Piezoelectric Metamaterial with Negative and Zero Poisson's Ratios

K. A. Khan, S. Al-Mansoor, S. Z. Khan, M. A. Khan

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25 Scopus citations


This study presents the finite element-based micromechanical modeling approach to obtain the electromechanical properties of the piezoelectric metamaterial based on honeycomb (HC) cellular networks. The symmetry of the periodic structure was employed to derive mixed boundary conditions (MBCs) analogous to periodic boundary conditions (PBCs). Three classes of hexagonal HC cellular networks, namely, a conventional HC (CHC), a re-entrant HC (RE), and a semi-re-entrant HC (SRE) were considered. The representative volume elements (RVEs) of these three classes of cellular materials were created, and finite element analyses were carried out to analyze the effect of orientation of the ligament on their effective electromechanical properties and their suitability in specific engineering applications. The longitudinally poled piezoelectric HC cellular networks showed an enhanced behavior as compared to the monolithic piezoelectric materials. Moreover, longitudinally poled HC cellular networks demonstrated that, as compared to the bulk constituent, their hydrostatic figure of merit increased and their acoustic impedance decreased by one order of magnitude, respectively, indicating their applicability for the design on hydrophones. Moreover, results showed that cellular metamaterial with tunable electromechanical characteristics and a variety of auxetic behaviors such as negative, positive, or zero Poisson's ratios could be developed. Such novel HC network-based functional cellular materials are likely to facilitate the design of light-weight devices for various next-generation sensors and actuators.

Original languageBritish English
Article number04019101
JournalJournal of Engineering Mechanics
Issue number12
StatePublished - 1 Dec 2019


  • Cellular materials
  • Effective electromechanical response
  • Honeycomb cellular networks
  • Micromechanical modeling
  • Piezoelectric materials
  • Smart auxetic structures


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