  Materials that change their shape in response to external stimuli opens up
new prospects for efficient and versatile design and shaping of
three-dimensional objects. Here, we present a novel class of micro-structures
exhibiting an extension-bending coupling (EBC) effect, that can be harnessed as
an elementary building block for shape-shifting panels. They are built with a
single material as a network of undulated ribbons. The deformations mechanisms
of both single and connected undulated ribbons are analysed using the finite
element method to explain the main features of the EBC mechanism. For a
particular micro-structure of the proposed class, the complete elastic
stiffness tensor is computed combining two-scale homogenization with
Kirchhoff-Love plate theory. The range of achievable EBC ratio is then assessed
with respect to the geometric parameters of the unit cell. Patterned specimens
are manufactured using a commercial FFF Ultimaker 3-d printer and are
mechanically tested at finite strain up to 20%. The displacement measured by
point tracking match the predictions from the finite element simulations and
indicate that the structure maintain its properties at finite strain. Moreover,
a tensile test load with point-like boundary is proposed to highlight
exceptional out of plane displacement. We envision these structures to be
leveraged in combination with responsive materials for the actuation of soft
robots, compliant systems and reconfigurable structures, as alternatives to
external mechanical motors, control systems and power devices.
