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Mathematics and Mechanics of Solids
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Nonlinear Constitutive Laws in Viscoelasticity

C.S. Drapaca

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

S. Sivaloganathan

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

G. Tenti

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

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

This version was published on October 1, 2007

Mathematics and Mechanics of Solids, Vol. 12, No. 5, 475-501 (2007)
DOI: 10.1177/1081286506062450
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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]