Abstract
In this study, we develop a general expression for the linearized properties of swollen elastomers undergoing large deformations. The free energy function of swollen elastomers is assumed to obey the Frenkel–Flory–Rehner hypothesis, i.e., the elastic and mixing contributions are additive. The elastic strain energy is not assumed to have a particular form but is assumed only to be a function of a set of strain-invariants. A linearization procedure is used to obtain the general expression for the Young's modulus and Poisson's ratio under an arbitrary base state. The derived expression includes a characteristic term, which has the ability to describe a transient state between the extreme states prescribed by two distinct conditions. The verification is performed by estimating the shear modulus and considering the original Flory–Rehner framework. In addition, to show the usefulness, an extended Gent model is examined to elucidate the interactions between limiting chain extensibility and the second strain-invariant.
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