Higher-Order Homogenization for One-Dimensional Wave Propagation in Poroelastic Composites
Asiya M. Kudarova, Karel N. van Dalen, Guy Drijkoningen · 2013
An effective model is derived for periodically layered poroelastic media, where layers represent mesoscopic-scale heterogeneities that are larger than the pore and grain sizes but smaller than the wavelength. Each layer is homogeneous, described by Biot's equations of poroelasticity. The proposed model has only real-valued frequency-independent effective coefficients determined analytically exclusively by the physical parameters of the layers. It serves as an alternative to the existing models with frequency-dependent effective elastic properties. Homogenization is based on asymptotic expansions with multiple spatial scales and results in equations of motion containing higher-order derivatives. It is valid for wavelengths much larger than the period of the system. This approach, being widely used in elasticity, is extended to poroelasticity in this work. The exact analytical solution, obtained by the application of Floquet's theory to poroelastic composites, is used to validate the model.