PREDICTIONS OF EFFECTIVE OUT-PLANE SHEAR MODULUS AND SIZE EFFECT OF HEXAGONAL HONEYCOMB

给出了预测六边形蜂窝材料等效剪切模量及其尺寸效应的圆筒扭转力学模型和扭转能量法,建立了等效面外剪切模量G₁₃相对于材料体分比ν、周向单胞数n、圆筒半径r和单胞层数参数m变化的解析表达式;同时将扭转能量法、有限元数值模拟计算和G-A经典细观力学方法进行了比较,从理论上揭示并验证了尺寸效应的存在性. 结果表明,当蜂窝体胞尺寸相对结构尺寸无穷小时,预测结果趋近于细观力学方法的结果. 此外,利用周期性蜂窝材料的结构对称特性,使用体胞子结构有限元计算模型进行等效面外剪切模量及其尺寸效应的预测,在不影响计算结果的前提下极大地提高了计算效率.     

航空用芳纶纸蜂窝各向异性行为研究

采用Arcan加载装置对航空用芳纶纸蜂窝试件进行一系列面外压剪复合加载实验,以此研究材料各向异性行为。实验结果表明:随着面内方向角增加,芳纶纸蜂窝面内等效剪切模量、等效剪切强度显著减小,实验屈服面显著扩张,材料表现出明显的各向异性。基于实验结果,确定了测试蜂窝面内等效剪切模量、等效剪切强度上下限值及其比值关系,并与理论值进行比较。一个适用于各向异性材料的屈服准则与实验屈服面进行比较,比较结果表明:屈服准则能大致描述蜂窝各向异性屈服行为。     

构造上正交各向异性凹凸板等效刚度的研究

针对构造上正交各向异性凹凸板等效刚度的研究问题,考虑经典弹性薄板理论和凹凸板的几何周期特性,划分出了以凸起为中心的典型单元,首先研究了典型单元的刚度特性,再通过刚度组合方法得到了凹凸板的等效弯曲刚度;然后以四边简支正交各向异性凹凸板为例,基于经典薄板理论中纳维二重三角级数推广到正交各向异性板的解,利用本文的等效刚度公式分别计算了在集中载荷作用下板的挠度和其自身的固有频率。计算结果与ANSYS有限元的模拟结果进行对比,理论计算与有限元模拟结果一致,验证了本文等效解析方法的合理性和精确性。最后讨论了凹凸板的各项尺寸参数对刚度等效精度的影响,并对其原因进行了分析。本文给出的等效刚度解析方法便于工程应用,尤其在应对大规模凹凸板刚度求解中具有计算简便的优点,研究结果对凹凸板静力学和动力学的研究以及实际工程应用具有重要的指导意义。     

基于偶应力理论的格栅材料等效介质模型

考察了结构最小尺寸与材料特征长度量级相当的格栅材料等效性能,建议了基于偶应力理论的格栅材料等效介质模型以及确定等效模量的代表体元模型,给出了相应的位移边界条件. 在此基础上导出了正交各向异性偶应力介质的特征长度表达式和偶应力介质梁的抗弯刚度表达式,定义了偶应力影响因子\delta以表征梁的偶应力效应. 具体计算了几种典型的格栅材料的等效偶应力模量以及格栅梁在一定工况下的挠曲线,并与相应的有限元离散解进行对比,结果表明,等效结果具有较高精度,且当宏观结构的尺寸和微结构尺寸相差不大时,宏观结构表现出强烈的偶应力效应.偶应力介质的特征长度表征了偶应力效应的强弱,进而分析了格栅材料的相对密度,单胞尺寸以及几何构型对等效介质特征长度的影响.      

锚固正交各向异性岩体的本构关系和破坏准则

从理论上对由系统锚杆加固的正交各向异性岩体,取出包含锚杆的表征单元.根据“等效材料”的概念,在原岩体的本构关系和破坏准则中计人锚杆刚度和强度的“贡献”,从而建立了相应锚固岩体的木构关系和破坏准则.然后列举算例,考察了表征单元的应力-应变关系和破坏强度随锚杆安置角度变化的各向异性表现.最后将计算与一个简单试验的结果作了对比,看到二者的吻合程度较好,因而初步地验证了所提力学模型的可靠性.     

考虑材料各向异性的熔丝制造PLA点阵结构弹性各向同性设计

增材制造技术的兴起激发了国内外学者对结构创新设计的热情. 然而, 增材制造材料的各向异性为结构力学性能的预测与设计带来了一定的困难. 为了准确预测熔丝制造聚乳酸(PLA)材料和点阵结构的弹性性能, 并实现点阵结构的弹性各向同性设计, 首先, 本文采用正交各向异性弹性模型来描述PLA材料的弹性行为, 通过实验和计算得到了正交各向异性模型需要的9个独立的弹性常数. 然后, 设计了一种力学性能可调的二维组合桁架点阵结构, 基于代表体元法, 在不考虑材料各向异性的情况下推导出了其平面内等效弹性性能的解析表达式及弹性各向同性条件. 最后, 根据PLA材料的各向异性调整点阵结构内部杆件的弹性模量和厚度, 并基于代表体元法重新推导出了点阵结构平面内等效弹性性能的解析表达式及其弹性各向同性条件. 研究结果表明, 正交各向异性弹性模型适用于描述熔丝制造PLA材料的弹性行为, 基于该模型能够准确预测PLA材料在任意方向上的弹性模量. 在预测与设计熔丝制造点阵结构的力学性能时需要充分考虑材料的各向异性. 在考虑材料的各向异性之后, 基于代表体元法调整点阵结构的几何尺寸, 能够实现部分点阵结构的弹性各向同性设计.      

