A new constitutive model for aging viscoelastic materials

A new model for an aging viscoelastic material under thermal loading is derived. It is known that a number of models in viscoelasticity can be interpreted as systems of springs and dashpots. We suggest another approach that treats a viscoelastic material as a system of elastic links (springs) whose number varies in time. According to this model some new elastic connections (links) arise in the system and some old ones vanish in the process of deformation. The specific feature of the new model is that the natural configuration of new springs coincides with the actual configuration of the system at the current instant of time. This leads to standard hereditary dependencies in a viscoelastic material which are described by relaxation or creep kernels. In the suggested model, the relaxation kernel K(t,s) determines the number of springs that arise by the instant s and exist at time t. Analysis of experimental data shows a good agreement with our numerical results for both infinitesimal and finite strains. In the present paper, the model of adaptive springs is extended to thermoviscoelastic materials. By employing a model of a system with a varying number of springs, we offer a new approach to describe themore » mechanical behavior of thermoviscoelastic materials. For a uniform in time temperature this approach implies the standard time-temperature analogy, but for the temperature varying in time it does differ from this well-known principle. To demonstrate the features of the proposed model we consider Lame`s problem for a pipe made of a viscoelastic polymer material under the temperature varying in time. We compare the results of numerical simulations based on the new and standard models for an aging viscoelastic material. It is also shown that our model is closer to experimental data than the standard one based on the time-temperature analogy.« less