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 language | English (US) |
|---|---|
| Title of host publication | Advanced Structured Materials |
| Publisher | Springer Verlag |
| Pages | 1-15 |
| Number of pages | 15 |
| Volume | 67 |
| DOIs | |
| State | Published - 2017 |
Publication series
| Name | Advanced Structured Materials |
|---|---|
| Volume | 67 |
| ISSN (Print) | 18698433 |
| ISSN (Electronic) | 18698441 |
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ASJC Scopus subject areas
- Materials Science(all)
Cite this
Variational multi-phase continuum theories of poroelasticity : A short retrospective. / Serpieri, Roberto; Travascio, Francesco.
Advanced Structured Materials. Vol. 67 Springer Verlag, 2017. p. 1-15 (Advanced Structured Materials; Vol. 67).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
TY - CHAP
T1 - Variational multi-phase continuum theories of poroelasticity
T2 - A short retrospective
AU - Serpieri, Roberto
AU - Travascio, Francesco
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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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U2 - 10.1007/978-981-10-3452-7_1
DO - 10.1007/978-981-10-3452-7_1
M3 - Chapter
AN - SCOPUS:85010289608
VL - 67
T3 - Advanced Structured Materials
SP - 1
EP - 15
BT - Advanced Structured Materials
PB - Springer Verlag
ER -