Rheology pp 369-374 | Cite as

Numerical Calculation of Relaxation Distributions

  • Emory Menefee


In linear viscoelasticity, the spectrum of relaxation times, H(τ), or retardation times, L(τ), represent the common connection among numerous measurable functions such as stress relaxation, creep recovery, dynamic storage and loss moduli, and even shear dependent viscosity. In general, these spectra are defined by convolution integrals such as, for example, the following:
$$F(t) = \int_\infty ^\infty {H(\tau )\exp ( - t/\tau )d\ln } \tau $$
$$F(\omega ) = \int_{{ - \infty }}^{\infty } {{{\omega }^{2}}{{\tau }^{2}}H(\tau ) {{{(1 + {{\omega }^{2}}{{\tau }^{2}})}}^{{ - 1}}}d\ln \tau }$$
These and other representations are discussed by Ferry1. The kernel functions exp(-t/ τ) and (1 +ω2“τ 2)”1 are cutoffs with values ranging from 0 to 1 that diminish and eventually eliminate the contribution of elements for which the relaxation time τ is greater than the experimental time t, or 1/ω , or 1/∈ .


Stress Relaxation Steady Shearing Linear Viscoelasticity Relaxation Spectrum Numerical Inversion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Emory Menefee
    • 1
  1. 1.Western Regional Research CenterU.S. Department of AgricultureAlbanyUSA

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