Structure-energy analysis of models of nonlinearly viscoelastic materials with several aging and viscosity functions

Abstract

We consider generalized one-dimensional Maxwell and Kelvin-Voigt models of viscoelastic materials in which the properties of elastic and viscous elements are determined by the corresponding secant moduli and viscosity coefficients, which are functions of the parameters determined by the deformation process. In contrast to the nonlinear endochronic theory of aging viscoelastic materials (NETAVEM), in which one and the same aging function is used to describe the properties of all elastic elements and one and the same viscosity function is used to describe the properties of all viscous elements [1, 2], it is assumed that the type of these functions is distinct for each elementary model. For the generalized Maxwell and Kelvin-Voigt models under study, we obtain representations of the specific work of internal forces as the sum of four terms of different physical meaning. There representations are similar to those given in [1, 2] for NETAVEM. An example of construction of viscoelasticity constitutive relations containing two aging functions and one viscosity function is given for a material whose properties are sensitive to the strain rate. The simultaneous use of several aging and viscosity functions to describe the properties of structure elements of the model and the use of several components of specific work as arguments of these functions allows us to extend the scope of the models under study.