  We study the geometrically nonlinear behavior of uniformly compressed
tensegrity prisms, through fully elastic and rigid--elastic models. The
presented models predict a variety of mechanical behaviors in the regime of
large displacements, including an extreme stiffening-type response, already
known in the literature, and a newly discovered, extreme softening behavior.
The latter may lead to a snap buckling event producing an axial collapse of the
structure. The switching from one mechanical regime to another depends on the
aspect ratio of the structure, the magnitude of the applied prestress, and the
material properties of the constituent elements. We discuss potential acoustic
applications of such behaviors, which are related to the design and manufacture
of tensegrity lattices and innovative phononic crystals.
