Saccomandi, G. and Vergori, L. (2016) Large time approximation for shearing motions. SIAM Journal on Applied Mathematics, 76(5), pp. 1964-1983. (doi: 10.1137/16M1076599)
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Abstract
Small- and large-amplitude oscillatory shear tests are widely used by experimentalists to measure, respectively, linear and nonlinear properties of viscoelastic materials. These tests are based on the quasi-static approximation according to which the strain varies sinusoidally with time after a number of loading cycles. Despite the extensive use of the quasi-static approximation in solid mechanics, few attempts have been made to justify rigorously such an approximation. The validity of the quasi-static approximation is studied here in the framework of the Mooney--Rivlin Kelvin--Voigt viscoelastic model by solving the equations of motion analytically. For a general nonlinear model, the quasi-static approximation is instead derived by means of a perturbation analysis.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Vergori, Dr Luigi |
| Authors: | Saccomandi, G., and Vergori, L. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | SIAM Journal on Applied Mathematics |
| Publisher: | Society for Industrial and Applied Mathematics |
| ISSN: | 0036-1399 |
| ISSN (Online): | 1095-712X |
| Published Online: | 04 October 2016 |
| Copyright Holders: | Copyright © 2016 Society for Industrial and Applied Mathematics |
| First Published: | First published in SIAM Journal on Applied Mathematics 76(5):1964-1983 |
| Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |
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