A coupled theory of fluid permeation and large deformations for elastomeric materials
Author(s)Anand, Lallit; Chester, Shawn Alexander
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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.
DepartmentMassachusetts Institute of Technology. Department of Mechanical Engineering
Journal of the Mechanics and Physics of Solids
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.
Author's final manuscript