A non-linear integral representation for viscoelastic behaviour

Pipkin, A. C.<sup>1</sup>; Rogers, T. G.<sup>2</sup>

Affiliations

¹Division of Applied Mathematics, Brown University, Rhode Island

²Department of Theoretical Mechanics, University of Nottingham, England

Abstract

An integral series representation is obtained for non-linear viscoelastic response to an arbitrary strain (or stress) history. The series is arranged so that experimental data can be incorporated directly. Each of the terms has a definite intrinsic meaning that is independent of the choice of strain measure. The first term is a single integral with a non-linear integrand determined completely by single-step creep or relaxation tests. The nth term is obtained directly by the difference, if any is observed, between the experimental results for n-step tests and the prediction based on (n−1)-step data. The series has the distinctive property that it terminates at the nth term whenever the strain (or stress) history is an n-step history.

Previously published experimental data on non-linear viscoelastic behaviour are re-interpreted on the basis of this theory; in most cases they agree very closely with the single integral approximation given by the first term alone.

The generalization to three-dimensional form and the implications of isotropy are also given.

Links

DOI: 10.1016/0022-5096(68)90016-1

WoS: A1968A469400004

History

Received: 1967-10-23

Cited By (16)

Year	Entry
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1979	Lakes RS, Katz JL. Viscoelastic properties of wet cortical bone, III: a non-linear constitutive equation. J Biomech. 1979;12(9):689-698.
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2015	Wood GW. Interspecies Scaling in Blast Neurotrauma [PhD thesis]. Duke University; 2015.
1975	Lakes RS. Viscoelastic and Dielectric Relaxation in Cortical Bone [PhD thesis]. Troy, NY: Rensselaer Polytechnic Institute; July 1975.
1997	Richards M. Strain Environment Effects on New Bone Formation and Precursor Tissue Differentiation During Distraction [PhD thesis]. University of Michigan; 1997.
2020	Sedal A. Continuum Mechanical Models for Design and Characterization of Soft Robots [PhD thesis]. University of Michigan; 2020.
2002	Gardiner JC. Computational Modeling of Ligament Mechanics [PhD thesis]. University of Utah; May 2002.
2008	Lucas SR. A Microstructural Viscoelastic Ligament Failure Model [PhD thesis]. Charlottesville, VA: University of Virginia; January 2008.