Albert Giraud

Approximate Representation of a Compliance Contribution Tensor for a Cylindrical Inhomogeneity Normal to the Axis of Symmetry of a Transversely Isotropic Material

The paper focuses on the assessment of the effect produced by a strongly prolate spheroidal pore in a transversely-isotropic material when the axis of rotation of the spheroid is perpendicular to the axis of transverse isotropy. We propose a simple approximation method to get components of the pore compliance contribution tensor. The results are compared with exact numerical solution. It is shown that for moderate anisotropy (like one of cortical bone, for example) the method produces accurate results.

Local fields and effective conductivity tensor of ellipsoidal particle composite with anisotropic constituents

An accurate semi-analytical solution of the conductivity problem for a composite with anisotropic matrix and arbitrarily oriented anisotropic ellipsoidal inhomogeneities has been obtained. The developed approach combines the superposition principle with the multipole expansion of perturbation fields of inhomogeneities in terms of ellipsoidal harmonics and reduces the boundary value problem to an infinite system of linear algebraic equations for the induced multipole moments of inhomogeneities. A complete full-field solution is obtained for the multi-particle models comprising inhomogeneities of diverse shape, size, orientation and properties which enables an adequate account for the microstructure parameters. The solution is valid for the general-type anisotropy of constituents and arbitrary orientation of the orthotropy axes. The effective conductivity tensor of the particulate composite with anisotropic constituents is evaluated in the framework of the generalized Maxwell homogenization scheme. Application of the developed method to composites with imperfect ellipsoidal interfaces is straightforward. Their incorporation yields probably the most general model of a composite that may be considered in the framework of analytical approach.

Stability, accuracy, and efficiency of numerical methods for coupled fluid flow in porous rocks

In this chapter, numerical methods for modeling of fluid-driven cracks in rocks are presented. The modeling of the coupled fluid flow in continuous media is first reminded, with presentation of several applications. Then the modeling of the fractured rock is considered. A review of the most common methods for coupled fluid flow in fractured porous rocks is presented and the manuscript focuses on the extended finite element method (XFEM) method combined with hydromechanical couplings. Several problems in relation with fluid-driven crack in porous rocks are foreseen, such as partial saturation, anisotropy, or crack initiation. Some details about numerical issues are also given.

A Micro-Mechanical Analysis of Induced Anisotropic Damage in Initially Anisotropic Materials

This paper is devoted to a micro-mechanical study of induced anisotropic micro-cracks in initially anisotropic materials. The effective elastic properties of cracked materials are determined by a rigorous up-scaling homogenization procedure based on an efficient numerical method to calculate Hill polarization tensor. A linear damage criterion is defined in the framework of irreversible thermodynamics to describe the growth of damage. Multiple families of micro-cracks in different orientations are taken into account by using the Gauss-type numerical integration method. Numerical assessments are proposed by using a PCW estimation and a set of 33 families of micro-cracks for uniaxial tension and compression tests. Induced crack density distributions are investigated for both isotropic and anisotropic materials. Effects of the initial anisotropy on crack propagation process are clearly demonstrated.

THM modeling of the CO2 injection in coal: influence of Biot's coefficient and Langmuir's adsorption parameters

CO2 injection in coal can modify the petro-physical properties. Indeed, the coal matrix swelling reduces the porosity and the permeability of coal on the one hand. On the other hand, the increase in gas pressure induces the decrease in the effective stresses and therefore the increase in the spacing between the matrix blocks. We used a theoretical model for the variation of the Eulerian porosity which takes into account the adsorption process. This process is classically modeled with the Langmuir’s isotherm. After implementation in Code_Aster (EDF), we investigated through numerical simulations (1D and 2D axisymmetric) the influence of the Biot’s coefficient and the Langmuir’s adsorption parameters during CO2 injection in coal. This simulations showed that the increase in Langmuir’s parameters, as well as the increase in the Biot’s coefficient, promotes the reduction of the porosity when the gas pressure increases.