Determination of Rheological Parameters of Polymer Materials Using Nonlinear Optimization Methods

Abstract

The article proposes a new method for determining the rheological characteristics of polymers based on the Maxwell-Gurevich nonlinear creep law. In contrast to the previous works, the presented method gives an opportunity to obtain the indicated characteristics from tests for any of the simplest deformation types. The problem of finding the rheological parameters of the material is considered as a nonlinear optimization problem. The objective function is the sum of the experimental values deviations’ squares on the creep curve from the theoretical ones. The variable input parameters of the objective function are the initial relaxation viscosity and speed module. The theoretical creep curve is constructed numerically using the fourth-order Runge-Kutta method. The solution of the nonlinear optimization problem is performed in the Matlab environment by the interior point method. The values the initial relaxation viscosity and speed module, at which the objective function takes the minimum value, are found. To test the technique, the inverse problem was solved. For the given values of the material’s rheological parameters, a theoretical creep curve in bending was constructed, and the values the initial relaxation viscosity and speed module are found from it. The technique has also been tested on the experimental stress relaxation curves of secondary polyvinyl chloride and pure shear polyurethane foam creep curves. A higher quality of the experimental curves’ approximation is shown in comparison with the existing techniques. The developed technique makes it possible to determine the rheological characteristics of materials from the tests for bending, central tension (compression), torsion, pure shear, and it is enough to test only one type of deformation, and not a series, as it had been suggested earlier by some researchers.KeywordsCreepRelaxationRheological parametersBendingNonlinear optimizationExperimental processingLeast squares method