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

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Variational Continuum Multiphase Poroelasticity

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 67))

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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.

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  1. Dipartimento di Ingegneria, Università degli Studi del Sannio, Benevento, Italy

    Roberto Serpieri

  2. University of Miami, Biomechanics Research Laboratory, Coral Gables, FL, USA

    Francesco Travascio

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  1. Roberto Serpieri
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Serpieri, R., Travascio, F. (2017). Variational Multi-phase Continuum Theories of Poroelasticity: A Short Retrospective. In: Variational Continuum Multiphase Poroelasticity. Advanced Structured Materials, vol 67. Springer, Singapore. https://doi.org/10.1007/978-981-10-3452-7_1

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