DETERMINATION OF MATERIAL FUNCTIONS IN THE NONLINEAR THEORY OF THERMOVISCOELASTICITY USING ITS HIERARCHICAL STRUCTURE

The endochronous version of the nonlinear theory of thermoviscoelasticity is considered which is developed to describe the mechanical behavior of filled polymeric materials. In the one-dimensional case, an identification method is suggested for the determination of material constants and functions. This method uses the experimental data and features of the hierarchical structure of constitutive relations. A structure consisting of three levels is considered. The first level corresponds to tensorially linear Boltzmann-Volterra operators in the form of Stieltjes integrals. This enables one to describe the creep and relaxation phenomena. On the second level, reduced times are introduced into the relaxation kernels. These times depend on the temperature, stress and/or strain tensor invariants, damage parameter, and parameters distinguishing the loading and relief processes. The third level gives an additional possibility of taking into account the specific operating conditions of the structure and, as a result, permits one to include the stress or temperature gradients, stress and strain rates, and other parameters in the set of arguments influencing the reduced times. The utilization of the experimental data on the uniaxial loading of specimens for the identification of the material function describing the rate of change of the reduced time within the framework of a one-dimensional nonlinear model of the Maxwell type is discussed in detail. A numerical method for solving the nonlinear system of integrodifferential equations of the foregoing model is presented. Three variants of the solution are considered. They differ in the type of the experimental data. The accuracy of the method is estimated by the comparison of the numerical results with the exact solution of the problem involving the singular dependence of the material function on the specific dissipated energy. Based on a series of uniaxial stress relaxation tests, the material function is identified as a function of the current strain and specific dissipated energy. A series of tensile tests at constant strain rate are used as the control series. The uniaxial tension diagrams predicted by the theory differ on average by less than 9.6% from those constructed on the basis of the experimental data. In contrast, the diagrams predicted by the linear theory of viscoelasticity yield the stresses exceeding the test data by a factor of 2.5-4.