ОПРЕДЕЛЕНИЕ РЕОЛОГИЧЕСКИХ ПАРАМЕТРОВ ПОЛИМЕРНЫХ МАТЕРИАЛОВ С ИСПОЛЬЗОВАНИЕМ МЕТОДОВ НЕЛИНЕЙНОЙ ОПТИМИЗАЦИИ

Abstract

The article is devoted to the problem of processing the experimental creep curves of polymers. The task is to determine their rheological characteristics from tests for any of the simplest types of deformation. The basis for the approximation of the experimental curves is the nonlinear Maxwell-Gurevich equation.
 The task of finding the rheological parameters of the material is posed as a nonlinear optimization problem. The objective function is the sum of the squared deviations of the experimental values on the creep curve from the theoretical ones. Variable input parameters of the objective function are the initial relaxation viscosity and velocity modulus m*. A theoretical creep curve is constructed numerically using the fourth-order Runge-Kutta method. The nonlinear optimization problem is solved in the Matlab environment using the internal point method. The values m* and are found for which the objective function takes the minimum value.
 To test the technique, the inverse problem was solved. For given values of the rheological parameters of the material, a theoretical curve of creep under bending was constructed, and the values m* and were found from it. The technique was also tested on experimental stress relaxation curves of secondary polyvinyl chloride and creep curves of polyurethane foam with a pure shear.
 A higher quality approximation of experimental curves is shown in comparison with existing methods. The developed technique allows us to determine the rheological characteristics of materials from tests for bending, central tension (compression), torsion, shear, and it is enough to test only one type of deformation, and not a series, as was suggested earlier by some researchers