优于刚度平均法预测的结果。     

Closed-form effective elastic constants of frame-like periodic cellular solids by a symbolic object-oriented finite element program

In this study, the effective elastic constants of several 2D and 3D frame-like periodic cellular solids with different unit-cell topologies are analytically derived using the homogenization method based on equivalent strain energy. The analytical expressions of strain energy of a unit cell under different strain modes are determined using a generic symbolic object-oriented finite element (FE) program written in MATLAB. The obtained analytical expressions of the strain energy are then used to symbolically compute the effective elastic constants that include Young’s moduli, Poisson’s ratios, and shear moduli. The obtained analytical effective elastic constants are numerically verified using results from an ordinary numerical FE program. The obtained closed-form effective elastic constants are also compared with some existing solutions from the literature. This study demonstrates that symbolic computation platforms can be properly used to provide efficient methodologies for finding useful analytical solutions of mechanical problems. Without the symbolic object-oriented FE program in this study, elaborate and tedious analytical analysis has to be manually performed for each different unit cell. The symbolic object-oriented FE program provides analytical analysis of unit cells that is accurate and fast. The object-oriented programming technique allows the symbolic FE program in this study to be efficiently implemented.     

Finite Element Analysis of 2.5D Woven Composites,Part I: Microstructure and 3D Finite Element Model

A new parameterized finite element model, called the Full-cell model, has been established based on the practical microstructure of 2.5D angle-interlock woven composites. This model considering the surface layer structure can predict the mechanical properties and estimate the structural performance such as the fiber volume fraction and inclination angle. According to introducing a set of periodic boundary condition, a reasonable overall stress field and periodic deformation are obtained. Furthermore, the model investigates the relationships among the woven parameters and elastic moduli, and shows the structural variation along with the corresponding woven parameters. Comparing the results calculated by FEM with the experiments, the veracity of calculation and reasonability based on the Full-cell model are confirmed. In the meantime, the predicted results based on the Full-cell model are more closed to the test results compared to those based on the Inner-cell model.     

基于五相球模型确定含涂层空心微球复合材料的有效模量

利用推广的五相球模型得到了含涂层空心微球填充复合材料的有效体积模量、剪切模量和杨氏模量预测的理论公式。分析了复合材料有效模量同空心微球壁的厚度、填充体积分数、涂层厚度等参数的关系。为了说明本文结果的有效性, 将五相球模型退化为不含涂层空心球填充复合材料的情况, 并与文献中的实验数据进行对比。算例计算表明: 涂层较薄时, 填料体积分数越大, 空心微球壁相对越厚, 弹性模量就越大。当填料体积分数最大时, 在空心微球壁相对最薄处, 弹性模量最低。      

MgO-Al2O3-SiO2-TiO2-Y2O3玻璃的弹性模量

根据硬盘基板用材料的要求，制备了MgO-Al2O3-SiO2-TiO2-Y2O3高弹性模量玻璃（120GPa)，玻璃的弹性模量随组成的变化服从Makishima-Mackenzie理论，MgO,Al2O3,TiO2,Y2O3等具有较高单位体积离解能的氧化物有利于提高玻璃的弹性模量，但玻璃弹性模量的理论计算值低于测试值，这是因为Makishima-Mackenzie理论没有考虑玻璃内阳离子的具体配位，对MgO,Y2O3堆积密度因子的堆导存在误差，因此利用Makishima-Mackenzie理论发展高弹性模量玻璃时应对MgO,Y2O3等氧化物的计算进行修正。     

Compressive Behavior of 3D Woven Composite Stiffened Panels: Experimental and Numerical Study

The structural behavior and damage propagation of 3D woven composite stiffened panels with different woven patterns under axial-compression are here investigated. The panel is 2.5D interlock woven composites (2.5DIWC), while the straight-stiffeners are 3D woven orthogonal composites (3DWOC). They are coupled together with the Z-fibers from the stiffener passing straight thought the thickness of the panel. A “T-shape” model, in which the fiber bundle structure and resin matrix are drawn out to simulate the real situation of the connection area, is established to predict elastic constants and strength of the connection region. Based on Hashin failure criterion, a progressive damage model is carried out to simulate the compressive behavior of the stiffened panel. The 3D woven composite stiffened panels are manufactured using RTM process and then tested. A good agreement between experimental results and numerical predicted values for the compressive failure load is obtained. From initial damage to final collapse, the panel and stiffeners will not separate each other in the connection region. The main failure mode of 3D woven composite stiffened panels is compressive failure of fiber near the loading end corner.     

Environmental fatigue crack propagation in medium strength titanium sheet alloys

Results are reported for an investigation of environmental fatigue crack propagation resistance in four commercial titanium alloys of medium strength. The materials were IMI 130 (commercially pure titanium with low oxygen content), Ti-70 (commercially pure titanium with high oxygen content), IMI 230 (Ti-2.5 Cu) and Ti-5Al-2.5Sn. The environments were dry argon, normal air, distilled water and 3.5% aqueous NaCl. The conclusions were (1) the ranking of the materials in terms of conventional mechanical properties does not permit a ranking in terms of crack propagation resistance, (2) the material with the highest elastic moduli, Ti-5Al-2.5Sn, also had the best crack propagation resistance in the absence of stress corrosion, (3) there is a correspondence between the degree of isotropy of the static yield strength and the orientation dependence of crack propagation resistance, (4) for all the materials there was a trend of higher crack growth rates at similar ΔK values in the order; dry argon, air, distilled water, 3.5% aqueous NaCl, (5) in the aqueous environments only Ti-5Al-2.5Sn gave evidence of stress corrosion cracking.     

