Conductivity of composites with multiple polygonal aggregates, theoretical estimates and numerical solutions from polarization series

Effective permeability of anisotropic porous materials containing periodically or randomly distributed cracks

“…The interest of using (10) instead of (9) is that it is more convenient to study both limit cases: superconductor K → ∞ or insulator K → 0. Unlike δK.R 0 and K 0 .δR, tensor A is always bounded in these two limits (Nguyen and To, 2018).…”

“…Specifically, we study how to estimate the effective permeability from the distribution of identical cracks. Starting from a periodic model (see e.g Nemat-Nasser et al, 1993;Nguyen et al, 2016;To et al, 2013;Nguyen and To, 2018), an integral equation in terms of polarization inside the ellipsoid is first established for the general case where the porous matrix is anisotropic. Then, the effective permeability is estimated, based on a direct approximation of the average polarization in the integral equation.…”

A review of nonlinear FFT-based computational homogenization methods

“…FFT-based methods were applied to predict the electrical response of composites [82], the thermal diffusivity of periodic porous materials [199], also accounting for thermal barrier coatings [200] and imperfect interfaces [201]. A coupling to the Nemat-Nasser-Iwakuma-Hejazi estimates for conductivity was proposed [202], and the conductivity of polygonal aggregates [203] was addressed. Also, FFT-based methods were applied to compute the through-thickness conductivity of heterogeneous plates [204] and for an inverse reconstruction of the local conductivity [205].…”