A coupled theory of fluid permeation and large deformations for elastomeric materials
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Author(s)
Anand, Lallit
Chester, Shawn Alexander
Date Issued
July 2010
Journal
Journal of the Mechanics and Physics of Solids
Publisher
Elsevier
Citation
Chester, Shawn A., and Lallit Anand. “A Coupled Theory of Fluid Permeation and Large Deformations for Elastomeric Materials.” Journal of the Mechanics and Physics of Solids 58.11 (2010) : 1879-1906.
Version
Author's final manuscript
Abstract
An elastomeric gel is a cross-linked polymer network swollen with a solvent (fluid). A continuum-mechanical
theory to describe the various coupled aspects of fluid permeation and large deformations (e.g., swelling and
squeezing) of elastomeric gels is formulated. The basic mechanical force balance laws and the balance law
for the fluid content are reviewed, and the constitutive theory that we develop is consistent with modern
treatments of continuum thermodynamics, and material frame-indifference. In discussing special constitutive
equations we limit our attention to isotropic materials, and consider a model for the free energy based on a
Flory-Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled
with a non-Gaussian statistical-mechanical model for the change in configurational entropy — a model
which accounts for the limited extensibility of polymer chains. As representative examples of application of
the theory, we study (a) three-dimensional swelling-equilibrium of an elastomeric gel in an unconstrained,
stress-free state; and (b) the following one-dimensional transient problems: (i) free-swelling of a gel; (ii)
consolidation of an already swollen gel; and (iii) pressure-difference-driven diffusion of organic solvents across
elastomeric membranes.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1016/j.jmps.2010.07.020
