An energy-based method to determine material constants in nonlinear rheology with applications

作者：Abali B Emek^*; Wu Cheng Chieh; Mueller Wolfgang H

来源：Continuum Mechanics and Thermodynamics, 2016, 28(5): 1221-1246.

DOI：10.1007/s00161-015-0472-z

• Material equations
• Constitutive relations
• Nonlinear rheology
• Simple-shear rheometer
• Inverse analysis

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.

• 出版日期2016-9