Details
| Original language | English |
|---|---|
| Article number | 105820 |
| Journal | Journal of the Mechanics and Physics of Solids |
| Volume | 193 |
| Early online date | 8 Aug 2024 |
| Publication status | Published - Dec 2024 |
Abstract
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.
Keywords
- Cross-coupling, Flexoelectric, Inversion symmetry, Second-order Willis metamaterial, Strain gradient
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Condensed Matter Physics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
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In: Journal of the Mechanics and Physics of Solids, Vol. 193, 105820, 12.2024.
Research output: Contribution to journal › Article › Research › peer review
}
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 - 2024/12
Y1 - 2024/12
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 -