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Variational Multi-phase Continuum Theories of Poroelasticity: A Short Retrospective

  • Roberto SerpieriEmail author
  • Francesco Travascio
Chapter
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Part of the Advanced Structured Materials book series (STRUCTMAT, volume 67)

Abstract

This chapter aims at offering a comprehensive overview on the family of two-phase continuum poroelasticity theories whose formulations are based on the application of classical variational methods, or on variants of Hamilton’s Least Action Principle. The reader will be walked through several theoretical approaches to poroelasticity, starting from the early use of variational concepts by Biot, then covering the variational frameworks which employ porosity-enriched kinematics, such as those proposed by Cowin and co-workers and by Bedford and Drumheller, to conclude with the most recent variational theories of multiphase poroelasticity. Arguments are provided to show that, as a widespread opinion in the poroelasticity community, even the formulation of a simplest two-phase purely-mechanical poroelastic continuum theory remains, under several respects, a still-open problem of applied continuum mechanics, with the closure problem representing a crucial issue where important divergencies are found among the several proposed frameworks. Concluding remarks are finally drawn, pointing out the existence of delicate open issues even in the subclass of variational two-phase theories of poroelasticity.

Keywords

Solid Volume Fraction Variational Framework Kinematic Descriptor External Body Force Porosity Balance Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Dipartimento di IngegneriaUniversità degli Studi del SannioBeneventoItaly
  2. 2.University of MiamiBiomechanics Research LaboratoryCoral GablesUSA

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