Djimedo Kondo

Micromechanical approach to the behavior of poroelastic materials

A micromechanical analysis of the behavior of saturated elastic porous media is presented. Pores are connected and saturated with a fluid at uniform pressure. The non-linear macroscopic response of the porous medium is assumed to be related to the existence of a network of microcracks in the solid phase. The progressive closure of cracks during loading is viewed to control the material non-linearity. Using averaging schemes based on both the classical and modified secant methods, the non-linearity of the overall response is shown to be sometimes controlled by an effective stress. The modified secant method accounts in a certain way for the non-uniform distribution of strains within the solid phase. Different definitions of the effective stress are found, each of them being a combination of the overall stress with the fluid pressure. The hypothesis of connexion between pores and microcracks is discussed in details. The consequences of this hypothesis on the non-linear overall response are illustrated and comparisons are made with experimental data.

Poroelasticity and damage theory for saturated cracked media

First, basic results of linear homogenization applied to porous media are presented and applied in order to derive a linear poroelasticity theory for saturated cracked materials. The emphasis is put on the geometrical modelling of the cracks as well as on the cracks-induced anisotropy. The effect of interactions between cracks and the role of the spatial distribution of cracks on the poroelastic properties are also analyzed. The non linear poroelastic behavior of cracked media due to the progressive cracks closure is also investigated. The last section is devoted to damage induced by crack propagation.

A new technique for finite element limit-analysis of Hill materials, with an application to the assessment of criteria for anisotropic plastic porous solids

Abstract The present work is devoted to the numerical limit-analysis of Hill materials with particular emphasis on anisotropically plastic porous solids. Its aim is to provide an efficient method of limit-analysis based on the standard finite element method including elasticity, and present a few applications. We first present the numerical implementation of Hill’s criterion. We then describe the procedure used for the numerical limit-analysis, which basically consists of using a single large load step ensuring that the limit-load is reached, without updating the geometry. Also, the convergence of the elasto–plastic iterations is accelerated by suitably adjusting the elastic properties of the material. The method is applied to assess Gurson-like criteria for orthotropically plastic materials containing spheroidal voids. This is done by performing numerical limit-analyses of elementary cells made of a Hill material and containing confocal spheroidal voids, subjected to classical conditions of homogeneous boundary strain rate. The numerical results are compared to the model predictions for both the yield surface and the flow rule, and this permits to discuss the accuracy of the theoretical models considered.

Micromechanics of damage propagation in fluid-saturated cracked media

ABSTRACT This paper proposes a brief overview of the micromechanics approach to the modelling of crack-induced damage. To begin with, the main lines of the micromechanics reasoning are presented and applied to cracked media. We then introduce the so-called dilute and Mori-Tanaka homogenization schemes which are herein implemented in the context of a solid matrix weakened by opened or closed cracks. The above modelling is extended to the situation of fluid-filled cracks, yielding a micromechanics theory of poroelastic damage. Finally, the combination of the previous findings with a standard thermodynamics argument allows to deal with the essential question of damage evolution which is regarded here as the consequence of cracks propagation.

Strain localization in Fontainebleau sandstone: Macroscopic and microscopic investigations

Abstract The paper concerns a study of strain localization in a sandstone. At first, the material properties and the experimental device are described. The experimental method for detecting strain localization is based on multiple measurements of strains and displacements. By comparisons, these measurements give indications on a strain inhomogeneity. First tests have been performed on cylindrical samples and the results shown that the procedure is not systematically efficient for this kind of experiments. Prismatic samples are then used. In order to control the localization initiation and to follow up the shear banding the last tests are performed on prismatic samples containing a little hole. The shear bands characteristics (onset, orientation, width) are given for all these tests on prismatic sample. Their variation with confining pressure is emphasized. Finally, some details on the deformation mechanisms inside the bands are provided by visual and microscopic observations.

Computations of effective moduli for microcracked materials: a boundary element approach

Abstract The paper deals with a computational investigation on effective moduli of brittle materials weakened by microcracks. The study is based on a suitable adaptation of an indirect boundary element method, namely the displacement discontinuity method. Various aspects of microcracks size and orientation are investigated. For tensile loading (open cracks), the numerical results show good agreement with the classical non-interacting cracks approximation. Comparisons with some not fully random configurations are also presented. When crack-boundary interactions are taken into account, the results agree rather well with the differential approximation, but calculations under compressive loadings are much more complicated because of friction and sliding on crack faces, so an iterative algorithm for sliding and frictional cracks is used. The effective compliance in this case shows very little increase compared with the case of tensile loadings. Comparisons with some theoretical approximations are presented.

A damage model for ductile porous materials with a spherically anisotropic matrix

In the present study, we investigate the macroscopic strength of ductile porous materials having a Hill-type radial anisotropic matrix. The procedure is based on a limit analysis (LA)-based kinematic approach of a rigid plastic hollow sphere. We first established the exact solution (stress and velocity fields) to the problem of the hollow sphere subjected to an external hydrostatic loading. Then, we propose, for general loadings, an appropriate trial velocity field which allows to implement the kinematic LA procedure. The resulting macroscopic criterion, whose closed-form expression is provided, extends the well-known Gurson criterion to materials with radial anisotropy. Numerical limit analyses are provided by performing standard finite elements computations which validate the new criterion. Finally, the yield criterion is supplemented by a plastic flow rule and evolution equations of the internal parameters, allowing to study the predictions of the complete model for axisymmetric proportional loadings at fixed stress triaxiality. A strong influence of the radial anisotropy is observed on the stress softening and the growth of the porosity.

On micromechanical damage modeling in geomechanics: Influence of numerical integration scheme

Tunnel excavations in deep rocks provide stress perturbations which initiate diffuse and/or localized damage propagation in the material. This damage phenomenon can lead to significant irreversible deformations and changes in rock properties. In this paper, we propose to model such behavior by considering a micromechanically-based damage approach. The resulting micromechanical model, which also accounts for initial stress, is described and assessed through the numerical analysis of a synthetic tunnel drilling in Opalinus Clay. A particular emphasis is put on the numerical integration of the model. In particular, an appropriate choice of the latter is required to ensure the numerical stability and a confident prediction of excavation damaged zone around tunnels.

Diffusive transport in disordered media. Application to the determination of the tortuosity and the permeability of cracked materials.

This Chapter deals with molecular diffusion in saturated porous media. It provides a micromechanical basis to the phenomenological concept of tortuosity which is classically introduced in order to capture the barrier effect of the solid-fluid interface. Various Eshelby-based estimates of the effective diffusion tensor are derived in the isotropic case. The influence of cracks on the tortuosity is also investigated. Finally, it is shown that the permeability of a cracked porous medium can be estimated with the help of the same mathematical tools.

Homogenization of saturated double porous media with Eshelby-like velocity field

In this paper, we focus on strength properties of double porous materials having a Drucker-Prager solid phase at microscale. The porosity consists in two populations of micropores and mesopores saturated with different pressures. To this end, we consider a hollow sphere subjected to a uniform strain rate boundary conditions. For the microscale to mesoscale transition, we take advantage of available results by Maghous et al. (2009), while the meso to macro upscaling is performed by implementing a kinematical limit analysis approach using Eshelby-like trial velocity fields. This two-step homogenization procedure delivers analytical expression of the macroscopic criterion for the considered class of saturated double porous media. This generalizes and improves previous results established by Shen et al. (2014). The results are discussed in terms of the existence or not of effective stresses. Some illustrations are provided.