Spatiotemporally Programmable Metasurfaces via Viscoelastic Shell Snapping

Many species can dynamically alter their skin textures to enhance their motility and survivability. Despite the enormous efforts on designing bio-inspired materials with tunable surface textures, developing spatiotemporally programmable and reconfigurable textural morphing without complex control remains challenging. Here we propose a design strategy to achieve metasurfaces with such properties. The metasurfaces comprise an array of unit cells with broadly tailored temporal responses. By arranging the unit cells differently, the metasurfaces can exhibit various spatiotemporal responses, which can be easily reconfigured by disassembling and rearranging the unit cells. Specifically, we adopt viscoelastic shells as the unit cells, which can be pneumatically actuated to a concave state, and recover the initial convex state some time after the load is removed. We computationally and experimentally show that the recovery time can be widely tuned by the geometry and material viscoelasticity of the shells. By assembling such shells with different recovery time, we build metasurfaces with pre-programmed spatiotemporal textural morphing under simple pneumatic actuation, and demonstrate temporal evolution of patterns, such as digit numbers and emoji, and spatiotemporal control of friction. This work opens up new avenues in designing spatiotemporal morphing metasurfaces that could be employed for programming mechanical, optical and electrical properties. Corresponding author: Lihua Jin, Email: [email protected]

A Justification of Two-Dimensional Nonlinear Viscoelastic Shells Model

By applying formal asymptotic analysis and Laplace transformation, we obtain two-dimensional nonlinear viscoelastic shells model satisfied by the leading term of asymptotic expansion of the solution to the three-dimensional equations.