Micromechanical analysis of the effective stiffness of poroelastic composites

Within this work we investigate the role that the microstructure of a poroelastic material has on the resulting elastic parameters. We are considering the effect that multiple elastic and fluid phases at the same scale (LMRP model (L. Miller and R. Penta, 2020)) have on the estimation of the materials elastic parameters when compared with a standard poroelastic approach. We present a summary of both the LMRP model and the comparable standard poroelastic approach both derived via the asymptotic homogenization approach. We provide the 3D periodic cell problems with associated boundary loads that are required to be solved to obtain the effective elasticity tensor for both model setups. We then perform a 2D reduction of the cell problems, again presenting the 2D boundary loads that are required to solve the problems numerically. The results of our numerical simulations show that whenever investigating a poroelastic composite material with porosity exceeding 5% then the LMRP model should be considered more appropriate in incorporating the structural details in the Young's moduli E₁ and E₃ and the shear C₄₄. Whenever the porosity exceeds 20% it should also be used to investigate the shear C₆₆. We find that for materials with less than 5% porosity that the voids are so small that a standard poroelastic approach or the LMRP model produce the same results.