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An energy-based method to determine material constants in nonlinear rheology with applications
(2016)
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.
The determination of material parameters from displacement field measurement is being examined for linear elastic solid. A frequently used approach to compute material constants can be found in many studies. Even though they presented the approach in many different variations, but in the end they are essentially based on the same algorithm: Parameters are iteratively tuned until the computed results are in accordance with the measurements. The main drawback of this approach is that mainly commercial software is used that hinders us to investigate its inner evaluation process. This leads to the question, how the results from this commercial software can be trusted. On the contrary to these debatable approaches, we present a method that inverts the procedure of finite element method by using the most general model for a least-squares adjustment – the GAUSS-HELMERT Model.