含正交排列夹杂和缺陷材料的等效弹性模量和损伤

研究含正交排列夹杂和缺陷材料的等效弹性模量和损伤,推导了以Eshelby－Mori－Tanaka方法求解多相各向异性复合材料等效弹性模量的简便计算公式,针对含三相正交椭球状夹杂的正交各向异性材料,得到了由细观参量（夹杂的形状、方位和体积分数）表示的等效弹性模量的解析表达式．在此基础上,提出了一个宏细观结合的正交各向异性损伤模型,从而建立了以细观量为参量的含损伤材料的应力应变关系．最后,对影响材料损伤的细观结构参数进行了分析．     

铝蜂窝异面压缩的扩胞等效方法

基于铝蜂窝表观密度、质量、平台强度、异面弹性模量、压缩率、吸能量6个基本力学量,建立了正 六边形铝蜂窝等效前后胞元厚跨比(胞壁厚度与跨度的比)间的映射关系,得到相同厚跨比蜂窝结构具有相同 的力学属性与吸能特性。采用以大换小的扩胞途径,保持胞元厚跨比不变,通过改变蜂窝胞元结构几何参数, 提出了将致密孔格稀疏化的蜂窝扩胞等效分析流程,实现了致密蜂窝数值模拟时单元规模与计算时间的有 效减缩。基于显式有限元方法,建立了8种等间距扩胞铝蜂窝求解模型,结果验证了扩胞等效方法的可行性。 等效前后计算效率的对比分析显示了扩胞方法的高效性。但在异面方向尺度与胞元跨度相近时,扩胞等效方 法受到一定的局限。     

蜂窝夹芯剪切等效模量研究

蜂窝夹层轻型结构以其比强度、比刚度高，而在航空航天工程中被广泛采用．由于蜂窝形状、尺寸多样，使夹层结构设计、优化分析变得复杂，特别是蜂窝夹芯的剪切模量难以准确的等效计算．以薄板理论为基础采用有限元方法对单蜂窝分析的方法，获得蜂窝夹芯的剪切等效模量，与其它方法相比较，精度较高，与试验结果吻合较好．     

曲壁蜂窝夹层板的振动特性研究

曲壁蜂窝具有负刚度特性,可以在大变形过程中吸收能量、抗冲击,并且在冲击过后可以自我恢复而不像传统蜂窝被压溃。本文将曲梁构成的负刚度蜂窝作为芯层,建立夹层板的动力学模型;推导出了曲壁负刚度蜂窝胞元的等效弹性参数,将其周期性排列为蜂窝芯,应用Reddy高阶剪切变形理论、Von-Karman大变形关系和Hamilton原理推导了负刚度蜂窝夹层板的非线性动力学方程;应用Navier法计算了四边简支边界条件下的固有频率。并利用有限元软件ABAQUS建立模型,计算固有频率,与理论计算结果进行比较,结果显示二者的计算结果具有较好的一致性,验证了芯层等效弹性参数及模型的有效性。探讨了在蜂窝胞元具有较高吸能情形下,夹层板在不同芯层厚度、不同芯厚比以及不同胞元曲壁厚度时的固有频率的变化特性。     

基于三维模型的蜂窝材料有效弹性性能研究

采用三维模型预测了传统六角形蜂窝材料和带圆环结点六角形蜂窝材料的有效弹性性能.利用有限元法并结合周期边界条件计算了材料代表性体积单元的平均应力,进而由平均场理论获得了两种蜂窝材料全部的有效弹性常数.将传统蜂窝材料的计算结果与已有梁模型的计算结果和试验数据进行了对比,结果表明三维模型比梁模型具有更高的精度,分析了梁模型误...     

