热扩散复合材料的多尺度渐近均匀化分析
Multiscale asymptotic homogenization analysis of thermo-diffusive composite materials
摘要：
本文提出了一种分析热扩散作用下具有周期性微结构的复合材料的渐近均匀化方法。适当的降尺度关系相关联的微观领域的宏观位移，温度和质量浓度的介绍。材料的不均匀性的影响所描述的扰动函数来自递归细胞问题的解决方案。导出了等效一阶热扩散连续体的整体弹性常数和热扩散常数的精确表达式。所提出的方法适用于二维双相正交各向异性层状材料的情况下，有效的弹性和热扩散性能可以确定解析。考虑到这个说明性的例子，并假设周期性的体力，热和质量源作用在介质上，由一阶均匀化方法进行的解决方案进行了比较，通过非均匀模型得到的数值结果。
英文摘要：
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the macroscopic displacements, temperature and mass concentration are introduced. The effects of the material inhomogeneities are described by perturbation functions derived from the solution of recursive cell problems. Exact expressions for the overall elastic and thermodiffusive constants of the equivalent first order thermodiffusive continuum are derived. The proposed approach is applied to the case of a two-dimensional bi-phase orthotropic layered material, where the effective elastic and thermodiffusive properties can be determined analytically. Considering this illustrative example and assuming periodic body forces, heat and mass sources acting on the medium, the solution performed by the first order homogenization approach is compared with the numerical results obtained by the heterogeneous model.
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