  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.
