Curved thin sheets are ubiquitously found in nature and manmade structures from macro- to nanoscale. Within the framework of classical thin plate theory, the stiffness of thin sheets is independent of its bending state for small deflections. This assumption, however, goes against intuition. Simple experiments with a cantilever sheet made of paper show that the cantilever stiffness largely increases with small amounts of transversal curvature. We here demonstrate by using simple geometric arguments that thin sheets subject to two-dimensional bending necessarily develop internal stresses. The coupling between the internal stresses and the bending moments can increase the stiffness of the plate by several times. We develop 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.

Early detection of HIV infection is the best way to prevent spread of the disease and to improve the efficiency of the antiretroviral therapy. Nucleic acid amplification tests (NAAT) have become the gold-standard for detecting low-concentrations of the virus in blood. However, these methods are technically demanding and cost-prohibitive in developing countries. Immunoassays are more affordable and can be more easily adapted for point-of-care diagnosis. However, the sensitivity so far of these methods has been too low. We here report the development of a sandwich immunoassay that combines nanomechanical and optoplasmonic transduction methods for detecting the HIV-1 capsid antigen p24 in human serum. The immunoreactions take place on the surface of a compliant microcantilever where gold nanoparticles are used as both mechanical and plasmonic labels. The microcantilever acts as both a mechanical resonator and an optical cavity for the transduction of the mechanical and plasmonic signals. The limit of detection of the immunoassay is 10⁻¹⁷ g/mL that is equivalent to one virion in 10 mL of plasma. This is 5 orders of magnitude better than last generation of approved immunoassays and 2 orders of magnitude better than NAAT. This technology meets the demands to be produced en masse at low cost and the capability for miniaturization to be used at the point-of-care.

Microcantilever biosensors in the static operation mode translate molecular recognition into a surface stress signal. Surface stress is derived from the nanomechanical cantilever bending by applying Stoney's equation, derived more than 100 years ago. This equation ignores the clamping effect on the cantilever deformation, which induces significant errors in the quantification of the biosensing response. This leads to discrepancies in the surface stress induced by biomolecular interactions in measurements with cantilevers with different sizes and geometries. So far, more accurate solutions have been precluded by the formidable complexity of the theoretical problem that involves solving the two-dimensional biharmonic equation. In this paper, we present an accurate and simple analytical expression to quantify the response of microcantilever biosensors. The equation exhibits an excellent agreement with finite element simulations and DNA immobilization experiments on gold-coated microcantilevers.

The detailed characterization of the dynamical behavior of an oscillating cantilever is a crucial task in many applications of scanning probe microscopy, force spectroscopy, and cantilever based biosensors. In the present work we considered a direct and localized excitation of the cantilever obtained using the photothermal effect induced by a modulated laser beam that allows us to completely separate the dynamics of the system from spurious effects. We developed a theoretical model able to describe the experimental results with high accuracy; in particular, a good agreement is achieved, both for amplitude and phase, in the presence of resonances and antiresonances, depending on the different location of the excitation beam.