An analytical multiscale model is presented in this article for the analysis of functionally graded nanocomposites. The multiscale scheme is composed of a microscale problem whose solution provides the constitutive model for the macroscale problem. For nanoparticle‐reinforced composites, the microscale problem consists of three phases, namely the nanoparticle, the matrix, and an interphase layer between the matrix and the nanoparticle. An analytical micromechanical model based on Green's function is employed to solve the triple‐phase microscale problem. The homogenized properties of the FG nanocomposite are determined by the micromechanical problem and used in the macroscale level, at every macroscopic material point in which the constitutive model is required. As an example, a nanocomposite beam under bending is considered as the macroscale problem which is investigated by classical, first‐order, and third‐order shear deformation theories. The results obtained from the presented method are compared with the relevant data for similar problems using various higher‐order elasticity theories. By comparing the results of higher‐order theories and those obtained by the presented multiscale method, the internal length parameter of the higher‐order theories is correlated to the volume fraction of the interphase layer between the nanoparticle and the matrix.

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基于微力学分析的多尺度模型，用于分析功能梯度纳米复合材料

本文介绍了一种用于分析功能梯度纳米复合材料的多尺度分析模型。多尺度方案由一个微观问题组成，其解决方案为宏观问题提供了本构模型。对于纳米颗粒增强的复合材料，微观问题包括三个阶段，即纳米颗粒，基质以及基质和纳米颗粒之间的中间层。采用基于格林函数的解析微机械模型来解决三相微尺度问题。FG纳米复合材料的均质特性是由微观力学问题决定的，并在需要构造模型的每个宏观材料点以宏观水平使用。举个例子，弯曲下的纳米复合梁被认为是宏观问题，它是由经典，一阶和三阶剪切变形理论研究的。使用各种高阶弹性理论，将从所提出的方法获得的结果与类似问题的相关数据进行比较。通过比较高级理论的结果和通过提出的多尺度方法获得的结果，高级理论的内部长度参数与纳米粒子和基质之间的相间层的体积分数相关。