  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.
