  Understanding and controlling the shape of thin, soft objects has been the
focus of significant research efforts among physicists, biologists, and
engineers in the last decade. These studies aim to utilize advanced materials
in novel, adaptive ways such as fabricating smart actuators or mimicking living
tissues. Here, we present the controlled growth--like morphing of 2D sheets
into 3D shapes by preparing geometric composite structures that deform by
residual swelling. The morphing of these geometric composites is dictated by
both swelling and geometry, with diffusion controlling the swelling-induced
actuation, and geometric confinement dictating the structure's deformed shape.
Building on a simple mechanical analog, we present an analytical model that
quantitatively describes how the Gaussian and mean curvatures of a thin disk
are affected by the interplay among geometry, mechanics, and swelling. This
model is in excellent agreement with our experiments and numerics. We show that
the dynamics of residual swelling is dictated by a competition between two
characteristic diffusive length scales governed by geometry. Our results
provide the first 2D analog of Timoshenko's classical formula for the thermal
bending of bimetallic beams - our generalization explains how the Gaussian
curvature of a 2D geometric composite is affected by geometry and elasticity.
The understanding conferred by these results suggests that the controlled
shaping of geometric composites may provide a simple complement to traditional
manufacturing techniques.
