  Self-shaping of curved structures, especially those involving flexible thin
layers, has attracted increasing attention because of their broad potential
applications in e.g. nanoelectromechanical/micro-electromechanical systems
(NEMS/MEMS), sensors, artificial skins, stretchable electronics, robotics, and
drug delivery. Here, we provide an overview of recent experimental,
theoretical, and computational studies on the mechanical self-assembly of
strain-engineered thin layers, with an emphasis on systems in which the
competition between bending and stretchingenergy gives rise to a variety
ofdeformations,such as wrinkling, rolling, and twisting. We address the
principle of mechanical instabilities, which is often manifested in wrinkling
or multistability of strain-engineered thin layers. The principles of shape
selection and transition in helical ribbons are also systematically examined.
We hope that a more comprehensive understanding of the mechanical principles
underlying these rich phenomena can foster the development of new techniques
for manufacturing functional three- dimensional structures on demand for a
broad spectrum of engineering applications.
