MATLAB script and COMSOL models of the article "Transient computational homogenization of heterogeneous poroelastic media with local resonances"

A computational homogenization framework is proposed for solving transient wave propagation in the linear regime in heterogeneous poroelastic media that may exhibit local resonances due to microstructural heterogeneities. The microscale fluid-structure interaction problem and the macroscale are coupled through an extended version of the Hill-Mandel principle, leading to a variationally consistent averaging scheme of the microscale fields. The effective macroscopic constitutive relations are obtained by expressing the microscale problem with a reduced-order model that contains the longwave basis and the so-called local resonance basis, yielding the closed-form expressions for the homogenized material properties. The resulting macroscopic model is an enriched porous continuum with internal variables that represent the microscale dynamics at the macroscale, whereby the Biot model is recovered as a special case. Numerical examples demonstrate the framework’s validity in modeling wave transmission through a porous layer.<br>This software publication provides the MATLAB script and COMSOL models supporting the article.

提出了一种计算均匀化框架（computational homogenization framework），用于求解线性区域内非均匀多孔弹性介质中的瞬态波传播问题——这类介质可能因微观结构非均质性而表现出局部共振。
微观尺度流固耦合问题与宏观尺度通过扩展版的希尔-曼德尔原理（Hill-Mandel principle）耦合，从而得到微观场的变分一致平均方案。
通过使用包含长波基和所谓局部共振基的降阶模型（reduced-order model）来表示微观尺度问题，获得有效宏观本构关系，进而得到均匀化材料属性的闭式表达式。
最终的宏观模型是一种具有内变量的富集多孔连续体，这些内变量在宏观尺度上表征微观动力学；比奥模型（Biot model）可作为特例从中恢复。
数值算例验证了该框架在模拟多孔层波传输方面的有效性。
本软件出版物提供了支持该文章的MATLAB脚本和COMSOL模型。