Static chiral Willis continuum mechanics for three-dimensional chiral mechanical metamaterials

Muamer Kadic (1, 2) , Andre Diatta (2) , Tobias Frenzel (2) , Sebastien Guenneau (3) , Martin Wegener (2)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 KIT - Karlsruhe Institute of Technology
3 FRESNEL - Institut FRESNEL

Recent static experiments on twist effects in chiral three-dimensional mechanical metamaterials have been discussed in the context of micropolar Eringen continuum mechanics, which is a generalization of linear Cauchy elasticity. For cubic symmetry, Eringen elasticity comprises nine additional parameters with respect to linear Cauchy elasticity, of which three directly influence chiral effects. Here, we discuss the behavior of the static case of an alternative generalization of linear Cauchy elasticity, the Willis equations. We show that in the homogeneous static cubic case, only one additional parameter with respect to linear Cauchy elasticity results, which directly influences chiral effects. We show that the static Willis equations qualitatively describe the experimentally observed chiral twist effects, too. We connect the behavior to a characteristic length scale.

Domaines: Acoustique [physics.class-ph]; Mécanique des solides [physics.class-ph]; Micro et nanotechnologies/Microélectronique; Optique / photonique

Muamer Kadic, Andre Diatta, Tobias Frenzel, Sebastien Guenneau, Martin Wegener. Static chiral Willis continuum mechanics for three-dimensional chiral mechanical metamaterials. Physical Review B, 2019, 99 (21), ⟨10.1103/PhysRevB.99.214101⟩. ⟨hal-02399024⟩