A variational deduction of second gradient poroelasticity I: general theory

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

Vol. 3, No. 3, 2008

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

Abstract

Keywords

Milestones

Authors