Hierarchical heterogeneous one-dimensional problem in linear viscoelastic media

We address the homogenisation of a linear viscoelastic and hierarchical composite material in one-dimensional (1D) framework via three-scale asymptotic method. consider family heterogeneous problems with periodic, rapidly-oscillating piece-wise coefficients that model structure two levels organisation. Here, we assume continuity contact conditions at interfaces among constituents set straightforward geometrical configuration order to gain better insight multiscale problem. The main goal is provide general overview procedure validate approach by means comparison between solution original problem, homogenised problem formal solution. In addition, show presents clear improvement over recursive two-scale one, illustrate convergence solutions towards when parameters approach.