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

A numerical simulation for effective elastic moduli of plates with various distributions and sizes of cracks

“…When the crack density is lower than 0.3, all the numerical results are close to the predictions of the differential method. So, the numerical results by Renaud et al (1996) and Zhan et al (1999) are not plotted in the figures for clarity, as they only analyzed the crack density up to 0.3 and 0.35. However, it is noticed that the results by Zhan et al (1999) for crack density of 0.35 are significantly larger than the predictions of the differential method.…”

“…The validity of these approximations was not verified. The methods by Huang et al (1996), Renaud et al (1996), andZhan et al (1999) do not involve assumptions, and should lead to agreeable results. One possible reason for their discrepancies is that the sample size and/or number of cracks used are not sufficient for the effective moduli to stabilize.…”

“…For parallel cracks, their effective Young's moduli keep the same trend, but their effective shear moduli are agreeable with the differential method until crack density of 0.6. Renaud et al (1996) proposed a boundary element method to analyze 2-D cracked solids, which they called the displacement discontinuity method. They calculated a rectangular cracked plate for each crack density up to about 0.3.…”

Micromechanical analysis of coupling between anisotropic damage and friction in quasi brittle materials: Role of the homogenization scheme

“…The direct approach is generally based on the analysis of displacement discontinuity induced by microcracks and on the fracture mechanics for the propagation of cracks. This approach is used in various works on the determination of the effective properties of microcracked materials Hori, 1990, 1993;Krajcinovic, 1996;Kachanov, 1982;Renaud et al, 1996) and in micromechanical models, for instance, Kachanov (1982); Andrieux et al (1986), Gambarotta and Lagomarsino (1993) and Pensée and Kondo (2001), just to mention a few. The mathematical formulation of direct micromechanical models is relatively simple and does not involve a rigorous upscaling procedure.…”

The influence of crack-orientation distribution on the mechanical properties of pre-cracked brittle media

“…In parallel, numerical methods have been broadly applied to calculate the effective mechanical properties of solids with pre-existing cracks, such as the finite element method ( Makarynska et al, 2008;Shen and Li, 2004 ) and the boundary element method ( Huang et al, 1996;Renaud et al, 1996 ). The differential method provides the closest estimation at low crack density, whereas the generalized selfconsistent method or the non-interaction solution is more accurate than the other methods at high crack density.…”