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Application of Post–Widder inversion formula to the calculation of relaxation spectrum from relaxation modulus

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Abstract

There have been developed a number of algorithms for the determination of relaxation spectrum from viscoelastic data. When viscoelastic data are given by stress relaxation test, the relation between relaxation spectrum and relaxation modulus can be transformed to that of Laplace transform. Hence, calculation of relaxation spectrum from relaxation modulus is a problem of inverting Laplace transform. Among various mathematical methods for inverse Laplace transform, the Post–Widder formula has been chosen by a number of researchers. However, they did not solve the problem by use of advance numerical technic but used low-order approximations. We suggest a new numerical algorithm which can calculate higher order solutions. In principle, the order of the Post–Widder formula is not limited in our algorithm.

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The data used and/or analyzed in this study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors are supported by the Mid-Career Researcher Program, through the National Research Foundation of Korea (NRF), and funded by the Ministry of Education, Science, and Technology (2019R1I1A2A02063776).

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Authors and Affiliations

  1. Department of Polymer Science and Engineering, Kyungpook National University, Daegu, Korea

    Gyuhyeon Cho, Jehyeok Choi & Kwang Soo Cho

  2. School of Mechanical Engineering, Gyeongsang National University, Jinju, Korea

    Junghaeng Lee

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  1. Gyuhyeon Cho
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  2. Jehyeok Choi
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  4. Kwang Soo Cho
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Correspondence to Kwang Soo Cho.

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Cho, G., Choi, J., Lee, J. et al. Application of Post–Widder inversion formula to the calculation of relaxation spectrum from relaxation modulus. Korea-Aust. Rheol. J. 36, 79–88 (2024). https://doi.org/10.1007/s13367-023-00086-7

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