Elastoplastic modeling of circular fiber-reinforced ductile matrix composites considering a finite RVE

A micromechanical elastoplastic damage model considering a finite RVE is proposed to predict the overall elastoplastic damage behavior of circular fiber-reinforced ductile (matrix) composites. The constitutive damage model proposed in our preceding work (Kim and Lee, 2009) considering a finite Eshelby’s tensor (Li et al., 2005, Wang et al., 2005) is extended to accommodate the elastoplastic behavior of the composites. On the basis of the exterior-point Eshelby’s tensor for circular inclusions and the ensemble-averaged effective yield criterion, a micromechanical framework for predicting the effective elastoplastic damage behavior of ductile composites is derived. A series of numerical simulations are carried out to illustrate stress–strain response of the proposed micromechanical framework and to examine the influence of a Weibull parameter on the elastoplastic behavior of the composites. Furthermore, comparisons between the present predictions and experimental data available in the literature are made to further assess the predictive capability of the proposed model.     

Revisiting the generalized self-consistent scheme in composites: Clarification of some aspects and a new formulation

The determination of an effective property in composite materials necessitates the knowledge of some averaged field quantities in the constituents (like the average heat intensity or average strain) of a composite sample, which is subjected to homogeneous boundary conditions. In the generalized self-consistent scheme (GSCS) which is today a classical micromechanics model suited for the determination of the effective properties of matrix-based composites, those average quantities are estimated by using an auxiliary configuration in which a particulate phase is first surrounded by some matrix material and then embedded in the effective medium. In the present study, we revisit the GSCS both for two- and multi-phase matrix-based composites containing spherical particles, and clarify aspects related to the volume fractions of the particle core and matrix shell within the composite element which is embedded in the effective medium. The contribution of this study is believed to be mainly on the conceptual side and resides in a new formulation of the method in which the embedding volume fractions are determined in the course of the analysis by means of some fundamental relations on the averaged fields. The study is carried out in thermal conduction and elasticity and contains new results on the effective shear modulus of multi-phase composites.     

A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial

The present study is devoted to the development and validation of a nonlinear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modeled as an heterogeneous composite composed of an elastoplastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill [Hill, R., 1965. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89–101]. The approach consists in formulating the macroscopic tangent operator of the material by considering the nonlinear local behavior of each phase. Due to the matrix/inclusion morphology of the microstructure of the argillite, a Mori–Tanaka scheme is considered for the localization step. The developed model is first compared to Finite Element calculations and then validated and applied for the prediction of the macroscopic stress–strain responses of argillites.     

含夹杂复合材料宏观性能研究

本文综述并评价了有关含夹杂复合材料的有效弹性模量研究的代表性工作，包括自洽理论，微分法，Ｅｓｈｅｌｂｙ－Ｍｏｒｉ－Ｔａｎａｋａ法，Ｈａｓｈｉｎ和Ｓｈｔｒｉｋｍａｎ的变分法等。指出上述理论由于没有充分考虑复合材料内部的微结构特征，如夹杂的形状、几何尺寸、分布和夹杂间的相互影响，在夹杂的体积份数较大，如大于０．３时已不能有效地预报复合材料的有效弹性模量，随后介绍了近来才发展起来的一种新方法─—相关函数积分法，理论与实验的结果的比较表明，该方法在夹杂体积份数较大时仍然有效。     

Micromechanics predictions of the effective moduli of magnetoelectroelastic composite materials

In this paper, the self-consistent, generalized Mori–Tanaka and dilute micromechanics theories are extended to study the coupled magnetoelectroelastic composite materials. The heterogeneous inclusion problem of magnetoelectroelastic behavior is formulated in terms of five interaction tensors related to the Green's functions for an infinite three-dimensional transversely isotropic magnetoelectroelastic solid. These tensors are then used to predict the effective moduli of the magnetoelectroelastic solid based on the self-consistent, Mori–Tanaka and the dilute approaches. Numerical results are obtained for various types of inclusions. These results are employed to study the effects of the inclusion properties, such as moduli, volume fractions, shapes, etc., on the effective moduli of magnetoelectroelastic composites, in particular, the related magnetic properties. The results obtained using the self-consistent model, the generalized Mori–Tanaka's model and the dilute approach are compared with the existing experimental and theoretical results.     

Asymptotic modelling of heat conduction in a particulate composite with imperfect contact between the components

The paper outlines an approach to the analysis of periodically inhomogeneous composites with imperfect contact between the components. The heat-conduction problem for a particulate composite with an infinite matrix and simple cubic lattices of spherical inclusions is solved. Approximate solutions for the effective heat-conductivity coefficient and local heat fluxes at the microlevel are found. The results are obtained for arbitrary conductivity and volume fractions of the components     

Computational studies on high-stiffness,high-damping SiC–InSn particulate reinforced composites

With the objective of achieving composite material systems that feature high stiffness and high mechanical damping, consideration is given here to unit cell analysis of particulate composites with high volume fraction of inclusions. Effective elastic properties of the composite are computed with computational homogenization based on unit cell analysis. The correspondence principle together with the viscoelastic properties of the indium–tin eutectic matrix are then used to compute the effective viscoelastic properties of the composite. Comparison is made with parallel experiments upon composites with an indium–tin eutectic matrix and high volume fractions of silicon-carbide reinforcement. The analytical techniques indicate that combinations of relatively high stiffness and high damping can be achieved in particulate composites with high SiC volume fractions. Based on analysis, the tradeoffs between stiffness and damping characteristics are assessed by changing the volume fraction, size, packing, and gradation of the particulate reinforcement phases. Practical considerations associated with realization of such composites based on the surface energy between the SiC and the InSn are discussed.     

