Anisotropic wave dispersion and band‐gaps in mechanical metamaterials via the relaxed micromorphic model

Metamaterials made of bi-stable building blocks gain their promising effective properties from a micromechanical mechanism, namely buckling, rather than by the chemical composition of its constituent. Both discrete and continuum modelling of unstable metamaterials is a challenging task. It requires great care in the stability analysis and a kinematic enhanced continuum theory to adequately describe the softening behaviour and related size effects. This paper presents a detailed analytical and numerical investigation of the modelling capabilities of a gradient enhanced continuum model compared to a discrete modelling approach which has been proven to be qualitatively consistent with experimental results on small structures. It is demonstrated that the gradient model is capable of describing size effects with respect to stability of small structures; however, the limit of very large structures is found to be inconsistent with both the discrete model and the Maxwell rule of a classical continuum. Based on an analytical investigation of the size of the energy barrier between local minima, it is discussed how the consistency of the limit case of both discrete and continuum models can be restored by redefining the classical meaning of stability.

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Discrete and continuum modelling of size effects in architectured unstable metamaterials

Findeisen

Forest

Hohe

et al. 2020

Continuum Mech. Thermodyn.

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Microstructure-related Stoneley waves and their effect on the scattering properties of a 2D Cauchy/relaxed-micromorphic interface

et al. 2019

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Wave propagation in phononic materials based on the reduced micromorphic model by one-sided Fourier transform

2022

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A one-dimensional problem of wave propagation in phononic materials is solved under the reduced micromorphic model introduced recently. An efficient technique is used for the solution, based on one-sided Fourier transform. This allows obtaining an exact solution in closed form, which can be utilized to check approximate solutions obtained by other methods. The results are confirmed numerically by the method of finite differences. They illustrate the existence of frequency band gaps.

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Anisotropic wave dispersion and band‐gaps in mechanical metamaterials via the relaxed micromorphic model

Abstract: We propose a continuum model (the relaxed micromorphic model) to describe band-gap phenomena in metamaterials.

Cited by 3 publications

References 7 publications

Discrete and continuum modelling of size effects in architectured unstable metamaterials

Discrete and continuum modelling of size effects in architectured unstable metamaterials

Microstructure-related Stoneley waves and their effect on the scattering properties of a 2D Cauchy/relaxed-micromorphic interface

Wave propagation in phononic materials based on the reduced micromorphic model by one-sided Fourier transform

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