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Advanced Structured Materials

Variational Continuum Multiphase Poroelasticity

Theory and Applications

Authors: Serpieri, Roberto, Travascio, Francesco

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  • Collects the theoretical derivation of a variational macroscopic continuum theory together with applications to consolidation and stress partitioning problems of interest in geomechanics and biomechanics
  • Shows that the phenomenon of compression-induced liquefaction can be obtained as a natural implication of the theory
  • Exemplifies the capability of VMTPM to describe and predict a large class of linear and nonlinear mechanical behaviors observed in two-phase saturated materials
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eBook 101,14 €
price for Spain (gross)
  • ISBN 978-981-10-3452-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-981-10-3451-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-981-10-9876-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics.

The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations.

It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the stress tensor work-associated with the macroscopic strain of the solid phase are partitioned according to a relation which, from a formal point of view, turns out to be strictly compliant with Terzaghi's law, irrespective of the microstructural and constitutive features of a given medium. Moreover, it is shown that some experimental observations on saturated sandstones, generally considered as proof of deviations from Terzaghi's law, are ordinarily predicted by VMTPM.

As a peculiar prediction of VMTPM, the book shows that the phenomenon of compression-induced liquefaction experimentally observed in cohesionless mixtures can be obtained as a natural implication of this theory by a purely rational deduction. A characterization of the phenomenon of crack closure in fractured media is also inferred in terms of macroscopic strain and stress paths.

Altogether the results reported in this monograph exemplify the capability of VMTPM to describe and predict a large class of linear and nonlinear mechanical behaviors observed in two-phase saturated materials.

 

Reviews

“This book presents the derivation and some applications of a general two-phase variational continuum theory with microstructure developed by the authors of the book. … The book is well-written and is a notable contribution to the field of porous media. The mathematical concepts are clearly presented and the introduction and discussion of each chapter provide important insights into the chapter’s topic.” (Corina-Ștefania Dracapa, Mathematical Reviews, October, 2018)​

Table of contents (5 chapters)

Table of contents (5 chapters)
  • Variational Multi-phase Continuum Theories of Poroelasticity: A Short Retrospective

    Pages 1-15

    Serpieri, Roberto (et al.)

  • Variational Macroscopic Two-Phase Poroelasticity. Derivation of General Medium-Independent Equations and Stress Partitioning Laws

    Pages 17-73

    Serpieri, Roberto (et al.)

  • The Linear Isotropic Variational Theory and the Recovery of Biot’s Equations

    Pages 75-114

    Serpieri, Roberto (et al.)

  • Stress Partitioning in Two-Phase Media: Experiments and Remarks on Terzaghi’s Principle

    Pages 115-167

    Serpieri, Roberto (et al.)

  • Analysis of the Quasi-static Consolidation Problem of a Compressible Porous Medium

    Pages 169-181

    Serpieri, Roberto (et al.)

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-981-10-3452-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-981-10-3451-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
price for Spain (gross)
  • ISBN 978-981-10-9876-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Variational Continuum Multiphase Poroelasticity
Book Subtitle
Theory and Applications
Authors
Series Title
Advanced Structured Materials
Series Volume
67
Copyright
2017
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-10-3452-7
DOI
10.1007/978-981-10-3452-7
Hardcover ISBN
978-981-10-3451-0
Softcover ISBN
978-981-10-9876-5
Series ISSN
1869-8433
Edition Number
1
Number of Pages
XIII, 198
Number of Illustrations
4 b/w illustrations, 16 illustrations in colour
Topics