By Luc Dormieux
Meant as a primary advent to the micromechanics of porous media, this ebook entitled "Microporomechanics" bargains with the mechanics and physics of multiphase porous fabrics at nano and micro scales. it's composed of a logical and didactic increase from primary techniques to cutting-edge theories. It beneficial properties 4 elements: following a quick creation to the mathematical ideas for upscaling operations, the 1st half offers with the homogenization of shipping houses of porous media in the context of asymptotic growth options. the second one half bargains with linear microporomechanics, and introduces linear mean-field theories in keeping with the concept that of a consultant straight forward quantity for the homogenization of poroelastic homes of porous fabrics. The 3rd half is dedicated to Eshelby's challenge of ellipsoidal inclusions, on which a lot of the micromechanics innovations are dependent, and illustrates its software to linear diffusion and microporoelasticity. eventually, the fourth half extends the research to microporo-in-elasticity, that's the nonlinear homogenization of a big variety of usually encountered porous fabric behaviors, particularly, energy homogenization, nonsaturated microporomechanics, microporoplasticity and microporofracture and microporodamage conception.
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Extra info for Microporomechanics
The ﬂuid is assumed to be an incompressible Newtonian ﬂuid of shear viscosity μ f . 2 Viscous flow in a cylindrical pore space where (d P/d x ) e x denotes the pressure gradient. Since the pore pressure is uniform in each section, the pressure gradient is the same at both the microscopic and the macroscopic scale. e. 3) to ﬁnd out if both display a linear relation between the macroscopic ﬁltration velocity and the pressure gradient. Thus, from this comparison, the factor (πa 4 /8S)/μ f appears as the permeability K of this 1-D thought model, which captures the geometrical characteristics of the (no doubt too simplistic) cylindrical morphology of the pore space.
Let vi be the solution for α = e i , so that the solution v(α) is v = αi vi . 36) in the (e i ) base. 31) for α = e j ) are inversely proportional to μ f , tensor K also obeys this inverse proportionality. 32). 2). 41) Scale Effects on Permeability We are interested here in the scale effects on the permeability tensor that can be found from the micromechanics theory. 15) deﬁned in U f of the unit cell U. We now consider the domain U˜ f , which is the image of U f obtained by the homothety ˜ z) and v(˜ ˜ z) be a pressure and a H of center O and ratio λ: H(z) = λz.
106) There are several effects of deformation on the ﬂow through porous media. The ﬁrst possible coupling is due to the displacement of the solid–ﬂuid interface, which a priori inﬂuences the transport properties. The second one is the mechanical effect of the pore pressure on the overall deformation behavior of the porous material. The ﬁrst coupling is examined here with regard to Darcy’s law. The second coupling with the deformation behavior will be studied in Chapter 5, where we will see a consistent derivation of the macroscopic poroelasticity theory from homogenization techniques.