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

Abstract

a b s t r a c tThis 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, FE 2 . 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 FE 2 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.

Fully coupled hydromechanical multiscale model with microdynamic effects

“…It must be noted that if relation (25) is replaced by k ≤ k , the use of MüM at the macroscale level may lead to the wrong prediction of the observed behavior. Thus, an alternative relation has to be utilized for such case in Equation (21). On the other hand, it means that the transient behavior of the microscale level exhibits the macroscale volume forces, including the inertia and body forces, rather than the classical instantaneous linear momentum relation.…”

“…The homogenized stress and flux vectors, as well as the volume forces and storage function of the macroscale level, are accordingly derived in Equations (20) and (21). Hence, the governing equations of macroscale boundary value problem can be defined as…”

“…This method has been utilized for verity of solid mechanics material with finite plasticity, viscoplasticity,– and highly nonlinear behavior of complex microstructure by introducing the second‐order homogenization . In addition, the method has been implemented into thermal problems, thermomechanical, and hydromechanical coupling . With the growing interest in dynamic aspects where the microdynamic terms play a crucial role on overall response of the macroscale domain, various extensions of the Hill's averaging technique have been proposed in the presence of microdynamic effects –.…”

“…14,15 In addition, the method has been implemented into thermal problems, 16,17 thermomechanical, 18,19 and hydromechanical coupling. 20,21 With the growing interest in dynamic aspects where the microdynamic terms play a crucial role on overall response of the macroscale domain, various extensions of the Hill's averaging technique have been proposed in the presence of microdynamic effects. [22][23][24][25][26][27] Implementation of microtransient terms of flow equilibrium was first performed by Larsson et al 28 in uncoupled consolidation of saturated porous media, and then developed by Su et al 29 in coupled quasi-static consolidation.…”

Modeling the strain localization around an underground gallery with a hydro-mechanical double scale model; effect of anisotropy

“…Terms C i jkl form the stiffness matrix; terms B i j control the increase of total stress as a response to increase in pore pressure and can be compared with parameter b in Biot theory (Biot, 1941); terms E ikl describe the dependency of the permeability on deformation; G il contains the permeability tensor scaled by the fluid density; H i and N hold information on the fluid compressibility and are scaled by fluid fluxes and fluid mass content respectively; terms K kl contains information on the evolution of pore volume through deformation; remaining terms are, as an effect of the microscale model applied here, equal to zero. A more detailed evaluation of the different components of the tangent operators, and their physical interpretation in terms of poromechanical constitutive relations, can be found in Marinelli et al (2016).…”