论文标题
在确定复合材料的有效固有磁性中的渐近均匀化
Asymptotic Homogenization in the Determination of Effective Intrinsic Magnetic Properties of Composites
论文作者
论文摘要
我们提出了一个计算框架，用于确定复合材料的固有磁渗透性。为此，考虑到线性磁静力学，使用了矢量和标量电势配方。我们用于解决细胞问题的均质化算法是基于Lukkassen等人中提出的位移方法。 1995年，复合材料工程，5（5），519-531。我们建议使用渗透率张量椭圆形的子午偏心率作为各向异性指数，该指数量化了线性磁反应中的方向性程度。作为应用程序问题，考虑到具有重叠和非重叠单分散磁盘的2D常规和随机微观结构，所有这些磁盘均为周期性。我们表明，对于消失的校正函数，衍生的有效磁渗透率张量分别与矢量和标量电势配方分别给出了（下）Reuss和（上）VOIGT边界。我们在周期性边界条件下的结果表明，与常规复合材料的分析解决方案非常一致，而对于随机异质材料，它们与体积元素大小的收敛速度很快。给定包含体积分数的具有单分散磁盘的材料系统的预测提供了最高的磁渗透性，并且包含相互作用最大。相比之下，常规平方晶格中的磁盘排列导致磁渗透性最低和包含相互作用不足。这种差异超出了各向同性有效培养基理论的范围，该理论仅将相体积分数和形状用作仅统计微结构描述符。
We present a computational framework for two-scale asymptotic homogenization to determine the intrinsic magnetic permeability of composites. To this end, considering linear magnetostatics, both vector and scalar potential formulations are used. Our homogenization algorithm for solving the cell problem is based on the displacement method presented in Lukkassen et al. 1995, Composites Engineering, 5(5), 519-531. We propose the use of the meridional eccentricity of the permeability tensor ellipsoid as an anisotropy index quantifying the degree of directionality in the linear magnetic response. As application problems, 2D regular and random microstructures with overlapping and nonoverlapping monodisperse disks, all of which are periodic, are considered. We show that, for the vanishing corrector function, the derived effective magnetic permeability tensor gives the (lower) Reuss and (upper) Voigt bounds with the vector and scalar potential formulations, respectively. Our results with periodic boundary conditions show an excellent agreement with analytical solutions for regular composites, whereas, for random heterogeneous materials, their convergence with volume element size is fast. Predictions for material systems with monodisperse overlapping disks for a given inclusion volume fraction provide the highest magnetic permeability with the most increased inclusion interaction. In contrast, the disk arrangements in regular square lattices result in the lowest magnetic permeability and inadequate inclusion interaction. Such differences are beyond the reach of the isotropic effective medium theories, which use only the phase volume fraction and shape as mere statistical microstructural descriptors.
