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Reference: MacMinn, CW, Dufresne, ER and Wettlaufer, JS et al., (2016). Large deformations of a soft porous material. Physical Review Applied, 5 (4), 044020.Citable link to this page:


Large deformations of a soft porous material

Abstract: Compressing a porous material will decrease the volume of the pore space, driving fluid out. Similarly, injecting fluid into a porous material can expand the pore space, distorting the solid skeleton. This poromechanical coupling has applications ranging from cell and tissue mechanics to geomechanics and hydrogeology. The classical theory of linear poroelasticity captures this coupling by combining Darcy’s law with Terzaghi’s effective stress and linear elasticity in a linearized kinematic framework. Linear poroelasticity is a good model for very small deformations, but it becomes increasingly inappropriate for moderate to large deformations, which are common in the context of phenomena such as swelling and damage, and for soft materials such as gels and tissues. The well-known theory of large-deformation poroelasticity combines Darcy’s law with Terzaghi’s effective stress and nonlinear elasticity in a rigorous kinematic framework. This theory has been used extensively in biomechanics to model large elastic deformations in soft tissues and in geomechanics to model large elastoplastic deformations in soils. Here, we first provide an overview and discussion of this theory with an emphasis on the physics of poromechanical coupling. We present the largedeformation theory in an Eulerian framework to minimize the mathematical complexity, and we show how this nonlinear theory simplifies to linear poroelasticity under the assumption of small strain. We then compare the predictions of linear poroelasticity with those of large-deformation poroelasticity in the context of two uniaxial model problems: fluid outflow driven by an applied mechanical load (the consolidation problem) and compression driven by a steady fluid throughflow. We explore the steady and dynamical errors associated ith the linear model in both situations, as well as the impact of introducing a deformation-dependent permeability. We show that the error in linear poroelasticity is due primarily to kinematic nonlinearity and that this error (i) plays a surprisingly important role in the dynamics of the deformation and (ii) is amplified by nonlinear constitutive behavior, such as deformation-dependent permeability

Publication status:PublishedPeer Review status:Peer reviewedVersion:Publisher's versionDate of acceptance:2016-01-16 Funder: Yale Climate and Energy Institute   Funder: National Science Foundation   Notes:© 2016 American Physical Society

Bibliographic Details

Publisher: American Physical Society

Publisher Website:

Journal: Physical Review Appliedsee more from them

Publication Website:

Volume: 5

Issue: 4

Extent: 044020

Issue Date: 2016-04



Issn: 2331-7019

Uuid: uuid:b34949a1-59b2-436e-a3a8-9b0d99777f9e

Urn: uri:b34949a1-59b2-436e-a3a8-9b0d99777f9e

Pubs-id: pubs:571230 Item Description

Type: journal-article;

Version: Publisher's versionKeywords: physics.flu-dyn physics.flu-dyn cond-mat.soft Journal Article


Author: MacMinn, CW - facultyOxford, MPLS, Engineering Science - - - Dufresne, ER - - - Wettlaufer, JS - facultyOxford, MPLS, Mathematica



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