复合材料热传导系数均匀化计算的实现方法

均匀化理论可以有效预测周期性结构复合材料的等效热传导系数,然而其控制方程的载荷项形式特殊,通用有限元软件中没有对应的载荷形式,难以直接求解.提出一种本构关系及场变量的类比方法,证明了在此类比下等效热传导系数均匀化方程与等效弹性模量均匀化方程是等价的.根据求解等效弹性模量均匀化方程的热应变法,提出一种新的等效热传导系数均匀化方程数值求解方法.以ABAQUS为平台,预测单向纤维复合材料以及金属蜂窝夹芯板的等效热传导系数,计算结果与参考值吻合良好.该方法为基于通用有限元软件的复合材料等效热传导系数的均匀化计算提供了简便途径.     

渐进均匀化理论研究复合材料有效力学性能

本文利用渐进均匀化理论,详细叙述了求解具有周期性细观单元结构的复合材料有效力学性能的方法,并结合有限元理论和周期性边界条件,给出了求解渐进均匀化方程的过程,为实际工程问题提供了预测材料力学性能的方法.     

基于有限元法的正交各向异性复合材料结构材料参数识别

以大型商用有限元软件ABAQUS为计算平台,提出了正交各向异性复合材料结构材料参数的识别方法。将材料参数识别的问题转化为极小化目标函数的问题,其中目标函数定义为测量位移与有限元计算的相应位移之差的平方和。采用Levenberg-Marquardt方法极小化目标函数,其中灵敏度的计算基于复合材料的有限元离散结构的求解方程对识别的材料参数求导。数值算例表明本文中提出的方法是有效的。在识别参数过程中,参数的初值以及搜索范围的确定对于识别结果有着重要影响。因此必须充分利用材料参数的先验信息。ABAQUS是高效可靠的商用有限元软件,提出的参数识别方法基于这类商用软件,因而该方法有很强的实用性。     

等代数结构面网格剖分下三维弹性问题的代数多重网格法

在一种等代数结构面网格剖分下,建立了求解三维弹性问题有限元方程的代数多重网格法及相应的预处理共轭梯度法,详细描述了代数多重网格方法中网格粗化技术与插值算子的构造,并将所构造的代数多重网格法应用于某些实际问题如非均匀介质、高应力梯度问题的数值求解。结果表明,建立的代数多重网格法对求解三维弹性问题是十分有效的,具有很好的鲁棒性,较直接解法和其它常用迭代方法具有明显的优越性。     

基于均匀化理论的三维编织复合材料细观应力数值模拟

从基于小参数渐近展开和摄动方法的均匀化理论出发,给出了求解细观应力的数学表达式。通过有限元方法对三维编织复合材料的细观应力场进行数值模拟,并结合适当的强度准则对拉伸极限强度下单元的失效情况进行判断,得出材料强度的一种细观失效判据。通过该方法得到的应力计算结果与实验结论基本相符。      

基于均匀化理论的三维编织复合材料弯曲细观应力数值模拟

从基于小参数渐近展开的多尺度均匀化理论出发,对三维编织复合材料的弯曲细观应力进行数值模拟。首先给出了等效弹性模量和细观应力的均匀化列式及有限元求解方程,然后讨论了三维编织复合材料细观单胞周期性边界条件的施加方法,最后对三点弯曲作用下三种单胞内应力分布进行了数值模拟。通过模拟比较了不同类型单胞及不同编织角材料弯曲应力的差异,总结出一些有益的结论,这些结论与实验结论都比较吻合。     

三维四向大编织角复合材料的细观强度分析

编织角是影响三维编织复合材料力学性能的最重要因素.实验数据表明:大编织角复合材料在单向拉伸作用下的破坏形式较为复杂,其应力-应变曲线呈现非线性特性.本文建立了细观应力场的均匀化列式和有限元求解方法,运用该方法对三维大编织角复合材料的细观应力分布进行了数值模拟,结合相关的强度理论对材料进行失效分析,并进一步对材料的拉伸强度进行预测.强度计算结果与实验结果较为吻合.     

周期性材料非经典热传导时空间多尺度分析方法

研究了一种空间-时间多尺度的方法,来分析周期性材料中非傅立叶热传导问题。计算模型是根据空间-时间尺度的高阶均匀化理论建立的,通过引入放大空间尺度和缩小时间尺度,研究了由空间非均匀性引起的非傅立叶热传导的波动效应和非局部效应。合并不同阶的均匀化非傅立叶热传导方程,消去缩小时间尺度参数,得到四阶微分方程。并进一步用C0连续修正了高阶非局部热传导方程的有限元近似解,使问题的求解避免了对有限元离散的C1连续性要求。给出的数值算例讨论了各种情况下方法的正确性与有效性。      

