Stress guides in generic static mechanical metamaterials.

The confinement of waves within a waveguide can enable directional transmission of signals, which has found wide applications in communication, imaging, and signal isolation. Extending this concept to static systems, where material deformation is piled up along a spatial trajectory, remains elusive due to the sensitivity of localized deformation to structural defects and impurities. Here, we propose a general framework to characterize localized static deformation responses in two-dimensional generic static mechanical metamaterials, by exploiting the duality between space in static systems and time in one-dimensional non-reciprocal wave systems. An internal time-reverse symmetry is developed by the space-time duality. Upon breaking this symmetry, quasi-static load-induced deformation can be guided to travel along a designated path, thereby realizing a stress guide. A combination of time-reverse and inversion symmetries discloses the parity-time symmetry inherent in static systems, which can be leveraged to achieve directional deformation shielding. The tailorable stress guides can find applications in various scenarios, ranging from stress shielding and energy harvesting in structural tasks to information processing in mechanical computing devices.

Non-Hermitian topology in static mechanical metamaterials.

The combination of broken Hermiticity and band topology in physical systems unveils a novel bound state dubbed as the non-Hermitian skin effect (NHSE). Active control that breaks reciprocity is usually used to achieve NHSE, and gain and loss in energy are inevitably involved. Here, we demonstrate non-Hermitian topology in a mechanical metamaterial system by exploring its static deformation. Nonreciprocity is introduced via passive modulation of the lattice configuration without resorting to active control and energy gain/loss. Intriguing physics such as the reciprocal and higher-order skin effects can be tailored in the passive system. Our study provides an easy-to-implement platform for the exploration of non-Hermitian and nonreciprocal phenomena beyond conventional wave dynamics.