Towards the conception of complex engineering meta-structures: relaxed-micromorphic modelling of low-frequency mechanical diodes/high-frequency screens

Abstract

In this paper we show that an enriched continuum model of the micromorphic type (Relaxed Micromorphic Model) can be safely used to model metamaterials' response in view of their use for meta-structural design. We focus on the fact that the reduced model's structure, coupled with the introduction of well-posed interface conditions, allows us to easily test different combinations of metamaterials' and classical-materials bricks, so that we can eventually end-up with the conception of a meta-structure acting as a mechanical diode for low/medium frequencies and as a total screen for higher frequencies. Thanks to the reduced model's structure, we are also able to optimize this meta-structure so that the diode-behaviour is enhanced for both "pressure" and "shear" incident waves and for all possible angles of incidence.

Metamaterial shields for inner protection and outer tuning through a relaxed micromorphic approach

“…The unit cell (Fig. 1) used in this work has already been introduced and characterized in [38,40] and we recall its geometric and elastic properties in the table of Fig. 1.…”

“…This simplification enables us to explore complex metamaterials for elastic wave control in a way that would not be viable otherwise. For example, in [39] we designed a meta-structure capable of energy focusing which also acts as a shield, in [38] we conceived acoustic screens and acoustic absorbers, and in [40] we designed mechanical diodes.…”

“…the band-gap intervals) can be inferred from the dispersion diagram of the unit cell. The band-gap width can be tuned passively by acting on the geometry of the unit cell and on the materials constituting it [38,39,40], by introducing an elastic prestress [4,6], or actively by modifying these properties thanks to external solicitations in real time like in piezoelectric materials [3].…”

“…One important application is that of exploiting metamaterials' band-gaps to create elastic shielding devices protecting objects from elastic waves [8,25,29,37]. Depending on the devices' operating frequencies, these shields can act for seismic [20], acoustic [25,35,38,41,43] or ultrasonic [2,13,38,39,40] protection of objects that need to be isolated from the external environment.…”

Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua

“…The renewed interest in models of generalized continua comes in part from the fact that for small specimens one may observe size-effects, not accounted for by linear Cauchy elasticity. On the other hand, the description of man-made architecture materials/meta-materials need generalized continua to capture frequency band-gaps in the dynamic range, a prominent example being given by the relaxed micromorphic model [1,2,40,59,62].…”