Mechanical Fourier transform for programmable metamaterials.

Proactively programming materials toward target nonlinear mechanical behaviors is crucial to realize customizable functions for advanced devices and systems, which arouses persistent explorations for rapid and efficient inverse design strategies. Herein, we propose a "mechanical Fourier transform" strategy to program mechanical behaviors of materials by mimicking the concept of Fourier transform. In this strategy, an arbitrary target force-displacement curve is decomposed into multiple cosine curves and a constant curve, each of which is realized by a rationally designed multistable module in an array-structured metamaterial. Various target curves with distinct shapes can be rapidly programmed and reprogrammed through only amplitude modulation on the modules. Two exemplary metamaterials are demonstrated to validate the strategy with a macroscale prototype based on magnet lattice and a microscale prototype based on an etched silicon wafer. This strategy applies to a variety of scales, constituents, and structures, and paves a way for the property programming of materials.