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On the Numerical Determination of Relaxation and Retardation Spectra for Linearly Viscoelastic Materials

Clauser, John F. and Knauss, Wolfgang G. (1968) On the Numerical Determination of Relaxation and Retardation Spectra for Linearly Viscoelastic Materials. Transactions of the Society of Rheology, 12 (1). pp. 143-153. ISSN 0038-0032. doi:10.1122/1.549103.

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Knowledge of the relaxation spectrum is important because (1) it provides an intrinsic characterization of the mechanical properties for linearly viscoelastic materials and (2) it offers a rational way to derive the coefficients for a Prony or Dirichlet series representation of the relaxation modulus of importance to some engineering analyses. A numerical solution based on Simpson quadrature leads to an unstable solution in the sense that a decrease in integration intervals produces a progressively worse solution which oscillates between positive and negative values. This difficulty may be overcome by requiring that the curvature of the relaxation spectrum with respect to the relaxation times be minimized. The method is tested on the modified power law and good agreement with the exact and numerically determined relaxation spectrum is obtained. However, when the same method is used to determine the retardation spectrum, only the unstable solution is obtained, although the form of the integral equation is the same. This different behavior is attributed to the difference in the characteristics of the relaxation and retardation spectral functions.

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Additional Information:© 1968 Copyright The Society of Rheology. Received November 6, 1967. This work was supported by the Air Force Rocket Propulsion Laboratory, Edwards Air Force Base, under Contract AF 04(661)-9572 and the National Aeronautics and Space Administration, Research Contract NsG-172-60.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24
Deposited By: Wolfgang Gustav Knauss
Deposited On:14 Jun 2008
Last Modified:08 Nov 2021 19:00

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