Classical and higher order interface conditions in poroelasticity


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.

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  1. 1.

    Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26:182–185

    MathSciNet  Article  Google Scholar 

  2. 2.

    Coussy O (2011) Mechanics and physics of porous solids. Wiley, Chichester

    Google Scholar 

  3. 3.

    Lopatnikov S, Gillespie JW Jr (2010) Poroelasticity-I: governing equations of the mechanics of fluid-saturated porous materials. Transp Porous Media 84:471–492

    MathSciNet  Article  Google 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 89:475–486

    MathSciNet  Article  Google Scholar 

  5. 5.

    Lopatnikov S, Gillespie JW Jr (2012) Poroelasticity-III: conditions on the Interfaces. Transp Porous Media 93:597–607

    MathSciNet  Article  Google Scholar 

  6. 6.

    Geymonat G, Krasucki F, Lenci S (1999) Mathematical analysis of a bonded joint with a soft thin adhesive. Math Mech Solids 4:201–225

    MathSciNet  Article  Google Scholar 

  7. 7.

    Bessoud A-L, Krasucki F, Serpilli M (2011) Asymptotic analysis of shell-like inclusions with high rigidity. J Elast 103:153–172

    MathSciNet  Article  Google Scholar 

  8. 8.

    Lebon F, Rizzoni R (2010) Asymptotic analysis of a thin interface: the case involving similar rigidity. Int J Eng Sci 48:473–486

    MathSciNet  Article  Google Scholar 

  9. 9.

    Lebon F, Rizzoni R (2011) Asymptotic behavior of a hard thin linear interphase: an energy approach. Int J Solids Struct 48:441–449

    Article  Google Scholar 

  10. 10.

    Serpilli M, Lenci S (2012) Asymptotic modelling of the linear dynamics of laminated beams. Int J Solids Struct 49(9):1147–1157

    Article  Google Scholar 

  11. 11.

    Serpilli M, Krasucki F, Geymonat G (2013) An asymptotic strain gradient Reissner–Mindlin plate model. Meccanica 48(8):2007–2018

    MathSciNet  Article  Google Scholar 

  12. 12.

    Serpilli M (2015) Mathematical modeling of weak and strong piezoelectric interfaces. J Elast 121(2):235–254

    MathSciNet  Article  Google Scholar 

  13. 13.

    Serpilli M (2017) Asymptotic interface models in magneto-electro-thermo-elastic composites. Meccanica 52(6):1407–1424

    MathSciNet  Article  Google 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):1035–1062

    MathSciNet  Article  Google Scholar 

  15. 15.

    Mikelić A, Tambača J (2016) Derivation of a poroelastic flexural shell model. Multiscale Model Simul 14(1):364–397

    MathSciNet  Article  Google Scholar 

  16. 16.

    Mikelić A, Tambača J (2019) Derivation of a poroelastic elliptic membrane shell model. Appl Anal 98(1–2):136–161.

    MathSciNet  Article  MATH  Google 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):4137–4148

    Article  Google 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):169–213

    MathSciNet  Article  Google Scholar 

  19. 19.

    Ciarlet PG (1997) Mathematical elasticity, vol II: theory of plates. North-Holland, Amsterdam

    Google Scholar 

  20. 20.

    Jeannin L, Dormieux L (2017) Poroelastic behaviour of granular media with poroelastic interfaces. Mech Res Commun 83:27–31

    Article  Google 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.

    Google Scholar 

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Correspondence to Michele Serpilli.

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Serpilli, M. Classical and higher order interface conditions in poroelasticity. Ann. Solid Struct. Mech. 11, 1–10 (2019).

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  • Poroelastic materials
  • Interface problem
  • Asymptotic analysis