Stress peaks, stiffening and back-flow in bilayer poro-elastic metamaterials

Abstract

In the present work, we present a linear poroelastic model for a quasi-static oscillating bilayer beam made by two thick strata in perfect bond at their interface, characterized by different elastic moduli and permeability, both directly influenced by porosity. The solution is built up by considering the structure as a three-dimensional object and is obtained analytically for the full coupling of mass balance and mechanical equations, by imposing weak boundary conditions on the sole forces emerging at the lateral outermost surfaces, neglecting the inertial effects. After verifying the accuracy of the solution by comparing theoretical outcomes and numerical results from Finite Element simulations, ad hoc sensitivity analyses were then carried out in order to investigate the effects on the stress distribution and fluid flow due to prescribed inhomogeneities related to variations of material and geometrical parameters across the beam thickness, by keeping constant the total volume of the porous solid skeleton and applying self-equilibrated and oscillating in time axial forces and bending moments at two opposite sides of the structure. Some dynamic analyses were also performed to highlight proper periods and frequencies ranges where pulse loadings ensured the quasi-static response of the system, however discussing interferences due to transient regimes for selected cases on the basis of numerical analyses. Finally, we show that, by playing with ratios between elastic moduli, thickness and porosity of the two layers, a number of counterintuitive or even non-conventional behaviors can be observed, which give rise to unexpected back-flow phenomena and anomalous fluid content distributions, as well as to stress peaks kindled by moving the layer interface and overall stiffening that could be all exploited for the design of new multi-objective poroelastic metamaterials.