UTILIZATION OF STRUCTURAL COMPONENTS OF SPECIFIC WORK OF INTERNAL FORCES FOR THE DESCRIPTION OF STRENGTH OF VISCOELASTIC MATERIALS

摘要

The invariants of strain and stress tensors are widely used in state equations which take into account physically nonlinear material properties. These invariants do not depend on mechanical characteristics, and this facilitates their calculation but makes more difficult the description of complex rhcological properties of some materials, for instance, polymers. The utilization of formally time-reversible invariants as arguments of material functions and functionals characterizing reversible and irreversible processes of deformation, damage accumulation, aging, and healing increases the difficulty of finding suitable functions and functionals. As will be shown below, in many cases some other invariants (apart from those mentioned above) can be used, namely, one can use components of the specific work of internal forces. Analysis of these components for various types of loading and unloading allows us to evaluate predictions made on the basis of some theories about various experimentally observed physical phenomena. Thus, the analysis of the structure of the specific work of internal forces is useful for establishing a priori estimates of the applicability range of any theory. This idea is demonstrated by a nonlinear endochronous theory of aging viscoelastic materials based on the generalized Kelvin-Voigt model. Previously, similar investigations were carried out for the generalized nonlinear Maxwell model [1]. These models take into account the nonlinearity of elastic and viscous properties of materials and allow us to construct creep and relaxation curves with any given accuracy. For each of these models, the specific work is represented as the sum of five components, each with its own physical meaning: instantaneously and slowly reversible specific energies, specific scattered energy, specific aging energy, and the specific work of average stress on a volume deformation of free thermal expansion. These components are invariants and contain mechanical characteristics of materials. Their clear physical meaning makes them convenient for being taken as arguments of material functions and functionals. This is confirmed by experiments mentioned in [1-5], where the generalized Maxwell model is adopted as the theoretical basis. In the present paper, a similar confirmation is given on the basis of the generalized Kelvin-Voigt model, by means of theoretical analysis of the experimental dependence of the sound speed on the level of creep of a filled polymer sample under loading and unloading.