Transformable topological mechanical metamaterials

Mechanical metamaterials are engineered materials that gain their remarkable mechanical properties, such as negative Poisson's ratios, negative compressibility, phononic bandgaps, and topological phonon modes, from their structure rather than composition. Here we propose a new design principle, based on a uniform soft deformation of the whole structure, to allow metamaterials to be immediately and reversibly transformed between states with contrasting mechanical and acoustic properties. These properties are protected by the topological structure of the phonon band of the whole structure and are thus highly robust against disorder and noise. We discuss the general classification of all structures that exhibit such soft deformations, and provide specific examples to demonstrate how to utilize soft deformations to transform a system between different regimes such that remarkable changes in their properties, including edge stiffness and speed of sound, can be achieved.