Stress guides in generic static mechanical metamaterials

Electromagnetic, acoustic, and elastic waveguides are commonly used in communication, imaging, and signal isolation to facilitate efficient directional transmission of signals. However, static deformation lacks dynamic effects, making it challenging to achieve immunity to defects such as inclusions and symmetry breaking. Additionally, characterizing and tailoring accumulated static deformation is even more difficult. Nonetheless, Prof. Changqing Chen's group at Tsinghua University has developed a theory that quantifies the accumulated static deformation for mechanical metamaterials based on the intrinsic correlation between the spatial distribution of the static deformation field and the time-domain evolution of waves. They have also introduced the concept of a static stress waveguide, enabling the directional transmission of static signals.

While wave propagation in a medium does not typically exhibit defect sensitivity, the static deformation field of a material is localized at singularities, resulting in stress concentration. Moreover, the deformation response under external loads is closely connected to the microstructure of the material, allowing for modulation through structural design. However, the diverse microstructures of mechanical metamaterials currently lack a general theory to quantitatively characterize the sensitivity of localized static deformation fields to defects. A theory addressing this gap would greatly facilitate the design of mechanical metamaterials with various applications, such as stress shielding, energy harvesting, mechanical computation, and information storage.

Recently, Prof. Changqing Chen's group at Tsinghua University has developed a theory to characterize the localized static deformation field of two- and three-dimensional periodic mechanical metamaterials. They have established a duality between the time axis in a low-dimensional dynamic system and a spatial axis in a high-dimensional static system, enabling mapping of the directional distribution of the deformation field in space to the non-reciprocal transport of wave packets in the medium. This spatio-temporal duality is inherent in 2D/3D mechanical metamaterials and even continuous media. Building on this theory, the group has attributed the "wave" property to the static deformation field and introduced the concept of static stress waveguides, which guide localized deformation along a specified path in a tailorable manner. These findings have been published in the National Science Review 2024, under the title "Stress guides in generic static mechanical metamaterials," with Prof. Changqing Chen as the corresponding author.

Based on the duality of space and time, the group defines various "dynamic" quantities in the static system, such as "wave packet" and "group velocity." The static wave packet represents the accumulated deformation mode with a centralized coordinate in real space, and a concentrated wavenumber in reciprocal space and can be excited by a concentrated load at the boundary. On the other hand, the group velocity quantifies the skewing rate of the static wave packet during its spatial evolution. In this sense, a static wave packet with a nonvanishing group velocity can be directed along a specific path and act as a guide for stress. This is analogous to wave motion in non-reciprocal media. It should be noted that the definitions of wave packets and group velocities in static systems are universal and can be applied to any 2D/3D periodic mechanics metamaterials, and even some continuum media. Additionally, the group also examines the relationship between spatial symmetries in static systems (e.g., mirror-reflection symmetry) and internal symmetries in dynamic systems (e.g., time-reverse symmetry), which can be used to pattern ordered deformation modes. Furthermore, by utilizing the topological band theory in condensed matter physics, the group demonstrates a deformation blocking device, wherein an applied eccentric load is completely blocked at the boundary and facilitates deformation shielding within the bulk.

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