Master Equations for Viscoelastic Materials Taking into Account the Influence of Temperature and Humidity

We consider some historical aspects of the development of the theory of viscoelasticity and describe the last achievements of the Laboratory of Mechanics of Composites at the Institute of Machine Science of the Russian Academy of Sciences. It is emphasized that the extensive use of polymers and composites with polymeric matrices in contemporary engineering makes it necessary to perform complex investigations of their behavior for various loading modes at different temperatures and levels of humidity. Therefore, it is important to develop new models capable of using, under operating conditions, the same set of parameters for the analysis of creep, relaxation, loading at different rates, unloading, cyclic loading, etc. The sole known approach to the construction of equations satisfying all imposed requirements is connected with the use of the hereditary principle. We propose a new procedure of taking into account the influence of temperature and humidity in the hereditary-type nonlinear equations.