Fractional calculus is now a well-established tool in engineering science, with very promising applications in materials modelling. Indeed, several studies have shown that fractional operators can successfully describe complex long-memory and multiscale phenomena in materials, which can hardly be captured by standard mathematical approaches as, for instance, classical differential calculus. Furthermore, fractional calculus has recently proved to be an excellent framework for modelling non-conventional fractal and non-local media, opening valuable prospects on future engineered materials. The theme issue gathers cutting-edge theoretical, computational and experimental studies on advanced materials modelling via fractional calculus, with a focus on complex phenomena and non-conventional media. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

A wavelets-based method is developed to estimate the evolutionary power spectral density (EPSD) of nonstationary stochastic processes. The method relies on the property that the continuous wavelet transform of a nonstationary process can be treated as a stochastic process with EPSD given in terms of the EPSD of the process in a closed form. This yields an equation in the frequency domain relating the instantaneous mean-square value of the wavelet transform to the EPSD of the process. A number of these equations are considered, each related to a certain scale of the wavelet transform, in conjunction with representing the target EPSD as a sum of time-independent shape functions modulated by time-dependent coefficients; the squared moduli of the Fourier transforms of the wavelets associated with the selected scales are taken as shape functions. This leads to a linear system of equations which is solved to determine the unknown time-dependent coefficients; the same system matrix applies for all time instances...

The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this paper.

This study investigates the seismic response of a horizontal axis wind turbine on two bottom-fixed support structures for transitional water depths (30–60 m), a tripod and a jacket, both resting on pile foundations. Fully coupled, nonlinear time-domain simulations on full system models are carried out under combined wind–wave–earthquake loadings, for different load cases, considering fixed and flexible foundation models. It is shown that earthquake loading may cause a significant increase of stress resultant demands, even for moderate peak ground accelerations, and that fully coupled nonlinear time-domain simulations on full system models are essential to capture relevant information on the moment demand in the rotor blades, which cannot be predicted by analyses on simplified models allowed by existing standards. A comparison with some typical design load cases substantiates the need for an accurate seismic assessment in sites at risk from earthquakes.