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.
- Design Engineering Division and Computers in Engineering Division
Nonlinear Fractional Derivative Stress-Strain Relations for Polymer Gels Based on the Generalized Maxwell Model
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Fukunaga, M, & Shimizu, N. "Nonlinear Fractional Derivative Stress-Strain Relations for Polymer Gels Based on the Generalized Maxwell Model." Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C. San Diego, California, USA. August 30–September 2, 2009. pp. 1241-1246. ASME. https://doi.org/10.1115/DETC2009-87283
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