Electroelastic behavior modeling of piezoelectric composite materials containing spatially oriented reinforcements

In this work, a modeling of electroelastic composite materials is proposed. The extension of the heterogeneous inclusion problem of Eshelby for elastic to electroelastic behavior is formulated in terms of four interaction tensors related to Eshelby’s electroelastic tensors. Analytical formulations of interaction tensors are presented for ellipsoidal inclusions. These tensors are basically used to derive the self-consistent model, Mori–Tanaka and dilute approaches. Numerical solutions are based on numerical computations of these tensors for various types of inclusions. Using the obtained results, effective electroelastic moduli of piezoelectric multiphase composites are investigated by an iterative procedure in the context of self-consistent scheme. Generalised Mori–Tanaka’s model and dilute approach are re-formulated and the three models are deeply analysed. Concentration tensors corresponding to each model are presented and relationships of effective coefficients are given. Numerical results of effective electroelastic moduli are presented for various types of piezoelectric inclusions and for various orientations and compared to existing experimental and theoretical ones.     

Generalized self-consistent estimation of the apparent isotropic elastic moduli and minimum representative volume element size of heterogeneous media

Under investigation is a heterogeneous material consisting of an elastic homogeneous isotropic matrix in which layered elastic isotropic inclusions or pores are embedded. The generalized self-consistent model (GSCM) is extended so as to be capable of estimating the apparent elastic properties of a finite-size specimen smaller than a representative volume element (RVE). The kinematical or static apparent shear modulus is determined as a root of a cubic polynomial equation instead of a quadratic polynomial equation as in the classical GSCM of Christensen and Lo [Christensen, R.M., Lo, K.H., 1979. Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330]. It turns out that the extended GSCM establishes a link between the composite sphere assemblage model (CSAM) of Hashin [Hashin, Z., 1962. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29, 143–150] and the classical GSCM. Demanding that the normalized distance between the kinematical and static apparent moduli of a finite-size specimen be smaller than a certain tolerance, the minimum RVE size is estimated in a closed form.     

弹塑性复合材料力学性能的细观研究

应用细观力学的Eshelby等效夹杂理论研究了复合材料的弹塑性问题。以铝基复合材料为例,建立了多轴载荷下复合材料弹塑性应力-应变关系,并且理论预报与实验结果符合较好,分析了夹杂形状、体积分数及加载路径对材料宏观性能的影响。同时,还研究了热塑性复合材料热膨胀系数与工艺温度之间的变化规律,分析了热残余应变对材料设计的影响。     

Assessment of existing and introduction of a new and robust efficient definition of the representative volume element

Accurate numerical homogenization necessitates the thorough determination of the Representative Volume Element (RVE). There exists several seminal works on the notion of the RVE in homogenization, its definitions and methods of determination for efficient computation of composite effective properties. The objective of the current work is to assess the ability of numerical RVE determination methods to deliver accurate effective properties of composite materials. This paper demonstrates that common and well-established RVE determination methods, based on studying the convergence rate of the effective properties with respect to the volume element size, are invalid for the case of composites reinforced by randomly oriented fibers and yield erroneous estimates of their effective properties. Following the failure of traditional RVE determination methods, we proposed a new RVE determination criterion that is not based on the average property stability, but its statistical variations. Our new proposed criterion has been shown to be more accurate than other criteria in computing the effective properties of composites for aspect ratios up to 60. Moreover, the proposed criterion does not necessitate a convergence study over the volume element size, hence reducing considerably the RVE determination cost. Finally, our work questions the validity of many published works dealing with composites including heterogeneities of high aspect ratios.     

Constitutive modelling of cyclic plasticity of metal particulate-reinforced brittle matrix composites under compression-compression loading

The Mori-Tanaka approach is used to modelling metal particulate-reinforced brittle matrix composites under cyclic compressive loading. The J₂-flow theory is considered as the relevant physical law of plastic flow in inclusions. Ratchetting of the composite is prevented by the strong constraint exerted by the matrix on the inclusions, even under the assumption of evanescent kinematic hardening. However, the weakening constraint power of the matrix caused by microfracture damage around inclusions is closely coupled with the plasticity of inclusion and leads to ratchetting even when the plastic deformation of inclusions is described by an isotropic hardening rule. A detailed parametric study has revealed that ratchetting is followed by either plastic or elastic shakedown, depending on the load amplitude, composite parameters and the mean length of microcracks.     

