Second gradient poromechanics

Giulio Sciarra (1, 2) , Francesco Dell'Isola (3, 4) , Olivier Coussy (5)

1 Dipartimento Ingegneria Chimica Materiali Ambiente
2 GeM - Institut de Recherche en Génie Civil et Mécanique
3 Dipartimento di Ingegneria Strutturale e Geotecnica
4 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita
5 navier umr 8205 - Laboratoire Navier

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.

Mots clés: Second gradient materials; Porous media; Thermodynamics; Darcy law; Consolidation

Domaines: Mécanique [physics.med-ph]; Mécanique des solides [physics.class-ph]; Génie civil

Giulio Sciarra, Francesco Dell'Isola, Olivier Coussy. Second gradient poromechanics. International Journal of Solids and Structures, 2007, 44 (20), pp.6607-6629. ⟨10.1016/j.ijsolstr.2007.03.003⟩. ⟨hal-00503231⟩