Abstract
Many polymer-type materials show a rate-dependent and nonlinear rheological behavior. Such a response may be modeled by using a series of spring-dashpot systems. However, in order to cover different time scales the number of systems may become unreasonably large. A more appropriate treatment based on continuum mechanics will be presented herein. This approach uses representation theorems for deriving material equations and allows for a systematic increase in modeling complexity. Moreover, we propose an approach based on energy to determine thematerial parameters.This method results in a simple linear regression problemeven for highly nonlinearmaterial equations. Therefore, the inverse problem leads to a unique solution. The significance of the proposed method is that the stored and dissipated energies necessary for the procedure are measurable quantities. We apply the proposed method to a “semi-solid” material and measure its material parameters by using a simple-shear rheometer.
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Communicated by Andreas Öchsner.
The coauthor C.-C. Wu has written this paper in Technische Universität Berlin.
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Abali, B.E., Wu, CC. & Müller, W.H. An energy-based method to determine material constants in nonlinear rheology with applications. Continuum Mech. Thermodyn. 28, 1221–1246 (2016). https://doi.org/10.1007/s00161-015-0472-z
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DOI: https://doi.org/10.1007/s00161-015-0472-z