Dispersive computational continua

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• 作者：Vasilina Filonova ^{vf2197@columbia.edu" class="auth_mail" title="E-mail the corresponding author} ; Dimitrios Fafalis ^{df2472@columbia.edu" class="auth_mail" title="E-mail the corresponding author} ; Jacob Fish ; ^{fishj@columbia.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Homogenization ; Computational continua ; Dispersion analysis ; High-frequency ; Floquet&ndash ; Bloch wave
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：298
• 期：Complete
• 页码：58-79
• 全文大小：1082 K

文摘

The two primary objectives of the present manuscript are: (i) to develop a variant of the computational continua formulation (C²${}^2$) with outstanding dispersive properties, and (ii) to conduct a rigorous dispersion analysis of it. The ability of the C²${}^2$ formulation to capture dispersive behavior stems from its underlying formulation, which does not explicitly assume scale separation and accounts for microstructures of finite size. The dispersion study in heterogeneous elastic media with periodic microstructure has been conducted using both analytical and numerical approaches. The so-called analytical dispersion analysis is based on the Floquet–Bloch wave solution, while the numerical dispersion analysis is based on the modal analysis of the discrete coupled fine–coarse-scale equations. The dispersive curves obtained from the dispersive C²${}^2$ formulations were compared with the classical exact Floquet–Bloch wave solution, hereafter referred to as the reference dispersive curve. It has been observed that in the case of the unit cell sizes being either half of the coarse-scale element size or equal to it, the dispersive curves obtained by the dispersive C²${}^2$ formulation are practically identical to the reference solution. For other cases, the dispersive C${}^2$solution is in good agreement with the reference solution. The dispersion analysis results have been further verified by the wave propagation problem in a periodic heterogeneous medium with a wavelength comparable to the microstructural size.