Revisiting the constitutive equations of unsaturated porous solids using a Lagrangian saturation concept

Abstract

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Prediction of drying shrinkage beyond the pore isodeformation assumption

“…Since the porous space now deforms, instead of (1-1) we write (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) where ϕ J accounts for the change in the partial porosity φ J due to deformation only. In contrast to the standard Eulerian configuration referring to the current deformed configuration, as recently introduced in [Coussy 2007], the saturation S J can be regarded as a Lagrangian saturation related to phase J, since it refers to the undeformable configuration. More precisely, starting from full liquid saturation, φ 0 S L V is the volume in the undeformable configuration whose solid walls will still be wetted in the current deformed configuration [Coussy 2007].…”

“…In contrast to the standard Eulerian configuration referring to the current deformed configuration, as recently introduced in [Coussy 2007], the saturation S J can be regarded as a Lagrangian saturation related to phase J, since it refers to the undeformable configuration. More precisely, starting from full liquid saturation, φ 0 S L V is the volume in the undeformable configuration whose solid walls will still be wetted in the current deformed configuration [Coussy 2007]. This is sketched in Figure 2 for two distinct current deformed configurations, the undeformed reference configuration pertaining to liquid saturated conditions at zero pressure p L .…”

“…Using mesoscopic-macroscopic considerations [Coussy 1991;2007] or more refined upscaling methods [Dormieux et al 2006a], it can further be shown that 1…”

“…One assumption, sometimes made implicitly [Coussy 2004] or explored explicitly [Chateau and Dormieux 2002;Dormieux et al 2006a;Coussy 2007], is the isodeformation of the porous volumes respectively occupied by the liquid and the gas in the absence of any pore pressure. This assumption amounts to writing…”

Non-Isothermal Constitutive Relations and Heat Transfer Equations of a Two-Phase Medium

“…Based on the laws of irreversible thermodynamics, the problem of constitutive relations for the two-phase medium consisting of an elastic skeleton and liquids is discussed in detail in Coussy [10], Strzelecki et al [22], Uciechowska and Strzelecki [24]. In these works the assumption was made that the heat flows evenly through the porous medium, meaning that the temperature of the liquid and the skeleton is the same in any given area.…”