Integral Micromorphic Model for Band Gap in 1D Continuum

TL;DR

This paper introduces a novel integral micromorphic elastic continuum model to describe band gaps in 1D metamaterials, highlighting the importance of nonlocal modifications for accurately predicting wave propagation inhibition.

Contribution

The paper develops a new nonlocal integral micromorphic model that effectively captures band gaps in 1D continuum metamaterials, surpassing the limitations of local models.

Findings

Nonlocal modifications enable band gaps with nonzero micromorphic stiffness.

Local model only reproduces band gaps in artificial cases.

High penalty coefficients and low micromorphic stiffness are key for band gap formation.

Abstract

The design of band-gap metamaterials, i.e., metamaterials with the capability to inhibit wave propagation of a specific frequency range, has numerous potential engineering applications, such as acoustic filters and vibration isolation control. In order to describe the behavior of such materials, a novel integral micromorphic elastic continuum is introduced, and its ability to describe band gaps is studied in the one-dimensional setting. The nonlocal formulation is based on a modification of two terms in the expression for potential energy density. The corresponding dispersion equation is derived and converted to a dimensionless format, so that the effect of individual parameters can be described in the most efficient way. The results indicate that both suggested nonlocal modifications play an important role. The original local micromorphic model reproduces a band gap only in the special, somewhat artificial case, when the stiffness coefficient associated with the gradient of the micromorphic variable vanishes. On the other hand, the nonlocal formulation can provide band gaps even for nonzero values of this coefficient, provided that the penalty coefficient that enforces coupling between the micromorphic variable and nonlocal strain is sufficiently high and the micromorphic stiffness is sufficiently low.