Nonlocal Homogenization Model for Wave Dispersion and Attenuation in Elastic and Viscoelastic Periodic Layered Media

Abstract

This manuscript presents a new nonlocal homogenization model (NHM) for wave dispersion and attenuation in elastic and viscoelastic periodic layered media. Homogenization with multiple spatial scales based on asymptotic expansions of up to eighth order is employed to formulate the proposed nonlocal homogenization model. A momentum balance equation, nonlocal in both space and time, is formulated consistent with the gradient elasticity theory. A key contribution in this regard is that all model coefficients including high-order length-scale parameters are derived directly from microstructural material properties and geometry. The capability of the proposed model in capturing the characteristics of wave propagation in heterogeneous media is demonstrated in multiphase elastic and viscoelastic materials. The nonlocal homogenization model is shown to accurately predict wave dispersion and attenuation within the acoustic regime for both elastic and viscoelastic layered composites.

Frequency domain boundary value problem analyses of acoustic metamaterials described by an emergent generalized continuum

“…While most efforts in developing new homogenization frameworks have focused on local resonance phenomena, a homogenized description of the Bragg scattering phenomena is much more challenging and has been attempted in only a few papers. The reduced scale separation can be taken into account in asymptotic homogenization by adding highorder correction terms [13,[20][21][22][23]. However, this approach is still limited to the first (acoustic) dispersion branch and in some cases, the second (first optical) branch.…”

A dispersive homogenization model for composites and its RVE existence

“…To investigate the influence of material contrast on the dispersion tensor, the dispersion tensor is computed for a single microstructure with 15 × 15 fibers and a fiber volume fraction of 60%. The Young's modulus and density of the inclusion are varied proportionally as E i = cE m and ρ i = cρ m for c ∈ [2,4,9,16,30], respectively, with the Poisson's ratio unchanged. The six independent components of the dispersion tensor D M i jkl , normalized with respect to the values of the sample with the lowest property contrast, D M i jkl (c = 2), for the five cases are shown in Fig.…”

“…Based on a multiscale virtual power principle [25] as a notion of a generalized Hill-Mandel lemma, Pham et al [8] and Roca et al [27] developed computational homogenization schemes in which the transient dynamics equations are resolved at macroscopic and microscopic scale. Asymptotic homogenization with higherorder (or first-order) expansions was proposed in [28][29][30] to capture wave dispersion and attenuation within viscoelastic composites. Fish et al [31] introduced a general purpose asymptotic homogenization scheme in which the microinertia is resolved by introducing a eigenstrain term and is valid for nonlinear heterogeneous material.…”

Enriched homogenized model for viscoelastic plane wave propagation in periodic layered composites

“…Locally resonant metamaterials represent an emerging class of engineered morphologies which can exhibit unique wave attenuation and filtering characteristics. Periodic layered composites made up of at least three constituent materials belong to a subset of such metamaterials, as they can involve band gaps as well due to inner resonance arising from their specific microstructural arrangements [1][2][3]. When a wave propagates through a periodic heterogeneous media, a series of signal reflections and transmissions develop at the material interfaces.…”

“…With regards to the modelling of inner resonance, the validity of the asymptotic homogenization scheme was demonstrated under the specific condition that the stiffness contrast between the matrix and compliant layer was of the order of the squared ratio between the loading wavelength and the size of the unit cell [3]. A similar strategy was employed to analyse viscoelastic wave propagation through a tri-material composite with low stiffness contrasts [2]. Since it was stated therewith that the accuracy of their asymptotic-based model reduces with increasing stiffness contrast, the approach is not yet directly applicable for locally resonant metamaterials.…”