Large time approximation for shearing motions

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)

122381.pdf - Accepted Version



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
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 (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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