On the identification of microstretch elastic moduli of materials by using vibration data of plates

In the present work, the vibration problems of rectangular plates modeled by Eringen’s microstretch theory are investigated for the identification of the upper bounds of the microstretch moduli of the plate material. The calculated frequencies of the plates are obtained by extending the Ritz method to the microstretch plates. The three dimensional (3D) vibration analysis of the plates shows that some additional frequencies occur among the classical frequencies as characterizing the microstretch effects. Then it is also observed that these additional frequencies disappear and only the classical frequencies remain with the increasing values of microstretch constants. The inverse problem is established for the identification of the upper bounds of the microstretch elastic constants as an optimization problem where an error function is minimized.     

Effective creep behavior and complex moduli of fiber- and ribbon-reinforced polymer-matrix composites

This paper examines the influence of the cross-sectional aspect ratio (the thickness-to-width ratio, denoted by ) and volume concentration, c₁, of 2-D randomly oriented elliptic cylinders on the overall anisotropic creep and complex moduli of a viscoelastic composite. With such a microgeometry it is first shown that two Maxwell or two Voigt constituents generally do not make a Maxwell or a Voigt composite, but under the conditions that the ratios of the shear modulus to the shear viscosity are equal for both constituents and that both Poisson's ratios remain unchanged in the course of deformation, a Maxwell and a Voigt composite can be constructed. The transversely isotropic creep compliances are then examined as the cross-sectional shape of the elastic elliptic cylinders changes from a circular one ( = 1) to that of a long, thin ribbon ( → 0). Along all five loading directions the ribbon-reinforced composite consistently gives rise to the strongest creep resistance, and as the aspect ratio increases the creep resistance also continues to weaken, with the traditional circular fibers providing the poorest reinforcement. The real and imaginary parts of the five independent complex moduli are also investigated as a function of and c₁, and the loading frequency ω. It is found that the real parts of the complex moduli all increase with increasing ω, and as ω → ∞ these moduli all approach their respective elastic moduli. The imaginary parts of the complex moduli show two distinct trends; one is marked by a monotonic decrease with increasing c₁, and the other shows an initial increase before it decreases to zero. Finally, the complex plane/strain bulk moduli associated with various cross-sectional shapes are examined in light of the Gibiansky-Milton bounds, and it is found that all the theoretical results lie literally on the boundary of the bounds.     

Failure criteria for multiply flawed anisotropic materials

This study presents overall failure criteria for an infinite anisotropic solid containing multiple flaws subjected to a set of uniform applied loads. Based on the inclusion method, flaws are treated as elliptical inclusions where their elastic moduli are considered to be zero. The explicit expression of elastic fields is obtained for a cubic crystal multiply flawed solid through the use of the Mori-Tanaka mean field theory. The resulting expression is further utilized to find an interaction energy function between the applied loads and flaws. With this energy function, the energy release rates and critical stresses are acquired separately in a closed form for Mode I, II, and III. The closed forms for energy release rates and critical stresses reveal that they are a function of the aspect ratio and the volume fraction of flaws, the modes of the loading, and the material properties. As an illustrated numerical example, the energy release rates and the critical stresses that vary with both the aspect ratio and the volume fraction of the flaws in a cubic crystal material are discussed.     

Elastic properties of silicon oxynitride

Silicon oxynitride is a refactory material which appears to exhibit good mechanical and thermal properties. This work studies the elastic properties of hot-pressed samples with an addition of 5 wt% MgO. The samples are isotropic and homogeneous, and the three different methods of measurement used, operating in the frequency range 20 kHz to 10 MHz, give similar results. Young's modulus and shear modulus are low (about 22×10¹⁰ Pa and 9×10¹⁰ Pa, respectively), which leads to small thermal stresses and thus allows a good thermal shock resistance. The elastic moduli decrease linearly when the porosity increases over the range of 0 to 27%. Poisson's ratio is sensibly a constant equal to 0.2, and the rate of variation is the same for both moduli: 2.5, this value being superior to what could be expected from the usual theories.     

The wear resistance of glass fibre reinforced epoxy composites

Polymers are usually characterized by low moduli and strength. Epoxy, as a thermoset material, has a low wear resistance. Additions of glass fibres improve the elastic modulus and tensile strength and can improve the wear resistance. The composites were prepared by pultrusion of the glass fibres after saturation of epoxy. The fibre volume fraction was varied up to 50%. Tensile and wear tests were carried out to examine the improvement in the composite properties. A small deviation of the tensile strength and the elastic modulus from the calculated values using the rule of mixture was observed due to the existence of porosities. The wear resistance increases with increasing the sliding velocity, with decreasing the applied contact pressure and with selecting the most favourable glass fibre volume fraction.     

2.5维C/SiC复合材料板弹性参数识别方法研究

以大型商业有限元软件NASTRAN为计算平台,提出了基于模态试验结果的2.5维C/SiC复合材料板弹性参数识别方法。基于复合材料板的模态试验结果,采用模型修正的思想构造优化问题,其中目标函数定义为实测模态频率与计算频率之差的平方和,将以刚度平均法获得的复合材料弹性参数的理论预测值作为优化问题的初值,充分利用了材料参数的先验信息,然后对材料参数进行灵敏度分析,通过迭代求解识别出复合材料板的弹性参数。识别后,C/SiC复合材料板第1-4阶模态频率的复现精度明显提高,并能保证第5-8阶模态频率的预示精度。研究结果表明,方法能准确识别2.5维编织C/SiC复合材料的弹性参数,并为复合材料等效建模以及进一步动态特性研究提供参考。