Parameter estimation for a springpot–fractional dashpot viscoelastic model
Optimisation and numerical Laplace inversion
Publication date
2026-07-01
Document type
Konferenzbeitrag
Author
Organisational unit
Scopus ID
Conference
26th International Conference on Computational Science and Its Applications (ICCSA 2026) ; Braga, Portugal ; June 30 – July 3, 2026
Publisher
Springer Nature Switzerland
Book title
Computational Science and Its Applications – ICCSA 2026 Workshops
First page
285
Last page
297
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
Fractional-Dashpot
Optimisation
Rheology
Springpot
Talbot Method
Viscoelastic models
dtec.bw
Abstract
This work addresses the parameter estimation of a fractional viscoelastic model comprising a springpot and a fractional dashpot arranged in series. Key features of the model, including the relaxation modulus, are formulated in the Laplace domain and subsequently evaluated in the time domain through numerical inversion using the Talbot method. A two-step optimisation strategy is adopted to identify the model parameters efficiently. In the first stage, frequency-domain data, namely the storage and loss moduli, are used to estimate an initial set of parameters. In the second stage, these preliminary estimates are refined by performing an optimisation that incorporates both frequency-domain data and time-domain data (relaxation modulus). Since the relaxation modulus is obtained through an inverse Laplace transform and does not admit a closed-form expression in the time domain, a sequential iterative procedure is employed during the second stage. In this approach, the relaxation modulus is first computed numerically using the Talbot method, after which the parameters are updated through optimisation. This process is repeated iteratively until a prescribed tolerance is satisfied. Validation against experimental data obtained for a low-density polyethylene demonstrates that the proposed methodology accurately reproduces both frequency- and time-domain responses, highlighting the effectiveness of fractional models in capturing complex viscoelastic behaviour.
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