  Architected 2D lattice materials are appealing for shape-shifting
applications due to the tunable sign of Poisson's ratio. It is commonly
believed that the positive and negative Poisson's ratios lead to anticlastic
and synclastic curvatures respectively when the material is bent in one
direction. Here, taking 2D beam lattices with star-shaped unit cells as
examples, we show theoretically and demonstrate experimentally that this is not
always true. At a fixed Poisson's ratio, we find a transition between
anticlastic and synclastic bending curvatures controlled by the beam's
cross-sectional aspect ratio. Such an unexpected behavior roots in the
competition between torsion and bending of the beams, and can be well captured
by a Cosserat continuum model.
