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Mathematics and Mechanics of Solids
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Article

Nonlinear Constitutive Laws in Viscoelasticity

C. S. Drapaca*, S. Sivaloganathan, G. Tenti

Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

* To whom correspondence should be addressed.


  Abstract

The theory of viscoelasticity appears to play a central role in the description of materials which exhibit time dependent stress-strain behavior. Various materials like polymers, some soft biological tissues, and various foods have been already successfully modeled as nonlinear viscoelastic materials.The literature in these application areas is replete with different, seemingly unconnected nonlinear viscoelastic models. The aim of the present paper is to review the classical nonlinear viscoelastic models and provide a unifying framework using the continuum mechanics formalism.

Key Words: Nonlinear viscoelasticity, continuum mechanics, mathematical modeling

First published on April 7, 2006, doi:10.1177/1081286506062450

Mathematics and Mechanics of Solids 2007;12:475.

A more recent version of this article appeared on October 1, 2007

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A. Wineman
Nonlinear Viscoelastic Solids--A Review
Mathematics and Mechanics of Solids, May 1, 2009; 14(3): 300 - 366.
[Abstract] [PDF]