From arteries to boreholes: steady-state response of a poroelastic cylinder to fluid injection
Open Access
- 31 May 2017
- journal article
- research article
- Published by The Royal Society in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 473 (2201), 20160753
- https://doi.org/10.1098/rspa.2016.0753
Abstract
The radially outward flow of fluid into a porous medium occurs in many practical problems, from transport across vascular walls to the pressurization of boreholes. As the driving pressure becomes non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid has an increasingly strong impact on the flow. For very large pressures or very soft materials, as is the case for hydraulic fracturing and arterial flows, this coupling can lead to large deformations and, hence, to strong deviations from a classical, linear-poroelastic response. Here, we study this problem by analysing the steady-state response of a poroelastic cylinder to fluid injection. We consider the qualitative and quantitative impacts of kinematic and constitutive nonlinearity, highlighting the strong impact of deformation-dependent permeability. We show that the wall thickness (thick versus thin) and the outer boundary condition (free versus constrained) play a central role in controlling the mechanics.Keywords
Other Versions
Funding Information
- Engineering and Physical Sciences Research Council (Doctoral Training Award to LCA)
This publication has 37 references indexed in Scilit:
- Needle–tissue interaction forces – A survey of experimental dataMedical Engineering & Physics, 2012
- Elasticity and permeability of porous fibre-reinforced materials under large deformationsMechanics of Materials, 2012
- Physical Limits and Design Principles for Plant and Fungal MovementsScience, 2005
- Hencky's elasticity model and linear stress-strain relations in isotropic finite hyperelasticityActa Mechanica, 2002
- Poroelastic creep response analysis of a lumbar motion segment in compressionJournal of Biomechanics, 1996
- Water transport in the arterial wall—A theoretical studyJournal of Biomechanics, 1983
- Fluid Flow Through a Class of Highly-Deformable Porous Media. Part II: Experiments With WaterJournal of Fluids Engineering, 1981
- A mathematical model of water flux through aortic tissueBulletin of Mathematical Biology, 1979
- On H. Hencky’s Approximate Strain-Energy Function for Moderate DeformationsJournal of Applied Mechanics, 1979
- The Law of Elasticity for Isotropic and Quasi-Isotropic Substances by Finite DeformationsJournal of Rheology, 1931