Abstract
A new spectrum-based model for describing the behavior of time-dependent materials is presented. In this paper, unlike most prior modeling techniques, the time-dependent response of viscoelastic materials is not expressed through the use of series. Instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior. Another consequence of choosing the spectrum function of the type used in this paper is to have a few closed form analytic solutions in the theory of linear viscoelasticity. The Laplace transform technique is used to obtain the necessary formulae for viscoelastic Lame' functions, relaxation and bulk moduli, creep bulk and shear compliance, as well as Poisson's ratio. By using the Elastic–Viscoelastic Correspondence Principle (EVCP), material constants appearing in the proposed model are obtained by comparing the experimental data with the solution of the integral equation for a simple tensile test. The resulting viscoelastic functions describe the material properties which can then be used to express the behavior of a material in other loading configurations. The model's potential is demonstrated and its limitations are discussed.
Similar content being viewed by others
References
Alfrey, T. Jr.: Mechanical Behavior of High Polymers. Interscience Publishers, Inc., New York (1948)
Christensen, R.M.: Theory of Viscoelasticity. Academic Press, New York (1971)
Eringen, C.A.: Mechanics of Continua. Wiley, New York (1967)
Erdelyi, A. (ed.): Table of Integral Transforms, vol. I. McGraw-Hill, New York (1954)
Ferry, J.D.: Viscoelastic Properties of Polymers. Wiley, New York (1970)
Flugge, W.: Viscoelasticity. Blaisdell Publishing Company, Waltham, Mass (1967)
Gibson, R.F.: Principles of Composite Material Mechanics. McGraw-Hill, New York (1994)
Hilton, H.: Implications and constraints of time-independent poisson ratios in linear isotropic and anisotropic viscoelasticity. J. Elast. 63, 221–251 (2001)
Hilton, H., Yi, S.: The significance of (an) isotropic viscoelastic poisson ratio stress and time dependencies. Internat. J. Solids Struct. 35, 3081–3095 (1998)
Hansen, A.C., Walrath, D.E.: Mechanical testing and numerical analysis of composite materials. Final Report submitted to NSWC — Carderock Division, Grant: N00167-00-M-0468, University of Wyoming (2002)
Lakes, R.: The time dependent Poisson's ratio of viscoelastic materials can increase or decrease. Cell. Polym. 11, 466–469 (1992)
Sullivan, R.W.: An Analytical Method to Determine the Mechanical Properties of Linear Viscoelastic Solids. Ph.D. thesis, Mississippi State University (2003)
Schapery, R.A.: Stress analysis of viscoelastic composite materials. J. Compos. Mater. 1, 228–267 (1967)
Sullivan, R.W., Johnson, D.P.: Method for determination of viscoelastic parameters using the principle of correspondence. AIAA TN 40(9), 1907–1909 (2002)
Tschoegl, N.W.: The Phenomenological Theory of Linear Viscoelastic Behavior. Springer-Verlag, Heidelberg (1989)
Tschoegl, N.W., Knauss, W.G., Emri, I.: Poisson's ratio in linear viscoelasticity — a critical review. Mech. Time-Dependent Mater. 6, 3–51 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sullivan, R.W. On the use of a spectrum-based model for linear viscoelastic materials. Mech Time-Depend Mater 10, 215–228 (2006). https://doi.org/10.1007/s11043-006-9019-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11043-006-9019-9