Fractional viscoelastic behaviour under stochastic temperature process

Abstract This paper deals with the mechanical behaviour of a linear viscoelastic material modelled by a fractional Maxwell model and subject to a Gaussian stochastic temperature process. Two methods are introduced to evaluate the response in terms of strain of a material under a deterministic stress and subjected to a varying temperature. In the first approach the response is determined making the material parameters change at each time step, due to the temperature variation. The second method, takes advantage of the Time–Temperature Superposition Principle to lighten the calculations. In this regard, a stochastic characterisation for the Time–Temperature Superposition Principle method is proposed for a Gaussian stochastic temperature process. A numerical example, based on experimental data of an epoxy resin at different temperatures, is presented to simulate a creep test under a Gaussian stochastic temperature process with assigned power spectral density function. Comparison between the two considered methods is shown, and the accuracy of the proposed stochastic characterisation is assessed.