Coupled Mechanical–Electrical modeling of pantographic metamaterials with simplified flexoelectric bending

Abstract Pantographic metamaterials exhibit unique mechanical behaviors due to their mesostruc-ture of two orthogonal families of fibers connected by hinges. Such lattices naturally admit second gradient continuum descriptions because fiber bending enters the energy via the second gradient of the placement. Flexoelectricity, i.e. the generation of an electric polarization by strain gradients, is therefore a natural multiphysics coupling for this kind of metamaterials. Numerical simulations are presented to show the induced electric field on a specimen with pantographic mesostructure for bias extension, compression and shear tests.