Overall elastoplastic property for micropolar composites with randomly oriented ellipsoidal inclusions

Overall linear and non-linear properties for micropolar composites containing 3D and in-plane randomly oriented inclusions are examined with an analytical micromechanical method. This method is based on Eshelby solution for a general ellipsoidal inclusion in a micropolar media and secant moduli method. The influence of inclusion’s shape, size and orientation on the classical effective moduli, yielding surface and non-linear stress and strain relation are examined. The results show that the effective moduli and non-linear stress–strain curves are always higher for micropolar composites than the corresponding classical composites. When the inclusion’s size is sufficiently large, the classical results can be recovered.     

Material properties of piezoelectric composites by BEM and homogenization method

Applications of boundary element method (BEM) to piezoelectric composites in conjunction with homogenization approach for determining their effective material properties are discussed in this paper. The composites considered here consist of inclusion and matrix phases. The homogenization model for composites with inhomogeneities is developed and introduced into a BE formulation to provide an effective means for estimating overall material constants of two-phase composites. In this model, a representative volume element (RVE) is used whose volume average stress and strain are calculated by the boundary tractions and displacements of the RVE. Thus BEM is suitable for performing calculations on average stress and strain fields of the composites. Numerical results for a piezoelectric plate with circular inclusions are presented to illustrate the application of the proposed micromechanics––BE formulation.     

A numerical method for homogenization in non-linear elasticity

In this work, homogenization of heterogeneous materials in the context of elasticity is addressed, where the effective constitutive behavior of a heterogeneous material is sought. Both linear and non-linear elastic regimes are considered. Central to the homogenization process is the identification of a statistically representative volume element (RVE) for the heterogeneous material. In the linear regime, aspects of this identification is investigated and a numerical scheme is introduced to determine the RVE size. The approach followed in the linear regime is extended to the non-linear regime by introducing stress–strain state characterization parameters. Next, the concept of a material map, where one identifies the constitutive behavior of a material in a discrete sense, is discussed together with its implementation in the finite element method. The homogenization of the non-linearly elastic heterogeneous material is then realized through the computation of its effective material map using a numerically identified RVE. It is shown that the use of material maps for the macroscopic analysis of heterogeneous structures leads to significant reductions in computation time.     

Identification of probabilistic distribution parameters for the mesoscopic stochastic fracture model

As a kind of multiphase composite material, the basic mechanical behaviors of concrete are randomness and nonlinearity. The mesoscopic stochastic fracture model (MSFM) which can reflect the coupling effect of randomness and nonlinearity, has been widely used for the nonlinear analysis of concrete structures. In this paper, we proposed a new stochastic modeling principle to identify the probabilistic distribution parameters of MSFM. In order to reduce the modeling works, a dimension-reduced algorithm is proposed as well. In this paper, an overview of MSFM is firstly presented to introduce the background of the research. Then the stochastic harmonic function (SHF) representation is introduced to express the random field mentioned in the MSFM, and the probability density evolution method (PDEM) is applied to obtain the theoretical probability density function (PDF) of the stress–strain relationships. Furthermore, a stochastic modeling principle is proposed, in which minimizing the Kullback–Leibler divergence (KLD) is taken as the optimization object. Based on the framework of genetic algorithm, a dimension-reduced algorithm is proposed to identify the parameters with reference to the data from tested complete curves of uniaxial compressive and uniaxial tensile stress–strain relationship of concrete. The results indicate that the proposed principle and algorithm can be used to identify the parameters of MSFM accurately and efficiently.     

Development of micromechanical models for granular media

Micromechanical analysis has the potential to resolve many of the deficiencies of constitutive equations of granular continua by incorporating information obtained from particle-scale measurements. The outstanding problem in applying micromechanics to granular media is the projection scheme to relate continuum variables to particle-scale variables. Within the confines of a projection scheme that assumes affine motion, contact laws based on binary interactions do not fully capture important instabilities. Specifically, these contact laws do not consider mesoscale mechanics related to particle group behaviour such as force chains commonly seen in granular media. The implications of this are discussed in this paper by comparison of two micromechanical constitutive models to particle data observed in computer simulations using the discrete element method (DEM). The first model, in which relative deformations between isolated particle pairs are projected from continuum strain, fails to deliver the observed behaviour. The second model accounts for the contact mechanics at the mesoscale (i.e. particle group behaviour) and, accordingly, involves a nonaffine projection scheme. In contrast with the first, the second model is shown to display strain softening behaviour related to dilatancy and produce realistic shear bands in finite element simulations of a biaxial test. Importantly, the evolution of microscale variables is correctly replicated. This paper is dedicated to Professor Ching S. Chang on the occasion of his 60th birthday.     

