Variational multi-phase continuum theories of poroelasticity: A short retrospective

Roberto Serpieri, Francesco Travascio

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationAdvanced Structured Materials
PublisherSpringer Verlag
Pages1-15
Number of pages15
Volume67
DOIs
StatePublished - 2017

Publication series

NameAdvanced Structured Materials
Volume67
ISSN (Print)18698433
ISSN (Electronic)18698441

ASJC Scopus subject areas

  • Materials Science(all)

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    Serpieri, R., & Travascio, F. (2017). Variational multi-phase continuum theories of poroelasticity: A short retrospective. In Advanced Structured Materials (Vol. 67, pp. 1-15). (Advanced Structured Materials; Vol. 67). Springer Verlag. https://doi.org/10.1007/978-981-10-3452-7_1