Towards Two Time Axes: Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial

The discovery of novel topological phases of matter has quickly become important in the study of condensed matter physics, photonics, and more recently mechanics. However, most research on topological mechanical metamaterials, such as Maxwell lattices, takes place in the linear regime. In this study, the large deformation quasi-static response of a topological Maxwell lattice is studied through geometric simulations and experiments. We further show a mapping between our linearized, homogenized system, and a non-Hermitian, non-recriprocal, one-dimensional wave equation demonstrating an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and a one dimensional nonlinear dynamical active system. The holographic nature of the Maxwell Lattice allows for a space dimension to act as a ‘synthetic time’ dimension. This mapping opens the door to new questions about what happens when dynamics are incorporated into a system with a ‘synthetic time’ dimension, creating a system with two ‘time’ dimensions. Our study shows new tools for controlling stress and strain in lattices, and expands the applications of such metamaterials to adaptive and smart materials, and mechanical logic.