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Second gradient theories have to be used to capture how local microheterogeneities macroscopically affect the behavior of a continuum. In thispaper a configurational space for a solid matrix filled by an unknown amount offluid is introduced. The Euler-Lagrange equations valid for second gradientporomechanics, generalizing those due to Biot, are deduced by means of aLagrangian variational formulation. Starting from a generalized Clausius-Duheminequality, valid in the framework of second gradient theories, the existenceof a macroscopic solid skeleton Lagrangian deformation energy, depending on thesolid strain and the Lagrangian fluid mass density as well as on theirLagrangian gradients, is proven.

A Variational Deduction of Second Gradient Poroelasticity Part I: General Theory