蜂窝芯层的等效弹性参数

反映蜂窝材料等效弹性参数的Gibson公式结果简单，便于应用然而由于对应于蜂窝壁板伸缩变形的刚度被忽略，导致蜂窝夹层结构数值分析时，芯层材料的弹性矩阵表现出不确定性本文重新考虑了蜂窝壁板的伸缩变形对面内刚度的影响，对Gibson公式进行了修正本本文结果不但克服了Gibson公式的缺陷，同时提出了考虑蜂窝芯层面内刚度的一种简化方案,该方案可以方便地应用于蜂窝夹层结构的计算。     

Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures

An alternative strain energy method is proposed for the prediction of effective elastic properties of orthotropic materials in this paper. The method is implemented in the topology optimization procedure to design cellular solids. A comparative study is made between the strain energy method and the well-known homogenization method. Numerical results show that both methods agree well in the numerical prediction and sensitivity analysis of effective elastic tensor when homogeneous boundary conditions are properly specified. Two dimensional and three dimensional microstructures are optimized for maximum stiffness designs by combining the proposed method with the dual optimization algorithm of convex programming. Satisfactory results are obtained for a variety of design cases. The project supported by the National Natural Science Foundation of China (10372083, 90405016), 973 Program (2006CB601205) and the Aeronautical Science Foundation (04B53080). The English text was polished by Keren Wang.     

Stiffness and strength of hierarchical polycrystalline materials with imperfect interfaces

In this study we investigate the effect of imperfect (not perfectly bonded) interfaces on the stiffness and strength of hierarchical polycrystalline materials. As a case study we consider a honeycomb cellular polycrystal used for drilling and cutting tools. The conclusions of the analysis are, however, general and applicable to any material with structural hierarchy. Regarding the stiffness, generalized expressions for the Voigt and Reuss estimates of the bounds to the effective elastic modulus of heterogeneous materials are derived. The generalizations regard two aspects that are not included in the standard Reuss and Voigt estimates. The first novelty consists in considering finite thickness interfaces between the constituents undergoing damage up to final debonding. The second generalization consists of interfaces not perpendicular or parallel to the loading direction, i.e., when isostress or isostrain conditions are not satisfied. In this case, approximate expressions for the effective elastic modulus are obtained by performing a computational homogenization approach. In the second part of the paper, the homogenized response of a representative volume element (RVE) of the honeycomb cellular polycrystalline material with one or two levels of hierarchy is numerically investigated. This is put forward by using the cohesive zone model (CZM) for finite thickness interfaces recently proposed by the authors and implemented in the finite element program FEAP. From tensile tests we find that the interface nonlinearity significantly contributes to the deformability of the material. Increasing the number of hierarchical levels, the deformability increases. The RVE is tested in two different directions and, due to different orientations of the interfaces and Mixed Mode deformation, anisotropy in stiffness and strength is observed. Stiffness anisotropy is amplified by increasing the number of hierarchical levels. Finally, the interaction between interfaces at different hierarchical levels is numerically characterized. A condition for scale separation, which corresponds to the independence of the material tensile strength from the properties of the interfaces in the second level, is established. When this condition is fulfilled, the material microstructure at the second level can be efficiently replaced by an effective homogeneous continuum with a homogenized stress–strain response. From the engineering point of view, the proposed criterion of scale separation suggests how to design the optimal microstructure of a hierarchical level to maximize the material tensile strength. An interpretation of this phenomenon according to the concept of flaw tolerance is finally presented.     

A rigorous homogenization method for the determination of the overall ultimate strength of periodic discrete media and an application to general hexagonal lattices of beams

A rigorous method for the homogenization of general elastoplastic periodic lattices is presented. A discrete unit cell problem with finite number of degrees of freedom is solved for the determination of the overall elastic stiffness and ultimate strength of the lattice. Both static and kinematic methods are developed. It is shown that the overall yield strength domain of a large specimen, subjected to the so-called kinematically uniform boundary conditions, is asymptotically equal to the homogenized yield strength domain, as the size of the specimen goes to infinity. The method is applied to metallic honeycomb materials with arbitrary non-uniform cell wall thickness. New results concerning non-symmetric material distribution in the cell edges of the honeycomb are obtained. The model shows that the effects of this type of defect on the overall properties are less important than the already known effects of symmetric non-uniform cell wall thickness. Good agreement is observed between the proposed analytical beam model predictions and the finite element computations.     

Anisotropic effective higher-order response of heterogeneous Cauchy elastic materials

The homogenization results obtained by Bacca et al. (2013a), to identify the effective second-gradient elastic materials from heterogeneous Cauchy elastic solids, are extended here to the case of phases having non-isotropic tensors of inertia. It is shown that the nonlocal constitutive tensor for the homogenized material depends on both the inertia properties of the RVE and the difference between the effective and the matrix local elastic tensors. Results show that: (i) orthotropic nonlocal effects follow from homogenization of a dilute distribution of aligned elliptical holes and, in the limit case, of cracks; (ii) even under the dilute assumption and isotropic local effective behaviour, homogenization may lead to effective nonlocal orthotropic properties.     

Residual-stress measurement in orthotropic materials using the hole-drilling method

The hole-drilling method is used here to measure residual stresses in an orthotropic material. An existing stress-calculation method adapted from the isotropic case is shown not to be valid for orthotropic materials. A new stress-calculation method is described, based on the analytical solution for the displacement field around a hole in a stressed orthotropic plate. The validity of this method is assessed through a series of experimental measurements. A table of elastic compliances is provided for practical residual-stress measurements in a wide range of orthotropic materials.