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A variational
deduction of second gradient poroelasticity Part I: general
theory
Giulio Sciarra, Francesco dell’Isola, Nicoletta Ianiro and Angela Madeo |
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Vol. 3 (2008), No. 3, 507–526
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Abstract |
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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
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Milestones
Received: 8 March 2007
Revised: 27 July 2007
Accepted: 25 November 2007
Published: 1 May 2008
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Authors |
| Giulio Sciarra | |
| Dipartimento di Ingegneria Chimica
Materiali Ambiente Università di Roma “La Sapienza” Via Eudossiana 18 00184 Rome Italy |
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| 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 |
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| Angela Madeo | |
| Dipartimento di Metodi e Modelli
Matematici per le Scienze Applicate Università di Roma “La Sapienza” Via Scarpa 16 00161 Rome Italy |
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