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Stable fitting of noisy stress relaxation data

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Abstract

The mechanical behavior of a viscoelastic material can often be described by a spectrum of Maxwell-Wiechert elements. The inverse problem associated with estimating the parameters of this spectrum from the results of viscoelastic relaxation (ramp-and-hold) test is in general ill-posed and unstable, with estimates highly sensitive to initial conditions and noise. Here, we demonstrate stable estimation of a continuous viscoelastic spectrum from stress relaxation experiments using Tikhonov regularization. We assess the effects of noise and sampling frequency on these estimates, and describe regularization parameter selection. We demonstate the algorithm by estimating the viscoelastic relaxation spectra of soft vinyl samples.

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Funding

This work was funded in part by the National Institutes of Health through grant U01EB016422, and by the National Science Foundation through the Science and Technology Center for Engineering Mechanobiology, grant CMMI 1548571.

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Authors and Affiliations

  1. NSF Science and Technology Center for Engineering Mechanobiology, Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, MO, 63130, USA

    Roger A. Rowe, Kenneth M. Pryse & Guy M. Genin

  2. Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, MO, 60613, USA

    Elliot L. Elson

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  1. Roger A. Rowe
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  2. Kenneth M. Pryse
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  4. Guy M. Genin
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Correspondence to Guy M. Genin.

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Rowe, R.A., Pryse, K.M., Elson, E.L. et al. Stable fitting of noisy stress relaxation data. Mech Soft Mater 1, 9 (2019). https://doi.org/10.1007/s42558-019-0010-4

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