Mathematical homogenization theory for electroactive continuum

Two‐scale continuum equations are derived for heterogeneous continua with full nonlinear electromechanical coupling using nonlinear mathematical homogenization theory. The resulting coarse‐scale electromechanical continuum equations are free of coarse‐scale constitutive equations. The unit cell (or representative volume element) is subjected to the overall mechanical and electric field extracted from the solution of the coarse‐scale problem and is solved for arbitrary constitutive equations of fine‐scale constituents. The proposed method can be applied to analyze the behavior of electroactive materials with heterogeneous fine‐scale structure and can pave the way forward for designing advanced electroactive materials and devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Computational homogenization of regular cellular material according to classical elasticity

A two-scale computational homogenization method for deriving the effective elastic parameters of regular cell material is presented. In the present application, particle model is used as the micromechanical model and classical linear elasticity as the continuum model. The method is designed to render the same effective elastic parameters irrespective of the Representative Volume Element (RVE) used for a cell structure. This requires simultaneous fulfillment of the kinematic and kinetic conditions of computational homogenization derived in the study. Also, the relationship between the quantities of the micromechanical and continuum model needs to be invertible on a RVE. Effective elastic parameter expressions for eight planar cellular materials obtained with a typical cell as the RVE are compared to their counterparts in literature. As an application example, a new closed-form compliance expression covering e.g. the square, regular hexagon, rhombus, over-expanded hexagon, and re-entrant hexagon cell structures of literature is presented.     

Composite material design of two‐dimensional structures using the homogenization design method

Composite materials of two‐dimensional structures are designed using the homogenization design method. The composite material is made of two or three different material phases. Designing the composite material consists of finding a distribution of material phases that minimizes the mean compliance of the macrostructure subject to volume fraction constraints of the constituent phases, within a unit cell of periodic microstructures. At the start of the computational solution, the material distribution of the microstructure is represented as a pure mixture of the constituent phases. As the iteration procedure unfolds, the component phases separate themselves out to form distinctive interfaces. The effective material properties of the artificially mixed materials are defined by the interpolation of the constituents. The optimization problem is solved using the sequential linear programming method. Both the macrostructure and the microstructures are analysed using the finite element method in each iteration step. Several examples of optimal topology design of composite material are presented to demonstrate the validity of the present numerical algorithm. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

基于运动一致性的视频对象分割方法研究

视频运动对象检测和分割是图像处理中最具挑战性的问题之一。针对目前大部分分割算法相当复杂而且计算量大的问题，提出了一种基于运动一致性的视频对象分割方法。该方法从MPEG压缩码流中提取运动矢量场来分割视频对象，首先对运动矢量场进行滤波和校正，然后进行全局运动补偿得到对象的绝对运动矢量场，最后采用K-means聚类算法对运动矢量场进行聚类分析从而分割出感兴趣的视频运动对象。MPEG标准测试序列的试验结果证明，该方法是有效的。     

均质化法在分析非连续碳纳米管增强复合材料微观应力分布规律中的应用

利用具有精确周期性边界条件的均质化理论, 用宏微观有限元法分析了非连续碳纳米管呈规则和交错2 种排列情况下, 纳米管沿管长方向的应力分布规律。为保证传统的连续力学理论的适用性, 本文中的碳纳米管采用了用分子动力学方法简化的等效纤维模型。规则排列所得结果与应用Cox 剪滞理论及Lauke、Fu 等经典理论得出的结果比较发现: 除了经典理论中指出的碳纳米管长径比及纳米管体积含量2 个因素外, 纳米管形状及在基体中的排列方式对材料的力学性质也有较大影响。交错排列的纳米管在复合材料中有较高效率的应力转化和传递能力, 碳纳米管的端部间距(2 T_f ) 对应力的分布有较大的影响。结果显示出碳纳米管作为材料增强相的特殊性, 证明了均质化理论分析碳纳米管增强复合材料应力分布规律的可行性。      

Mesoscopic aspects of the computational homogenization with meshless modeling for masonry material

The multiscale homogenization scheme is becoming a diffused tool for the analysis of heterogeneous materials as masonry since it allows dealing with the complexity of formulating closed-form constitutive laws by retrieving the material response from the solution of a unit cell (UC) boundary value problem (BVP). The robustness of multiscale simulations depends on the robustness of the nested macroscopic and mesoscopic models. In this study, specific attention is paid to the meshless solution of the UC BVP under plane stress conditions, comparing performances related to the application of linear displacement or periodic boundary conditions (BCs). The effect of the geometry of the UC is also investigated since the BVP is formulated for the two simpliest UCs, according to a displacement-based variational formulation assuming the block indefinitely elastic and the mortar joints as zero-thickness elasto-plastic interfaces. It will be showed that the meshless discretization allows obtaining some advantages with respect to a standard FE mesh. The influence of the UC morphology as well as the BCs on the linear and nonlinear UC macroscopic response is discussed for pure modes of failure. The results can be constructive in view of performing a general Fe·Meshless or Meshless² analysis.     

