Abstract: By developing and applying a homogenization scheme for elastodynamics, Willis discovered that the momentum of composite materials is macroscopically coupled with their strain. This coupling is captured by the now-termed Willis tensor, which not only enlarges the design space of metamaterials, but is also necessary for obtaining a meaningful effective description that respects basic physical laws. In this talk, I will show how additional tensors of Willis type emerge by generalizing the homogenization theory of Willis to thermoelastic-, piezomagnetic- or piezoelectric media. As a result, the obtained effective constitutive equations have a tri-anisotropic form. I will provide examples for piezoelectric media that exhibit an effective electromomentum coupling. I will show that this coupling is necessary for describing the effective properties of piezoelectric media using a homogenized description that respects reciprocity and energy conservation. Finally, I will demonstrate how this coupling can be used to realize a device that actively control the phase of elastic waves.
Short bio: Gal Shmuel is an associate professor at the Faculty of Mechanical Engineering, Technion, Israel. Shmuel’s group studies the mechanics of active-, soft- and heterogeneous media. He is the 2021 ERC consolidators grant recipient for his current focus on metamaterials in elastodynamics. His recent contributions include the discovery of the electromomentum coupling in piezoelectric metamaterials, and more generally cross-coupling of Willis type in active composites; and the realization of exceptional points and non-Hermitian phenomena in conservative elastodynamics.