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We develop a two-stage computational method to assimilate linear viscoelastic material functions (LMFs), viz., stress relaxation modulus, creep compliance, and the complex modulus, by inferring a consensus discrete relaxation spectrum (DRS) that simultaneously fits all three LMFs. In the first stage, the DRS corresponding to the different LMFs is deduced independently, before they are combined heuristically to generate an initial guess for the consensus DRS. In the second stage, this initial guess is refined using nonlinear least squares regression. The effectiveness of this method for data fusion and validation is demonstrated by analyzing experimental data collected on two different polymer melt systems. We also investigate the performance of the method when the timescales probed by the LMFs do not overlap, or are limited to 4–6 decades, as is typically the case for thermorheologically complex materials. To explore these questions, we generate synthetic datasets by obscuring information from one of the experimental datasets. We find that the computational protocol works quite well. As expected, the quality of the inferred DRS is marginally impaired because information is suppressed.
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pyReSpect: A Computer Program to Extract Discrete and Continuous Spectra from Stress Relaxation Experiments
Abstract An open‐source software package “pyReSpect” is presented to extract relaxation spectra from stress relaxation experiments. It employs nonlinear Tikhonov regularization to obtain the continuous relaxation spectrum (CRS), and robust new algorithm to automatically determine a discrete relaxation spectrum (DRS) with a parsimonious number of modes. The new algorithm uses the CRS to guess the location of the modes, a nonlinear least squares optimization to fine‐tine the guess, and an information criterion to determine an optimal number of modes. The program is subjected to three validation tests, where data are generated from synthetic spectra, and three additional tests drawn from a variety of macromolecular architectures and sources. On the validation tests, pyReSpect is able to extract the original spectra. In all cases, the DRS follows the shape of the CRS, and offers additional regularization. Overall, pyReSpect is an excellent choice to obtain the DRS when the number and placement of modes is not known in advance.
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- Award ID(s):
- 1727870
- PAR ID:
- 10461545
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Macromolecular Theory and Simulations
- Volume:
- 28
- Issue:
- 3
- ISSN:
- 1022-1344
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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