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.