Second gradient poromechanics

Abstract

Second gradient theories have been developed in mechanics for treating different phenomena as capillarity in fluids, plasticity and friction in granular materials or shear band deformations. Here, there is an attempt of formulating a second gradient Biot like model for porous materials. In particular the interest is focused in describing the local dilatant behaviour of a porous material induced by pore opening elastic and capillary interaction phenomena among neighbouring pores and related micro-filtration phenomena by means of a continuum microstructured model. The main idea is to extend the classical macroscopic Biot model by including in the description second gradient effects. This is done by assuming that the surface contribution to the external work rate functional depends on the normal derivative of the velocity or equivalently assuming that the strain work rate functional depends on the porosity and strain gradients. According to classical thermodynamics suitable restrictions for stresses and second gradient internal actions (hyperstresses) are recovered, so as to determine a suitable extended form of the constitutive relation and Darcy's law. Finally a numerical application of the envisaged model to one-dimensional consolidation is developed; the obtained results generalize those by Terzaghi; in particular interesting phenomena occurring close to the consolidation external surface and the impermeable wall can be described, which were not accounted for previously. (C) 2007 Elsevier Ltd. All rights reserved

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

“…Strain gradient models (see e.g. [2,65] for classical references and [66,67] for more recent results) are good candidates for this purpose, as shown in [68][69][70]. A review of results on the theoretical foundation of a variational approach for higher gradient theories is [71].…”

On the contribution of Angelo Luongo to Mechanics: in honor of his 60th birthday

“…These procedures may also produce continuous models (see, e.g., [87,88]) where the microscopic microstructure is accounted for through constitutive anisotropy or constrained kinematics. Another relevant example is given by solids with interconnected pores, saturated, or partially saturated by compressible fluids (see, e.g., [89][90][91][92]). …”

From fractal media to continuum mechanics

“…(i) By taking as the starting point the "microscopic models" for interactions between the fluid flow and a deformable porous matrix [70][71][72][73] so as to obtain higher gradient fractal models.…”