The Importance of the Compatibility of Nonlinear Constitutive Theories With Their Linear Counterparts

[+] Author and Article Information
Ramon Quintanilla

Matemàtica Aplicada 2,  Universitat Politècnica de Catalunya, Colon 11, 09222 Terrassa, Barcelona, Spainramon.quintanilla@upc.edu

Giuseppe Saccomandi

Dipartimento di Ingegneria dell’Innovazione, Sezione di Ingegneria Industriale,  Università di Lecce, 73100 Lecce, Italygiuseppe.saccomandi@unile.it

J. Appl. Mech 74(3), 455-460 (May 24, 2006) (6 pages) doi:10.1115/1.2338053 History: Received October 13, 2005; Revised May 24, 2006

We show, by considering a special class of nonlinear viscoelastic materials, that consistency of a mechanical model with classical linear viscoelasticity, may be a fundamental condition to ensure a mathematical and physical well-posedness behavior. To illustrate our arguments we use a rectilinear class of shear motions that we investigate in the static and quasistatic case in the framework of a simple boundary value problem and the classical recovery phenomenon.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Solution 35 for typical values of the parameters

Grahic Jump Location
Figure 2

Recovery shear as in 44 in the case ϵ0=0 and ϵ0≠0



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