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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Biot MA (1955) Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 26:182–185
Coussy O (2011) Mechanics and physics of porous solids. Wiley, Chichester
Lopatnikov S, Gillespie JW Jr (2010) Poroelasticity-I: governing equations of the mechanics of fluid-saturated porous materials. Transp Porous Media 84:471–492
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
Lopatnikov S, Gillespie JW Jr (2012) Poroelasticity-III: conditions on the Interfaces. Transp Porous Media 93:597–607
Geymonat G, Krasucki F, Lenci S (1999) Mathematical analysis of a bonded joint with a soft thin adhesive. Math Mech Solids 4:201–225
Bessoud A-L, Krasucki F, Serpilli M (2011) Asymptotic analysis of shell-like inclusions with high rigidity. J Elast 103:153–172
Lebon F, Rizzoni R (2010) Asymptotic analysis of a thin interface: the case involving similar rigidity. Int J Eng Sci 48:473–486
Lebon F, Rizzoni R (2011) Asymptotic behavior of a hard thin linear interphase: an energy approach. Int J Solids Struct 48:441–449
Serpilli M, Lenci S (2012) Asymptotic modelling of the linear dynamics of laminated beams. Int J Solids Struct 49(9):1147–1157
Serpilli M, Krasucki F, Geymonat G (2013) An asymptotic strain gradient Reissner–Mindlin plate model. Meccanica 48(8):2007–2018
Serpilli M (2015) Mathematical modeling of weak and strong piezoelectric interfaces. J Elast 121(2):235–254
Serpilli M (2017) Asymptotic interface models in magneto-electro-thermo-elastic composites. Meccanica 52(6):1407–1424
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
Mikelić A, Tambača J (2016) Derivation of a poroelastic flexural shell model. Multiscale Model Simul 14(1):364–397
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
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
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
Ciarlet PG (1997) Mathematical elasticity, vol II: theory of plates. North-Holland, Amsterdam
Jeannin L, Dormieux L (2017) Poroelastic behaviour of granular media with poroelastic interfaces. Mech Res Commun 83:27–31
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
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Serpilli, M. Classical and higher order interface conditions in poroelasticity. Ann. Solid Struct. Mech. 11, 1–10 (2019). https://doi.org/10.1007/s12356-019-00052-5
- Poroelastic materials
- Interface problem
- Asymptotic analysis