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Classical and higher order interface conditions in poroelasticity

  • Michele SerpilliEmail author
Original Article
First Online:

Abstract

The paper deals with the derivation of non classical interface conditions in linear poroelasticity in the framework of the quasi-static diphasic Biot’s model. More precisely, we analyze the mechanical behavior of two linear isotropic poroelastic solids, bonded together by a thin layer, constituted by a linear isotropic poroelastic material, by means of an asymptotic analysis. After defining a small parameter \(\varepsilon\), which will tend to zero, associated with the thickness and the constitutive coefficients of the intermediate layer, we characterize three different limit models and their associated limit problems, the so-called soft, hard and rigid poroelastic interface models, respectively. First and higher order interface models are derived. Moreover, we identify the non classical transmission conditions at the interface between the two three-dimensional bodies in terms of the jump of the stresses, specific discharge, pressure and displacements.

Keywords

Poroelastic materials Interface problem Asymptotic analysis 
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Notes

References

  1. 1.
    Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26:182–185MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Coussy O (2011) Mechanics and physics of porous solids. Wiley, ChichesterGoogle Scholar
  3. 3.
    Lopatnikov S, Gillespie JW Jr (2010) Poroelasticity-I: governing equations of the mechanics of fluid-saturated porous materials. Transp Porous Media 84:471–492MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lopatnikov S, Gillespie JW Jr (2011) Poroelasticity-II: on the equilibrium state of the fluid-filled penetrable poroelastic body. Transp Porous Media 89:475–486MathSciNetCrossRefGoogle Scholar
  5. 5.
    Lopatnikov S, Gillespie JW Jr (2012) Poroelasticity-III: conditions on the Interfaces. Transp Porous Media 93:597–607MathSciNetCrossRefGoogle Scholar
  6. 6.
    Geymonat G, Krasucki F, Lenci S (1999) Mathematical analysis of a bonded joint with a soft thin adhesive. Math Mech Solids 4:201–225MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bessoud A-L, Krasucki F, Serpilli M (2011) Asymptotic analysis of shell-like inclusions with high rigidity. J Elast 103:153–172MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lebon F, Rizzoni R (2010) Asymptotic analysis of a thin interface: the case involving similar rigidity. Int J Eng Sci 48:473–486MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lebon F, Rizzoni R (2011) Asymptotic behavior of a hard thin linear interphase: an energy approach. Int J Solids Struct 48:441–449CrossRefzbMATHGoogle Scholar
  10. 10.
    Serpilli M, Lenci S (2012) Asymptotic modelling of the linear dynamics of laminated beams. Int J Solids Struct 49(9):1147–1157CrossRefGoogle Scholar
  11. 11.
    Serpilli M, Krasucki F, Geymonat G (2013) An asymptotic strain gradient Reissner–Mindlin plate model. Meccanica 48(8):2007–2018MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Serpilli M (2015) Mathematical modeling of weak and strong piezoelectric interfaces. J Elast 121(2):235–254MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Serpilli M (2017) Asymptotic interface models in magneto-electro-thermo-elastic composites. Meccanica 52(6):1407–1424MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Marciniak-Czochra A, Mikelić A (2014) A rigorous derivation of the equations for the clamped Biot-Kirchhoff-Love poroelastic plate. Arch Ration Mech Anal 215(3):1035–1062MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Mikelić A, Tambača J (2016) Derivation of a poroelastic flexural shell model. Multiscale Model Simul 14(1):364–397MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Mikelić A, Tambača J (2019) Derivation of a poroelastic elliptic membrane shell model. Appl Anal 98(1–2):136–161.  https://doi.org/10.1080/00036811.2018.1430784 MathSciNetCrossRefGoogle Scholar
  17. 17.
    Rizzoni R, Dumont S, Lebon F, Sacco E (2014) Higher order models for soft and hard elastic interfaces. Int J Solids Struct 51(23–24):4137–4148CrossRefGoogle Scholar
  18. 18.
    Girault V, Pencheva G, Wheeler MF, Wildey T (2011) Domain decomposition for poroelasticity and elasticity with DG jumps and mortars. Math Models Methods Appl Sci 21(1):169–213MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Ciarlet PG (1997) Mathematical elasticity, vol II: theory of plates. North-Holland, AmsterdamzbMATHGoogle Scholar
  20. 20.
    Jeannin L, Dormieux L (2017) Poroelastic behaviour of granular media with poroelastic interfaces. Mech Res Commun 83:27–31CrossRefGoogle Scholar
  21. 21.
    Geymonat G, Hendili S, Krasucki F, Serpilli M, Vidrascu M (2014) Asymptotic expansions and domain decomposition in domain decomposition methods XXI, vol 98. Lecture notes in computational science and engineering. Springer, Berlin, pp 749–757.  https://doi.org/10.1007/978331905789772 zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil and Building Engineering, and ArchitectureUniversità Politecnica delle MarcheAnconaItaly

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