Non-reciprocity in mechanically modulated elastic metamaterials with geometric asymmetry

Elastic metamaterials with time- and space-dependent effective material properties have received great attention as a means to generate non-reciprocal wave propagation in acoustic and elastic media. These materials have promise for applications such as acoustic communication devices with increased data throughput and improved vibration isolation components. One means to modulate the material properties of a heterogeneous medium is via nonlinear mechanical deformation on time scales that are slow compared to propagating waves. This approach has been explored by the authors using the finite element method (FEM) to demonstrate non-reciprocal elastic wave propagation in negative stiffness honeycombs with a time- and space-varying external pre-strain [Goldsberry et al., JASA 144, 1763 (2018)]. One benefit of FEM is that it can be used to study the degree of non-reciprocity when varying sub-wavelength geometry or geometric modulations that are difficult or impossible to represent using analytical models. The present work employs FEM to investigate non-reciprocity in elastic lattices consisting of unit cells with varied geometric asymmetry and more general forms of mechanical modulation. [Work supported by National Science Foundation EFRI under Award No. 1641078.]