  We introduce a new class of thin flexible structures that morph from a flat
shape into prescribed 3D shapes without an external stimulus such as mechanical
loads or heat. To achieve control over the target shape, two different concepts
are coupled. First, motivated by biological growth, strain mismatch is applied
between the flat composite layers to transform it into a 3D shape. Depending on
the amount of the applied strain mismatch, the transformation involves buckling
into one of the available finite number of mode shapes. Second, inspired by
kirigami, portions of the material are removed from one of the layers according
to a specific pattern. This dramatically increases the number of possible 3D
shapes and allows us to attain specific topologies. We devise an experimental
apparatus that allows precise control of the strain mismatch. An inverse
problem is posed, where starting from a given target shape, the physical
parameters that make these shapes possible are determined. To show how the
concept works, we focus on circular composite plates and design a kirigami
pattern that yields a hemispherical structure. Our analysis combines a
theoretical approach with numerical simulations and physical experiments to
understand and predict the transition from 2D to 3D shapes. The tools developed
here can be extended to attain arbitrary 3D shapes. The initially flat shape
suggests that conventional additive manufacturing techniques can be used to
functionalize the soft kirigami composites to fabricate, for example,
deployable 3D shapes, smart skins, and soft electromagnetic metasurfaces.
