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

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.
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https://hal.archives-ouvertes.fr/hal-00499566
Contributor : Francesco Dell'Isola <>
Submitted on : Saturday, July 10, 2010 - 10:10:33 AM
Last modification on : Saturday, July 17, 2010 - 11:40:14 AM
Long-term archiving on: : Thursday, December 1, 2016 - 4:26:05 PM

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  • HAL Id : hal-00499566, version 1

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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, Mathematical Sciences Publishers, 2008, pp.20. ⟨hal-00499566⟩

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