非标准热弹性力学中周期柯西材料的多场渐近均匀化格式
Multifield asymptotic homogenization scheme for periodic Cauchy materials in non-standard thermoelasticity
AI总结：
本文基于Green-Lindsay理论提出多场渐近均匀化格式，通过扰动函数和递推问题求解非标准热弹性周期材料中的布洛赫波传播，并以双相层状材料验证其有效性。
摘要：
本文提出了一种多场渐近均匀化格式，用于分析非标准热弹性周期材料中的布洛赫波传播，该格式基于考虑两个弛豫时间的Green-Lindsay理论。该过程包括若干步骤。首先，考虑微结构的特征尺寸，对微场进行渐近展开。利用推导出的微尺度场方程和渐近展开，在重复单胞Q内求解一系列递推微分问题。这些问题随后以扰动函数的形式表示，扰动函数包含了材料的几何、物理和力学性质以及微结构非均匀性。然后以一致的方式建立了降尺度关系，该关系通过扰动函数将微观场和宏观场及其梯度联系起来。随后，通过将降尺度关系代入微尺度场方程，得到无限阶平均场方程。为了求解这些平均场方程，基于微结构尺寸对宏观场进行渐近展开，从而得到一系列宏观递推问题。为了说明该方法，引入了一种双相层状材料作为示例。将由非局部均匀化格式得到的色散曲线与由Floquet-Bloch理论得到的色散曲线进行了比较。该分析有助于验证所提方法在预测所考虑的非标准热弹性周期材料中波传播行为方面的有效性和准确性。
英文摘要：
This article presents a multifield asymptotic homogenization scheme for the analysis of Bloch wave propagation in non-standard thermoelastic periodic materials, leveraging on the Green-Linsdsay theory that accounts for two relaxation times. The procedure involves several steps. Firstly, an asymptotic expansion of the micro-fields is performed, considering the characteristic size of the microstructure. By utilizing the derived microscale field equations and asymptotic expansions, a series of recursive differential problems are solved within the repetitive unit cell Q. These problems are then expressed in terms of perturbation functions, which incorporate the material's geometric, physical, and mechanical properties, as well as the microstructural heterogeneities. The down-scaling relation, which connects the microscopic and macroscopic fields along with their gradients through the perturbation functions, is then established in a consistent manner. Subsequently, the average field equations of infinite order are obtained by substituting the down-scaling relation into the microscale field equations. To solve these average field equations, an asymptotic expansion of the macroscopic fields is performed based on the microstructural size, resulting in a sequence of macroscopic recursive problems. To illustrate the methodology, a bi-phase layered material is introduced as an example. The dispersion curves obtained from the non-local homogenization scheme are compared with those obtained from the Floquet-Bloch theory. This analysis helps validate the effectiveness and accuracy of the proposed approach in predicting the wave propagation behavior in the considered non-standard thermoelastic periodic materials.
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