Homogenization of piezoelectric planar Willis materials undergoing antiplane shear Articles uri icon

authors

  • MUHAFRA, ALAN
  • KOSTA, MAJD
  • TORRENT, DANIEL
  • PERNAS SALOMON, RENE
  • SHMUEL, GAL

publication date

  • January 2022

start page

  • 102833

volume

  • 108

International Standard Serial Number (ISSN)

  • 0165-2125

Electronic International Standard Serial Number (EISSN)

  • 1878-433X

abstract

  • Homogenization theories provide models that simplify the constitutive description of heterogeneous media while retaining their macroscopic features. These theories have shown how the governing fields can be macroscopically coupled, even if they are microscopically independent. A prominent example is the Willis theory which predicted the strain–momentum coupling in elastodynamic metamaterials. Recently, a theory that is based on the Green"s function method predicted analogous electro–momentum coupling in piezoelectric metamaterials. Here, we develop a simpler scheme for fibrous piezoelectric composites undergoing antiplane shear waves. We employ a source-driven approach that delivers a unique set of effective properties for arbitrary frequency–wavevector pairs. We numerically show how the resultant homogenized model recovers exactly the dispersion of free waves in the composite. We also compute the effective properties in the long-wavelength limit and off the dispersion curves, and show that the resultant model satisfy causality, reciprocity and energy conservation. By contrast, we show how equivalent models that neglect the electromomentum coupling violate these physical laws

subjects

  • Materials science and engineering
  • Mechanical Engineering
  • Physics

keywords

  • dynamic homogenization; wills metamaterials; effective properties; fiber composites; bloch-floquet waves; piezoelectricity