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Variational Theories of Two-Phase Continuum Poroelastic Mixtures: A Short Survey

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Generalized Continua as Models for Classical and Advanced Materials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 42))

Abstract

A comprehensive survey is presented on two-phase and multi-phase continuum poroelasticity theories whose governing equations at a macroscopic level are based, to different extents, either on the application of classical variational principles or on variants of Hamilton’s least Action principle. As a focal discussion, the ‘closure problem’ is recalled, since it is widespread opinion in the multiphase poroelasticity community that even the simpler two-phase purely-mechanical problem of poroelasticity has to be regarded as a still-open problem of applied continuum mechanics. This contribution integrates a previous review by Bedford and Drumheller, and covers the period from the early use of variational concepts by Biot, together with the originary employment of porosity-enriched kinematics by Cowin and co-workers, up to variational theories of multiphase poroelasticity proposed in the most recent years.

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Authors and Affiliations

  1. Dipartimento di Ingegneria, Università degli Studi del Sannio, Piazza Roma, 21, 82100, Benevento, Italy

    Roberto Serpieri

  2. Dipartimento di Ingegneria Meccanica e Aerospaziale, Università di Roma La Sapienza, via Eudossiana 18, 00184, Rome, Italy

    Alessandro Della Corte

  3. Biomechanics Research Laboratory, Department of Industrial Engineering, University of Miami, 1251 Memorial Drive, MEB 276, Coral Gables, FL, 33146, USA

    Francesco Travascio

  4. Dipartimento di Strutture per l’Ingegneria e l’Architettura (DIST), Universitá degli Studi di Napoli Federico II, Via Claudio, 21, 80125, Naples, Italy

    Luciano Rosati

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  1. Roberto Serpieri
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  2. Alessandro Della Corte
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  4. Luciano Rosati
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Correspondence to Roberto Serpieri .

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  1. Universität Magdeburg, Otto‐von‐Guericke, Magdeburg, Germany

    Holm Altenbach

  2. Mines ParisTech, Paris, France

    Samuel Forest

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Serpieri, R., Della Corte, A., Travascio, F., Rosati, L. (2016). Variational Theories of Two-Phase Continuum Poroelastic Mixtures: A Short Survey. In: Altenbach, H., Forest, S. (eds) Generalized Continua as Models for Classical and Advanced Materials. Advanced Structured Materials, vol 42. Springer, Cham. https://doi.org/10.1007/978-3-319-31721-2_17

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