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On the homogenization analysis of composite materials based on discretized fluctuations on the micro-structure

机译：基于微观结构离散波动的复合材料均质化分析

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The paper investigates a numerical procedure for the computation of the overall macroscopic elasticity moduli of linear composite materials with periodic micro-structure. We consider a homogenized macro-continuum with locally attached representative micro-structure which characterizes a representative cell of a composite. The deformation of the micro-structure is assumed to be coupled with the local deformation at a typical point of the macro-continuum by three alternative constraints of the microscopic fluctuation field. The underlying key approach is a finite element discretization of the boundary value problem for the fluctuation field on the micro-structure of the composite. This results into a distinct closed-form representation of the overall elasticity moduli in terms of a Taylor-type upper bound term and a characteristic softening term which depends on global fluctuation stiffness matrices of the discretized micro-structure. With this representation in hand, overall moduli of periodic composites can be computed in a straightforward manner for a given finite element discretization of the micro-structure. We demonstrate the concept for three types of periodic composites and compare the results with well-known analytical estimates. [References: 22]
机译：本文研究了一种计算具有周期性微结构的线性复合材料的整体宏观弹性模量的数值程序。我们考虑具有局部附着的代表性微观结构的均质化宏观连续体，该微观微观结构表征了复合材料的代表性细胞。通过微观波动场的三个替代约束条件，假设微观结构的变形与宏观连续体典型点处的局部变形有关。基本的关键方法是对复合材料微观结构上的波动场的边值问题进行有限元离散化。这导致以泰勒型上界项和特征软化项（以离散化微结构的整体波动刚度矩阵为基础）的整体弹性模量的清晰闭合形式表示。有了这种表示方法，对于给定的微观结构有限元离散化，可以以直接的方式计算出周期复合材料的整体模量。我们演示了三种类型的周期复合材料的概念，并将结果与​​众所周知的分析估计值进行比较。 [参考：22]

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