基于单胞数字化模型的复合材料本构关系三维数值模拟

在渐进均匀化理论基础上, 建立了基于单胞数字化模型的复合材料宏观等效弹性性能的三维数值分析方法(DCB-FEA) 。该方法采用三维光栅化技术将三维单胞模型转化为三维光栅图形(数字化模型) , 并将光栅图形直接转化为三维有限元求解网格。产生的离散单元具有相同的几何尺寸和规则的形状, 单元刚度矩阵的数量将减少为单胞材料的个数。此外, 单胞数字化模型仅需记录每个离散单元的材料种类, 其他参数如单元节点编号、节点坐标等均可在求解过程中自动生成, 周期性边界条件也可以自动施加。随着分辨率的提高, 单胞数字化模型将产生更多数量的单元, 特别是对于三维单胞模型, 集成整体刚度矩阵时需要大量的计算机内存。采用基于Element-by-element 策略的预处理共轭梯度法( EBE- PCG) , 有限元方程的求解在单元级上进行, 避免了整体刚度矩阵的集成。通过对单向纤维增强复合材料的线弹性本构关系的数值模拟, 表明该方法可得到较为准确的复合材料等效模量。      

含界面相的单向纤维增强复合材料三维应力场的二重双尺度方法

提出了计算含界面相的单向纤维增强复合材料三维应力的二重双尺度方法。在性能预报方面,首先对界面相和纤维进行均匀化得到均匀化夹杂,然后对均匀化夹杂和基体进行均匀化得到宏观均匀材料;在应力场描述方面,从宏观均匀场出发,利用双尺度渐近展开技术经过两次应力场传递,依次得到单胞和应力集中区域的应力场。与有限元方法相结合,计算了宏观轴向均匀拉伸载荷条件下含界面相的单向纤维增强复合材料的三维应力场分布。数值结果表明在此载荷条件下最大应力发生在每根纤维的中截面内,靠近纤维与界面相的交界处。讨论了界面相性能对应力场分布的影响,结果显示纤维、界面相与基体力学性能的等差过渡有利于缓解纤维在界面附近的应力集中。      

Mechanical analysis of 3-D braided composites by the finite multiphase element method

A finite multiphase element method (FMEM), in which the element comprises more than one kind of material, has been proposed to predict the effective elastic properties of 3-D braided composites. This method is based on the variational principle and our previous geometric model that assumes the existence of different types of unit cells in the three regions in a 3-D braided composite, i.e. the interior, surface and corner. The numerical procedure involved two steps. First, a fine local mesh at the unit cell level is used to analyze the stress/strain of each unit cell. Then, a relatively coarse global mesh is used to obtain the overall responses of the composite at macroscopic level. By using the stress volume averaging method, the effective elastic properties of the composite can be calculated under the prescribed uniform strain boundary conditions. Finally, the predicted stress/strain curves are compared with experimental results, demonstrating the applicability of the FME method.     

Surface effects in composite materials: Two simple examples

It is well known that the local fields near the boundaries of composites are dissimilar to those existing within the bulk composite. Among all the methods used to study this area, the homogenization process for periodic structures gives the more accurate results, when it plays; but the method is in general heavy and so the main facts cannot be pointed out in a simple manner. The aim of the paper is to present two simple examples where analytical results are available almost right to the end. By using the homogenization process for periodic structures, macroscopic and local fields in a bilaminated composite are determined for two macroscopic boundary value problems: a percolation through a porous composite and a compression of an elastic composite. It is shown that the local fields obtained from the process and valid within the composite must be complemented by boundary layers along its boundaries. Because of these boundary layers, surface effects appear. For the simple compression test applied to an elastic composite, stresses can be infinite at the boundary, so that two modes of failure are predicted: a failure in the bulk material and a failure due to the boundary (surface effect). The first one can be macroscopically studied by using the concepts of the mechanics of continuous media. It is not possible for the second one.     

Boundary element method homogenization of the periodic linear elastic fiber composites

The paper presented is devoted to the Boundary Element Method based homogenization of the periodic transversely isotropic linear elastic fiber-reinforced composites. The composite material under consideration has deterministically defined elastic properties while its components are perfectly bonded. To have a good comparison with the FEM-based computational techniques used previously, the additional Finite Element discretization is presented and compared numerically against BEM homogenization implementation on the example of engineering glass–epoxy composite. The homogenization method proposed has rather general characteristics and, as it is shown, can be easily extended on n-component composites. On the contrary, we can consider and homogenize the heterogeneous media with randomly defined material properties using Monte-Carlo simulation technique or second order perturbation second probabilistic moment approach.     

