Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures

TL;DR

This paper demonstrates that the relaxed micromorphic continuum model accurately reproduces transient waveforms in anisotropic band-gap metastructures, outperforming classical models especially at higher frequencies, with reduced computational costs.

Contribution

The study introduces the relaxed micromorphic model as an effective continuum approach for transient wave analysis in anisotropic metastructures, capturing high-frequency behavior beyond classical theories.

Findings

Relaxed micromorphic model accurately predicts pulse propagation in band-gap frequencies.

Cauchy continuum only describes low-frequency behavior.

Computational efficiency is improved using the relaxed micromorphic model.

Abstract

In this paper, we show that the transient waveforms arising from several localised pulses in a micro-structured material can be reproduced by a corresponding generalised continuum of the relaxed micromorphic type. Specifically, we compare the dynamic response of a bounded micro-structured material to that of bounded continua with special kinematic properties: (i) the relaxed micromorphic continuum and (ii) an equivalent Cauchy linear elastic continuum. We show that, while the Cauchy theory is able to describe the overall behaviour of the metastructure only at low frequencies, the relaxed micromorphic model goes far beyond by giving a correct description of the pulse propagation in the frequency band-gap and at frequencies intersecting the optical branches. In addition, we observe a computational time reduction associated with the use of the relaxed micromorphic continuum, compared to the sensible computational time needed to perform a transient computation in a micro-structured domain.