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.