A coupled theory of fluid permeation and large deformations for elastomeric materials

Shawn A. Chester, Lallit Anand

Research output: Contribution to journalArticlepeer-review

220 Scopus citations

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 FloryHuggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statisticalmechanical model for the change in configurational entropya 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.

Original languageEnglish (US)
Pages (from-to)1879-1906
Number of pages28
JournalJournal of the Mechanics and Physics of Solids
Volume58
Issue number11
DOIs
StatePublished - Nov 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • Diffusion
  • Elastomeric materials
  • Gels
  • Large deformations
  • Thermodynamics

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