  Shape-morphing structures possess the ability to change their shapes from one
state to another, and therefore, offer great potential for a broad range of
applications. A typical paradigm of morphing is transforming from an initial
two-dimensional (2D) flat configuration into a three-dimensional (3D) target
structure. One popular fabrication method for these structures involves
programming cuts in specific locations of a thin sheet material
(i.e.~kirigami), forming a desired 3D shape upon application of external
mechanical load. In this paper, a novel inverse design strategy is proposed by
modifying the bending stiffness via introducing distributed modulus in
functionally graded composites (FGCs). The longitudinal modulus of each
cross-sectional slice can be controlled through the rule of mixtures, hence
matching the required modulus distribution along the elastic strip. Following
the proposed framework, a diverse range of structures is obtained with
different Gaussian curvatures in both numerical simulations and experiments. A
very good agreement is achieved between the measured shapes of morphed
structures and the targets. In addition, the compressive rigidity and specific
energy absorption during compression of FGC-based hemi-ellipsoidal morphing
structures with various aspect ratios were also examined numerically and
validated against experiments. By conducting systematical numerical
simulations, we also demonstrate the multifunctionality of the modulus-graded
shape-morphing composites. This new inverse design framework provides an
opportunity to create shape-morphing structures by utilising modulus-graded
composite materials, which can be employed in a variety of applications
involving multi-physical environments. Furthermore, this framework underscores
the versatility of the approach, enabling precise control over material
properties at a local level.
