Closure of parallel cracks: Micromechanical estimates versus finite element computations

Abstract

3D finite element simulations have been performed in order to assess the ability of four classical homogenization schemes to model the elastic behavior of solids with parallel cracks, namely the dilute, Mori-Tanaka, self-consistent and differential schemes. The cracks have been represented by right circular cylinders with aspect ratios as low as 10 −3 in the simulations whose centroids are randomly located in the REV. Special attention has been paid to the crack aspect ratio variation predicted by the different schemes, since the goal is ultimately to propose a non-linear micromechanical model of a cracked solid, taking complete crack closure into account.The results confirm earlier studies which showed that the differential scheme was best suited for this kind of morphology when computing elastic moduli, but additionally, we show that changes in crack aperture are also accurately predicted. It is however noted that the randomness in the positions of the cracks leads to significant scatter in the magnitude of the aperture variation inside a given simulation, which suggests that the cracks do not close simultaneously. As a consequence, nonlinear numerical simulations accounting for contact between the crack lips should be performed in order to completely validate a non-linear micromechanical model in alternate tension/compression loading cases.

Contribution of FE and FFT-based methods to the determination of the effective elastic and conduction properties of composite media with flat inclusions and infinite contrast

“…The aim of this paper is precisely to remedy these shortcomings by extending the micromechanical analysis to the hydraulic conductivity of the rock, and by assessing the performance of five classical micromechanical estimates in comparison with numerical simulations. The idea is to confirm previous results obtained in the context of linear elasticity (Bluthe et al [7]), and to see if the same scheme is selected in the case of linear conduction. This will allow for a consistent hydromechanical representation of the cracked rock at the scale of the structure in an upcoming contribution.…”

“…Note that in Bluthe et al [7], uniform strain boundary conditions were used, yielding equivalent results, which shows that the important part is to start from the microscopic strain and not the microscopic stress, irrespective of the boundary conditions. However, using uniform stress boundary conditions does present the advantage of being slightly more direct, since the effective compliance is naturally obtained whereas the effective stiffness had to be calculated first and then the relation had to be inverted.…”

“…On the other hand, the in-plane components of the effective stiffness tensor may still be affected because when inverting the compliance tensor, the 𝑆 ℎ𝑜𝑚 3333 component is necessarily mixed up with the in-plane components. The tensor U 𝑑,0 is a function of C 0 and the unit normal to the plane of the disk 𝒏, and its Mandel representation is recalled in Bluthe et al [7] for a transversely isotropic reference material.…”

“…FEM tools are ubiquitous nowadays in research and engineering, which is reflected in the literature by the fact that most of the recent comparisons between analytical estimates and numerical simulations for cracked media were based on FEM. Among these contributions, one can cite Dahm and Becker [11] and Charpin and Ehrlacher [10] in 2D, and Grechka [22], Vasylevskyi et al [35] and Bluthe et al [7] in 3D (see Bluthe et al [7] for more details on these papers). The previously mentioned contributions, as well as others based on different techniques, showed the good performance of the differential scheme in the case of linear elasticity.…”

“…The previously mentioned contributions, as well as others based on different techniques, showed the good performance of the differential scheme in the case of linear elasticity. Some papers claimed a better fit of the dilute scheme, but as explained in Bluthe et al [7], these authors used a stress-based estimate without consideration of the fact that the dilute scheme only applies for small values of the crack density parameter.…”