Among the attractive properties of metamaterials, the capability of focusing and localizing waves has recently attracted research interest to establish novel energy harvester configurations. In the same frame, in this work, we develop and optimize a system for concentrating mechanical energy carried by elastic anti-plane waves. The system, resembling a Fabry-Pérot interferometer, has two barriers composed of Locally Resonant Materials (LRMs) and separated by a homogeneous internal cavity. The attenuation properties of the LRMs allow for the localization of waves propagating at particular frequencies. With proper assumptions on the specific ternary LRMs, the separation of scales (between the considered wave lengths and the characteristic dimension of the employed unit cells) enables the use of a two-scale asymptotic technique for computing the effective behavior of the employed LRMs. This leads to a complete analytic description of the motion of the system. Here we report the results achieved by optimizing the geometry of the system for obtaining a maximum focusing of the incoming mechanical energy. The analytic results are then validated through numerical simulations.

Structural lattices with quasi-periodic patterns possess interesting dynamic features that can be exploited to control, localize and redirect propagating waves. In this work, we show that the properties of a large class of quasi-periodic locally resonant systems (approximated as periodic, with arbitrarily large period) can be performed by defining an equivalent discrete system. Several properties of wave propagation can a priori be demonstrated with reference to this system. Results in terms of bulk spectrum, showing the Hofstadter butterfly pattern, and of topological modes are then discussed in detail with reference to a simple example of quasi-periodic lattice. This article is part of the theme issue ‘Current developments in elastic and acoustic metamaterials science (Part 2)’.

In this paper we develop a new model for the simulation of the mechanical behavior of rayon twisted yarns, at macroscopic level. A yarn with its continuous filaments is represented by an equivalent three-dimensional solid of cylindrical shape, discretized by finite elements, with properly defined local anisotropic material properties. The new constitutive model, inspired by experimental results on rayon untwisted yarns, is formulated in the framework of the thermodynamics of irreversible processes and includes visco-elastic and visco-plastic dissipation mechanisms. The effect of twist is taken into account by including the direction of the fibers in the free energy definition. The overall model is validated comparing numerical and experimental results on twisted rayon yarns.

This work aims to describe and predict the complex mechanical behavior of polymeric cords used as reinforcements in tires. Starting from the observed microstructure of the cords and from macroscopic experimental tests performed on single-ply yarns, a comprehensive geometric and mechanical model is developed. The real geometry of the cord is replaced by an equivalent three-dimensional continuum of a cylindrical shape, with a properly defined non-isotropic inelastic constitutive behavior. The three-dimensional viscoelastic and viscoplastic material model developed by the authors for rayon fibers is employed for this purpose. The actual directions of filaments inside the cord are computed by an analytical model, accounting for the twist in the yarns and in the filaments inside each yarn. Such directions, relevant to points of the cord cross-section, are then averaged along the pitch of the cord to obtain mean directions which represent the virtual reinforcement directions to be used in the equivalent cylindrical-shaped model. This analysis strategy is implemented in a finite element procedure. For rayon cords, the developed simulation tool (fed with appropriate parameters) gives numerical results that compare well with the corresponding experimental results. This approach could be effectively utilized in the analysis of cord-reinforced rubber composites.