The linear isotropic variational theory and the recovery of biot’s equations

Roberto Serpieri, Francesco Travascio

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this chapter, the general framework presented in Chap. 2 is specialized to address linear isotropic two-phase poroelasticity. The elastic moduli of the resulting isotropic theory are derived with the special forms achieved by the governing PDEs for hyperbolic and parabolic problems. Next, the hyperbolic system is deployed to analyze the propagation of purely elastic waves. The chapter is concluded with a section dedicated to a comparison between the hyperbolic isotropic equations resulting from the present theory and their counterparts in Biot’s theory. This comparison shows the recovery by the medium-independent VMTPM framework of the essential structure of Biot’s PDEs. This recovery is herein deductively achieved in absence of heuristic statements, proceeding from the consideration of individual strain energies of the solid and fluid phases and from the minimal kinematic hypotheses of Chap. 2. This study is complemented by an analysis of the bounds of the elastic moduli of the isotropic theory, which is undertaken deploying a generalization to the present two-phase context of the Composite Sphere Assemblage homogenization technique by Hashin.

Original languageEnglish (US)
Title of host publicationAdvanced Structured Materials
PublisherSpringer Verlag
Pages75-114
Number of pages40
Volume67
DOIs
StatePublished - 2017

Publication series

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

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Elastic moduli
Recovery
Elastic waves
Strain energy
Kinematics
Fluids
Composite materials

ASJC Scopus subject areas

  • Materials Science(all)

Cite this

Serpieri, R., & Travascio, F. (2017). The linear isotropic variational theory and the recovery of biot’s equations. In Advanced Structured Materials (Vol. 67, pp. 75-114). (Advanced Structured Materials; Vol. 67). Springer Verlag. https://doi.org/10.1007/978-981-10-3452-7_3

The linear isotropic variational theory and the recovery of biot’s equations. / Serpieri, Roberto; Travascio, Francesco.

Advanced Structured Materials. Vol. 67 Springer Verlag, 2017. p. 75-114 (Advanced Structured Materials; Vol. 67).

Research output: Chapter in Book/Report/Conference proceedingChapter

Serpieri, R & Travascio, F 2017, The linear isotropic variational theory and the recovery of biot’s equations. in Advanced Structured Materials. vol. 67, Advanced Structured Materials, vol. 67, Springer Verlag, pp. 75-114. https://doi.org/10.1007/978-981-10-3452-7_3
Serpieri R, Travascio F. The linear isotropic variational theory and the recovery of biot’s equations. In Advanced Structured Materials. Vol. 67. Springer Verlag. 2017. p. 75-114. (Advanced Structured Materials). https://doi.org/10.1007/978-981-10-3452-7_3
Serpieri, Roberto ; Travascio, Francesco. / The linear isotropic variational theory and the recovery of biot’s equations. Advanced Structured Materials. Vol. 67 Springer Verlag, 2017. pp. 75-114 (Advanced Structured Materials).
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