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