  The Poynting effect generically manifests itself as the extension of the
material in the direction perpendicular to an applied shear deformation
(torsion) and is a material parameter hard to design. Here, we engineer a
metamaterial that can be programmed to contract or extend under torsion,
depending on its architecture. First, we show that our system exhibits a novel
type of inverted Poynting effect, where axial compression induces a nonlinear
torsion. Then we program the Poynting modulus of the structure from initial
negative values to zero and positive values via a pre-compression applied prior
to torsion. Our work opens avenues for programming nonlinear elastic response
of materials by rational design.