On semi‐analytical probabilistic finite element method for homogenization of the periodic fiber‐reinforced composites

The main aim of this paper is a development of the semi‐analytical probabilistic version of the finite element method (FEM) related to the homogenization problem. This approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method. It originates from the generalized stochastic perturbation‐based FEM, where Taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions. The hybrid computational implementation of the system MAPLE with homogenization‐oriented FEM code MCCEFF is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber‐reinforced composites. Although numerical illustration deals with a homogenization of a composite with material properties defined as Gaussian random variables, other composite parameters as well as other probabilistic distributions may be taken into account. The methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements, finite differences or volumes as well as for meshless numerical strategies. Copyright © 2011 John Wiley & Sons, Ltd.     

Effective mechanical properties of EM composite conductors: an analytical and finite element modeling approach

An analytical model and numerical approach to predict the effective mechanical properties of a composite conductor consisting of metallic core and insulation layers are presented in this paper. The analytical model was developed based on a two-step homogenizations and mechanics analysis for composite unit cell. The Step 1 homogenization derives the effective properties of the out-wrapped composite insulation layers. The Step 2 homogenization further smears the metallic core and the effective composite insulation layers to develop homogenized mechanical properties for composite conductor according to appropriate homogenization sequences. The procedure of using numerical approach and finite element method to determine the unit cell effective constants were also described and the results of the FEA prediction were presented. The analytical predictions were compared well to the numerical results for the nine material constants that characterize the effective mechanical properties of the composite conductor.     

On numerical evaluation of effective material properties for composite structures with rhombic fiber arrangements

This paper deals with unidirectional fiber reinforced composites with rhombic fiber arrangements. It is assumed, that there is a periodic structure on micro level, which can be taken by homogenization as a representative volume element (RVE) for the composite, where the composite phases have isotropic or transversely isotropic material characterizations. A special procedure is developed to handle the primary non-rectangular periodicity with common numerical homogenization techniques based on FE-models. Due to appropriate boundary conditions applied to the RVE elastic effective macroscopic coefficients are derived. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the special orthotropic behavior of such composites caused by the rhombic fiber arrangement.     

A dual homogenization and finite element approach for material characterization of textile composites

A novel procedure for predicting the effective nonlinear elastic moduli of textile composites through a combined approach of the homogenization method and the finite element formulation is presented. The homogenization method is first applied to investigate the meso-microscopic material behavior of a single fiber yarn based on the properties of the constituent phases. The obtained results are compared to existing analytical and experimental results to validate the homogenization method. Very good agreements have been obtained. A unit cell is then built to enclose the characteristic periodic pattern in the textile composites. Various numerical tests such as uni-axial and bi-axial extension and trellising tests are performed by 3D finite element analysis on the unit cell. Characteristic behaviors of force versus displacement are obtained. Meanwhile, trial mechanical elastic constants are imposed on a four-node shell element with the same outer size as the unit cell to match the force–displacement curves. The effective nonlinear mechanical stiffness tensor is thus obtained numerically as functions of elemental strains. The procedure is exemplified on a plain weave glass composite and is validated by comparing to experimental data. Using the proposed approach, the nonlinear behavior of textile composites can be anticipated accurately and efficiently.     

Analysis and optimization of heterogeneous materials using the variational asymptotic method for unit cell homogenization

The variational asymptotic method for unit cell homogenization is used to find the sensitivity of the effective properties of periodically heterogeneous materials, within a periodic base-cell. The sensitivities are found by the direct differentiation of the variational asymptotic method for unit cell homogenization (VAMUCH) and by the method of adjoint variables. This sensitivity theory is implemented using the finite element method and the engineering program VAMUCH. The methodology is used to design the periodic microstructure of a material that allows obtaining prescribed constitutive properties. The microstructure is modeled as a 2D periodic structure, but a complete set of 3D material properties are obtained. Furthermore, the present methodology can be used to perform the micromechanical analysis and related sensitivity analysis of heterogeneous materials that have 3D periodic structures. The effective material properties of the artificially mixed materials of the microstructure are obtained by the density approach, in which the solid material and void are mixed artificially.     

Numerical homogenization of heterogeneous and cellular materials utilizing the finite cell method

We present a new approach for the numerical homogenization of cellular and heterogeneous materials. The procedure is based on the finite cell method, which is applied to efficiently discretize representative volume elements for which effective material properties are computed. The starting point for our homogenization might be either a computer-aided design of a heterogeneous material or a three-dimensional computer tomography (CT-scan) of the specimen of interest. A fully automatic discretization in terms of finite cells, applying a hierarchic extension process to control the discretization error, is utilized to solve the corresponding boundary value problems arising during the homogenization. Special emphasis is placed on the numerical treatment of boundary conditions. To this end we apply the window method, which can be interpreted as a variant of the self-consistency method. Several numerical examples ranging from porous materials to fiber-reinforced composites will be presented, demonstrating the efficiency of our approach. The homogenization procedure will be also applied to a foam, a CT-scan of which is available.