Vol. 3, No. 3, 2008

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ISSN: 1559-3959
A variational deduction of second gradient poroelasticity Part I: general theory

Giulio Sciarra, Francesco dell’Isola, Nicoletta Ianiro and Angela Madeo

Vol. 3 (2008), No. 3, 507–526
Abstract

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.

Keywords
poromechanics, second gradient materials, lagrangian variational principle
Milestones
Received: 8 March 2007
Revised: 27 July 2007
Accepted: 25 November 2007
Published: 1 May 2008
Authors
Giulio Sciarra
Dipartimento di Ingegneria Chimica Materiali Ambiente
Università di Roma “La Sapienza”
Via Eudossiana 18
00184 Rome
Italy
Francesco dell’Isola
Dipartimento di Ingegneria Strutturale e Geotecnica
Università di Roma “La Sapienza”
Via Eudossiana 18
00184 Rome
Italy
Laboratorio di Strutture e Materiali Intelligenti
Palazzo Caetani (Ala Nord)
04012 Cisterna di Latina (Lt)
Italy
Nicoletta Ianiro
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
Università di Roma “La Sapienza”
Via Scarpa 16
00161 Rome
Italy
Angela Madeo
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
Università di Roma “La Sapienza”
Via Scarpa 16
00161 Rome
Italy