Abstract
In this paper, we formulate two nonlinear stress-strain relations including memory effect in the dynamical behavior of gels that are the kind of viscoelastic materials. The basic assumption of the model is made that the gels consist of blobs of high polymers. Hereditary response of blobs to the stress determines the average stress-strain relation of the material. Two stress-strain relations are derived for different models of gels. These stress-strain relations are compared with the fractional derivative version of Lodge’s rubber-like liquids and the empirical nonlinear fractional derivative model proposed by Fukunaga et. al. at FDA08.
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