Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 58, Issue 11, Pages 1879-1906Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2010.07.020
Keywords
Gels; Elastomeric materials; Diffusion; Large deformations; Thermodynamics
Funding
- National Science Foundation [DMI-0517966]
- Singapore-MIT Alliance
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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. (C) 2010 Elsevier Ltd. All rights reserved.
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