TY - JOUR

T1 - Second-order Willis metamaterials

T2 - Gradient elasto-momentum coupling in flexoelectric composites

AU - Huynh, Hai D.

AU - Nanthakumar, S. S.

AU - Zhuang, Xiaoying

N1 - Publisher Copyright: © 2024 The Authors

PY - 2024/8/8

Y1 - 2024/8/8

N2 - Willis materials are composites whose the overall constitutive relations exhibit coupling between momentum and strain. Recently, piezoelectric Willis materials have been studied, allowing the macroscopic momentum to be additionally coupled to the non-mechanical stimulus. Such metamaterials classified as first-order Willis materials generate cross-couplings due to their asymmetric microstructures in order to realize novel phenomena in wave propagation. In this work, we study Willis materials that are flexoelectric and offer an electric field induced by a strain gradient. We show that in the case of flexoelectric Willis materials, the momentum also gets coupled to the strain gradient term under an effective description. Hereby, an ensemble averaging-based dynamic homogenization theory is developed for flexoelectric composites to compute constitutive relations of the macroscopic fields. This second-order Willis metamaterial offers a novel coupling termed gradient elasto-momentum coupling. The presence of non-uniform strain that can break the inversion symmetry of a unit cell is thus significant in generating the imaginary portion of all cross-couplings in the absence of asymmetric microstructures.

AB - Willis materials are composites whose the overall constitutive relations exhibit coupling between momentum and strain. Recently, piezoelectric Willis materials have been studied, allowing the macroscopic momentum to be additionally coupled to the non-mechanical stimulus. Such metamaterials classified as first-order Willis materials generate cross-couplings due to their asymmetric microstructures in order to realize novel phenomena in wave propagation. In this work, we study Willis materials that are flexoelectric and offer an electric field induced by a strain gradient. We show that in the case of flexoelectric Willis materials, the momentum also gets coupled to the strain gradient term under an effective description. Hereby, an ensemble averaging-based dynamic homogenization theory is developed for flexoelectric composites to compute constitutive relations of the macroscopic fields. This second-order Willis metamaterial offers a novel coupling termed gradient elasto-momentum coupling. The presence of non-uniform strain that can break the inversion symmetry of a unit cell is thus significant in generating the imaginary portion of all cross-couplings in the absence of asymmetric microstructures.

KW - Cross-coupling

KW - Flexoelectric

KW - Inversion symmetry

KW - Second-order Willis metamaterial

KW - Strain gradient

UR - http://www.scopus.com/inward/record.url?scp=85203247198&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2024.105820

DO - 10.1016/j.jmps.2024.105820

M3 - Article

AN - SCOPUS:85203247198

VL - 193

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

M1 - 105820

ER -