A VARIATIONAL DEDUCTION OF SECOND GRADIENT POROELASTICITY PART I: GENERAL THEORY

Giulio Sciarra (1) , Francesco Dell'Isola (2, 3) , Nicoletta Ianiro (4) , Angela Madeo (4)

1 Dipartimento Ingegneria Chimica Materiali Ambiente
2 Dipartimento di Ingegneria Strutturale e Geotecnica
3 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita
4 MeMoMat - Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate

Second gradient theories have to be used to capture how local micro heterogeneities macroscopically affect the behavior of a continuum. In this paper a configurational space for a solid matrix filled by an unknown amount of fluid is introduced. The Euler–Lagrange equations valid for second gradient poromechanics, generalizing those due to Biot, are deduced by means of a Lagrangian variational formulation. Starting from a generalized Clausius–Duhem inequality, valid in the framework of second gradient theories, the existence of a macroscopic solid skeleton Lagrangian deformation energy, depending on the solid strain and the Lagrangian fluid mass density as well as on their Lagrangian gradients, is proven.

Domains: Mechanics [physics.med-ph]

Giulio Sciarra, Francesco Dell'Isola, Nicoletta Ianiro, Angela Madeo. A VARIATIONAL DEDUCTION OF SECOND GRADIENT POROELASTICITY PART I: GENERAL THEORY. Journal of Mechanics of Materials and Structures, 2008, pp.20. ⟨hal-00499566⟩