Estimation of macroscopic properties of heterogeneous materials has always posed significant problems. Procedures based on numerical homogenization, although very flexible, consume a lot of time and computing power. Thus, many attempts have been made to develop analytical models that could provide robust and computationally efficient tools for this purpose. The goal of this paper is to develop a reliable analytical approach to finding the effective elastic–plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to examine the anisotropy induced by regular inhomogeneity arrangements. The proposed framework is based on the idea of Molinari & El Mouden (1996) to improve classical mean-field models of thermoelastic media by taking into account the interactions between each pair of inhomogeneities within the material volume, known as a cluster model. Both elastic and elasto-plastic regimes are examined. A new extension of the original formulation, aimed to account for the non-linear plastic regime, is performed with the use of the modified tangent linearization of the metal matrix constitutive law. The model uses the second stress moment to track the accumulated plastic strain in the matrix. In the examples, arrangements of spherical inhomogeneities in three Bravais lattices of cubic symmetry (Regular Cubic, Body-Centered Cubic and Face-Centered Cubic) are considered for two basic material scenarios: “hard-in-soft” (MMC) and “soft-in-hard” (PM). As a means of verification, the results of micromechanical mean-field modeling are compared with those of numerical homogenization performed using the Finite Element Method (FEM). In the elastic regime, a comparison is also made with several other micromechanical models dedicated to periodic composites. Within both regimes, the results obtained by the cluster model are qualitatively and quantitatively consistent with FEM calculations, especially for volume fractions of inclusions up to 40%.

中文翻译：

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弹塑性复合材料中规则颗粒分布的各向异性效应：改进的切线簇模型和数值均匀化


异质材料宏观特性的估计一直是一个重大问题。基于数值均质化的程序虽然非常灵活，但消耗大量时间和计算能力。因此，人们已经做出了许多尝试来开发分析模型，这些模型可以为此目的提供强大且计算高效的工具。本文的目标是开发一种可靠的分析方法，以找到具有预定义颗粒或空隙分布的金属基复合材料（MMC）和多孔金属（PM）的有效弹塑性响应，并检查由规则的不均匀排列。所提出的框架基于 Molinari & El Mouden (1996) 的想法，通过考虑材料体积内每对不均匀性之间的相互作用（称为簇模型）来改进热弹性介质的经典平均场模型。弹性和弹塑性状态都被检查。通过使用金属基体本构定律的修正切线线性化，对原始公式进行了新的扩展，旨在解释非线性塑性状态。该模型使用第二应力矩来跟踪基体中累积的塑性应变。在示例中，针对两种基本材料场景考虑了三种立方对称布拉维晶格（正则立方、体心立方和面心立方）中球面不均匀性的排列：“硬中软”(MMC) 和“软” -in-hard”（PM）。作为验证手段，将微机械平均场建模的结果与使用有限元法 (FEM) 执行的数值均匀化的结果进行比较。 在弹性状态下，还与其他几种专用于周期性复合材料的微观力学模型进行了比较。在这两种情况下，聚类模型获得的结果在定性和定量上与 FEM 计算一致，特别是对于高达 40% 的夹杂物体积分数。