Fractional Viscoelasticity Under Combined Stress and Temperature Variations

Nowadays polymeric materials or composites with polymeric matrices are widely used in a very wide range of applications such as aerospace, automotive, biomedical and also civil engineering. From a mechanical point of view, polymers are characterized by high viscoelastic properties and high sensitiveness of mechanical parameters from temperature. Analytical predictions in real-life conditions of mechanical behaviour of such a kind of materials is not trivial for the intrinsic hereditariness that imply the knowledge of all the history of the material at hand in order to predict the response to applied external loads. If temperature variations are also present in the materials, a reliable evaluation of the response may be performed only if the variations of the material parameters with the temperature are taken into account. In recent papers of the authors the response of a fractional viscoelastic material subjected to stochastic temperature process and under deterministic loads has been faced up. In this work we study the problem of a fractional viscoelastic materials subjected to deterministic temperature history and forced by a stochastic load. It is shown that, if interpreted in the correct way, the Boltzmann superposition principle can be still used. Moreover, by means of a proper discretization approach, it is possible the evaluate the response of the system also when the load is a stochastic process in order to perform Monte Carlo simulations.