Modeling of granular solids with computational homogenization: Comparison with Biot׳s theory

• Hydromechanical modeling with a double-scale model.
• Numerical homogenization.
• Comparison with the classical poromechanics theory.

This paper discusses the numerical results for a consolidation test studied by using a hydromechanical model formulated within a numerical homogenization approach, the so-called finite element squared method, FE2. This model is characterized by two observation scales: at the microscopic scale, the microstructure of the material is described as an assembly of hyperelastic grains connected by cohesive interfaces that define a network of channels in which fluid can percolate. This microstructure, periodically distributed in the small-scale, identifies the Representative Elementary Volume of the material. At the macroscopic scale, the material is treated as a continuum and the corresponding constitutive equations are obtained by means of a numerical homogenization process on the microscopic problem. In this manner, the total stress of the mixture, the density of the mixture, the fluid mass flow and the fluid mass content can be computed. The objective of this work is to compare the numerical results with the analytical solution of a classical oedometric test using the poroelastic theory of Biot (1941) [1]. For this purpose, it is shown that the hydromechanical behavior obtained with the selected FE2 method is characterized by a classical Biot-like porous medium and the resulting macroscopic properties can be illustrated in light of the hydromechanical mechanisms at the microscopic scale.