NDLI: General quantitative analysis of stress partitioning and boundary conditions in undrained biphasic porous media via a purely macroscopic and purely variational approach

Content Provider	Springer Nature Link
Author	Serpieri, Roberto Travascio, Francesco
Copyright Year	2015
Abstract	In poroelasticity, the effective stress law relates the external stress applied to the medium to the macroscopic strain of the solid phase and the interstitial pressure of the fluid saturating the mixture. Such relationship has been formerly introduced by Terzaghi in form of a principle. To date, no poroelastic theory is capable of recovering a stress partitioning law in agreement with Terzaghi’s postulated one in the absence of ad hoc constitutive assumptions on the medium. We recently proposed a variational macroscopic continuum description of two-phase poroelasticity to derive a general biphasic formulation at finite deformations, termed variational macroscopic theory of porous media (VMTPM). Such approach proceeds from the inclusion of the intrinsic volumetric strain among the kinematic descriptors aside to macroscopic displacements, and as a variational theory, uses the Hamilton least-action principle as the unique primitive concept of mechanics invoked to derive momentum balance equations. In a previous related work it was shown that, for the subclass of undrained problems, VMTPM predicts that stress is partitioned in the two phases in strict compliance with Terzaghi’s law, irrespective of the microstructural and constitutive features of a given medium. In the present contribution, we further develop the linearized framework of VMTPM to arrive at a general operative formula that allows the quantitative determination of stress partitioning in a jacketed test over a generic isotropic biphasic specimen. This formula is quantitative and general, in that it relates the partial phase stresses to the externally applied stress as function of partitioning coefficients that are all derived by strictly following a purely variational and purely macroscopic approach, and in the absence of any specific hypothesis on the microstructural or constitutive features of a given medium. To achieve this result, the stiffness coefficients of the theory are derived by using exclusively variational arguments. We derive the boundary conditions attained across the boundary of a poroelastic saturated medium in contact with an impermeable surface also based on purely variational arguments. A technique to retrieve bounds for the resulting elastic moduli, based on Hashin’s composite spheres assemblage method, is also reported. Notably, in spite of the minimal mechanical hypotheses introduced, a rich mechanical behavior is observed.
Starting Page	235
Ending Page	261
Page Count	27
File Format	PDF
ISSN	09351175
Journal	Continuum Mechanics and Thermodynamics
Volume Number	28
Issue Number	1-2
e-ISSN	14320959
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-03-22
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Effective stress Terzaghi’s law Jacketed test Least-action principle Classical Continuum Physics Engineering Thermodynamics, Heat and Mass Transfer Theoretical and Applied Mechanics Structural Materials
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mechanics of Materials Materials Science

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