Distribution functions in linear viscoelastic theory

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Abstract
The relaxation function of stress can be interpreted in terms of the distribution function of relaxation times. The retardation function of strain can be interpreted in terms of the distribution function of strain. The two distribution functions, or spectra, belonging to the same physical system are related by integral transforms. These transforms have been discussed in earlier papers. However, the discussion was not entirely satisfactory because it missed the appearance of single lines associated with truncated spectra, and because it employed integrals over improper and ill‐defined functions. This paper gives an alternative treatment which is believed to be more satisfactory mathematically. The distribution functions are found to be the imaginary components of two complex, analytical functions which are the generating functions of all other functions of viscoelastic theory.

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