Micromechanics based ply level material degradation model for unidirectional composites

The damaged response of a composite lamina depends on various mechanisms that take place at the microlevel, i.e., at the level of the fiber and matrix. The present work focuses on developing a ply level continuum damage model for point-wise stiffness degradation through simplified representation of the microlevel damage. A three dimensional micromechanical analysis of a single cell representative volume element is carried out for various volume fraction, and levels of damage. The model brings out the coupled effect of damage on the effective point-wise ply level stiffness. Further, the numerical results are employed to develop a functional continuum representation of stiffness degradation as a function of the damage parameters and fiber volume fraction perturbations. The micromechanics model is consistent with experimentally observed stiffness degradation, i.e., a strong influence of fiber breakage and fiber matrix debond, and a weak influence of normal cracking of matrix. The proposed model can be considered as an improved version of the widely accepted diffused (meso) damage models, i.e., DML. The study also gives a generalized and consistent definition for the free energy, which can be used for modeling growth of damage.     

Continuous approximation of material distribution for topology optimization

In this paper, we propose a checkerboard‐free topology optimization method without introducing any additional constraint parameter. This aim is accomplished by the introduction of finite element approximation for continuous material distribution in a fixed design domain. That is, the continuous distribution of microstructures, or equivalently design variables, is realized in the whole design domain in the context of the homogenization design method (HDM), by the discretization with finite element interpolations. By virtue of this continuous FE approximation of design variables, discontinuous distribution like checkerboard patterns disappear without any filtering schemes. We call this proposed method the method of continuous approximation of material distribution (CAMD) to emphasize the continuity imposed on the ‘material field’. Two representative numerical examples are presented to demonstrate the capability and the efficiency of the proposed approach against some classes of numerical instabilities. Copyright © 2004 John Wiley & Sons, Ltd.     

Mesh superposition-based multiscale stress analysis of composites using homogenization theory and re-localization technique considering fiber location variation

In this article, the accuracy of multiscale stress analysis of heterogeneous materials (unidirectional fiber-reinforced composite) was improved by considering microscopic geometrical variation using the mesh superposition method. When analyzing the stress distribution in a composite with the finite element method considering the variation of the fiber location, updating the mesh significantly is necessary; however, generating an appropriate mesh for a large geometrical variation is difficult. Therefore, we focused on the mesh superposition method, which can easily generate a numerical FE model, even if the internal structure is complex, because the matrix and inclusion can be expressed by the global mesh and local mesh independently. However, in the original mesh superposition method, the analysis accuracy may be degraded owing to the mesh overlap conditions. Therefore, an improved method was applied to the homogenization theory-based analysis. In this article, the effectiveness of the proposed approach was discussed by comparing the numerical results of this method with those of conventional mesh superposition method and standard finite element method. From the numerical results, accuracy improvement by the proposed approach for the multiscale stochastic stress analysis is confirmed.     

Analysis of damaged material containing periodically distributed elliptical microcracks by using the homogenization method based on the superposition method

The presence of multiple microcracks in a structural component causes material degradation such as reduction in the stiffness or reduction in the fracture toughness of the component. In this paper, the homogenization method is used to evaluate mechanical properties of the damaged material. The adaptation of the superposition method to the homogenization method is also presented. The proposed method makes use of the finite element solution of uncracked solid and the analytical solution. The effective elastic moduli of damaged materials containing lattice-distribution microcracks are estimated by the proposed method. Furthermore, the stress fields and the stress intensity factors of the elliptical microcracks in the damaged material at a micro-mechanics scale are evaluated to illustrate microscopic behavior such as crack interaction.     

Refined theory for the analysis of laminated orthotropic structures

A new higher-order theory for the analysis of laminated orthotropic plates and shells subject to both mechanical and thermal loads is developed. Using the variational approach the system of governing differential equations and corresponding boundary conditions are derived. Two refined models of the stress and strain state are considered, their application and accuracy are discussed. The analytical solution is obtained for plates and shells with the Navier boundary conditions on the side surfaces. The results of calculations are given and compared with an exact three-dimensional solution available in the literature. The influence of the laminated structure upon the exactness of results and the characteristics of stress–strain state is studied and discussed.     

Tsallis entropy in dual homogenization of random composites using the stochastic finite element method

This work concerns an application of the Tsallis entropy to homogenization problem of the fiber‐reinforced and also of the particle‐filled composites with random material and geometrical characteristics. Calculation of the effective material parameters is done with two alternative homogenization methods—the first is based upon the deformation energy of the Representative Volume Element (RVE) subjected to the few specific deformations, while the second uses explicitly the so‐called homogenization functions determined under periodic boundary conditions imposed on this RVE. Probabilistic homogenization is made with the use of three concurrent non‐deterministic methods, namely Monte‐Carlo simulation, iterative generalized stochastic perturbation technique as well as the semi‐analytical approach. The last two approaches are based on the Least Squares Method with polynomial basis of the statistically optimized order— this basis serves for further differentiation in the 10th‐order stochastic perturbation technique, while semi‐analytical method uses it in probabilistic integrals. These three approaches are implemented all as the extensions of the traditional Finite Element Method (FEM) with contrastively different mesh sizes, and they serve in computations of Tsallis entropies of the homogenized tensor components as the functions of input coefficient of variation.