广义自洽Mori-Tanaka模型及涂层夹杂体复合材料的有效模量

经典广义自洽模型的最大不足是需要确定相材料的位移及应变场,这一过程十分繁杂,而且最后得到的有交剪切模量无法显式表达难以应用,该文摈弃这一经典做法,而从广义自洽模型的应变等价条件出发,在夹杂应变均匀的近似假定下,将Ｈｉｌｌ界面条件应用于整个二相体内,从而得到一种可以预报涂层夹杂体复合材料有效模量的广义自洽Ｍｏｒｉ－Ｔａｎａｋａ模型,与已有的实验及理论的比较表明,该模型准确可靠,而且有效体积和剪切模量     

基于细观力学方法的混凝土热膨胀系数预测

建立混凝土材料的有效性质与微结构参数之间的关系,是混凝土材料优化设计的基础。本文用细观力学方法对复合材料宏观有效热膨胀系数进行研究,得到了含有一球形夹杂物的无限大介质在均匀变温作用下的应力场。假定混凝土为由骨料和砂浆基质组成的二相复合材料,根据混凝土宏观体积热膨胀量与组成混凝土的各相介质细观体积热膨胀量相等的原则,采用基于Mori-Tanaka方法的混凝土宏观有效剪切模量,推导出混凝土有效热膨胀系数的解答。对稀疏解法、自洽方法和有限单元数值试验结果的比较说明,本文提出的基于自洽方法的混凝土宏观有效热膨胀系数的理论公式能够较好的描述混凝土的热学特性,该方法可以推广到多相复合材料宏观有效热膨胀系数的预测中。     

Modeling of anisotropic polydispersed composites by progressive micromechanical approach

A progressive micromechanical method is presented in order to predict the elastic constants of polydispersed composites including multi-directional or randomly oriented reinforcement particles. Heterogeneities of various types are introduced into the matrices in a gradual manner. At each step, the Mori-Tanaka method is used to obtain the stiffness tensor of the intermediate medium used as a matrix of the following step. The proposed method is capable of introducing any kind of heterogeneities based on their dimensions, orientations, mechanical properties, and volume fractions to the matrix. Furthermore, suitable probability density functions can be defined for physical and structural parameters of the composite, including the level of the filler-matrix interfacial bonding, the aspect ratio, and the orientation of reinforcement particles. The efficiency of the iterative approach and the convergence of the solution are studied by computing the stiffness tensors of unidirectional and bidirectional particulate composites. The results of the present study are also compared with the literature data for a randomly oriented particulate composite.     

计算微裂纹损伤材料有效模量的一种简单方法

给出了一种基于Taylor模型的有效介质方法。用以计算微裂纹相互作用对有效本构关系的影响,该方法假设每一个微裂纹位于一种有效介质之中,该有效介质的弹性模量由不考虑微裂纹相互作用的Taylor模型计算、和自洽方法相比,这种方法计算简单,而且结果更准确。     

纤维增强金属基复合材料整体蠕变性能的细观力学分析

高温下金属基复合材料的蠕变主要由基体蠕变和界面扩散蠕变两部分构成,以往的研究中常常只考虑其中一种蠕变机理,从而导致得到的规律具有较大的局限性．本文提出了一种可预测金属基复合材料整体蠕变性能的细观力学方法,同时考虑了基体蠕变和界面扩散蠕变两种蠕变机理,导出了具有张量形式并满足不可压缩性的界面扩散蠕变应变表达式．采用Mori-Tanaka法和自洽法二者结果的平均以便更准确地计算纤维中的应力,揭示了两种蠕变机理相互影响的竞争关系．研究了恒定双轴荷载下的总体蠕变和固定位移约束下的应力松弛这两种常见蠕变问题,探究了基体蠕变与界面扩散蠕变两种蠕变机理在总蠕变中发挥的作用,考察了不同加载条件和不同纤维体积分数对复合材料整体蠕变行为的影响．     

Thermomechanical Multiscale Constitutive Modeling: Accounting for Microstructural Thermal Effects

In this work we present a thermomechanical multiscale constitutive model for materials with microstructure. In these materials thermal effects at microscale have an impact on the effective macroscopic stress. As a result, it turns out that the homogenized stress depends upon the macroscopic temperature and its gradient. In order to allow this interplay to be thermodynamically valid, we resort to a macroscopic extended thermodynamics whose elements are derived from the microscopic behavior using homogenization concepts. Hence, the thermodynamics implications of this new class of multiscale models are discussed. A variational approach based on the Hill–Mandel Principle of Macro-homogeneity, and which makes use of the volume averaging concept over a local representative volume element (RVE), is employed to derive the thermal and mechanical equilibrium problems at the RVE level and the corresponding homogenization expressions for the effective heat flux and stress. The material behavior at the RVE level is described through standard phenomenological constitutive models. To sum up, the novel contribution of the model presented here is that it allows to include the microscopic temperature fluctuation field, obtained from the multiscale thermal analysis, in the micro-mechanical problem at the RVE level while keeping thermodynamic consistency.