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Effective governing equations for poroelastic growing media. (English) Zbl 1346.74159

Summary: A new mathematical model is developed for the macroscopic behaviour of a porous linear elastic solid, saturated with a slowly flowing incompressible, viscous fluid, with surface accretion of the solid phase. The derivation uses a formal two-scale asymptotic expansion to exploit the well-separated length scales of the material: the pores are small compared to the macroscale, with a spatially periodic microstructure. Surface accretion occurs at the interface between the solid and fluid phases, resulting in growth of the solid phase through mass exchange from the fluid at a prescribed rate (and vice versa). The averaging derives a new poroelastic model, which reduces to the classical result of R. Burridge and J. B. Keller [J. Acoust. Soc. Am. 70, 1140–1146 (1981; Zbl 0519.73038)] in the limit of no growth. The new model is of relevance to a large range of applications including packed snow, tissue growth, biofilms and subsurface rocks or soils.

MSC:

74Q15 Effective constitutive equations in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76S05 Flows in porous media; filtration; seepage

Citations:

Zbl 0519.73038
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