Published today in Scientific Reports 6, Article number: 29627 (2016). This work presents a theory that describes the stiffness of curved thin sheets with simple equations in terms of the longitudinal and transversal curvatures. The theory predicts experimental results with a macroscopic cantilever sheet as well as numerical simulations by the finite element method. The results shed new light on plant and insect wing biomechanics and provide an easy route to engineer micro- and nanomechanical structures based on thin materials with extraordinary stiffness tunability. This work shows that small amounts of two-dimensional bending of thin plates lead to the development of in-plane stresses, and thus bending is not in general so energetically cheap as believed hitherto. Biaxial curving of thin sheets is perhaps the most efficient way to reinforce the mechanical stability of thin sheets. This ancient mechanism found in nature and in man-made structures has remained unexplained in physics. The theoretical model and simple equations provided here solve this long-standing problem shedding light in our understanding of thin sheet mechanics and bringing new and useful mathematical tools to a wide variety of fields such as natural science, mechanical engineering and micro/nanotechnology.
