Direct influence of residual stress on the bending stiffness of cantilever beams

Although the cantilever beam has been widely used as a sensor to measure various physical quantities, important issues such as how residual stress affects its bending stiffness and what are the underlying physical origins have not been fully understood. We perform both theoretical analyses and finite-element simulations to demonstrate for the first time that without changing the material tangent stiffness, residual stress within the beam can directly influence the bending stiffness of the beam. This direct influence arises from two origins: geometry nonlinearity and Poisson’s ratio effect. For a cantilever beam with adsorbed macromolecules on its surfaces, we find that longer macromolecular chains have lower normal stiffness and larger intermolecular forces, which makes the effect of the residual stress more pronounced. The excellent agreement between our theoretical predictions and finite-element calculation results validate our analysis. The present work provides an important framework for improving the sensitivity of a cantilever beam as a sensor. The paper can be found at http://dx.doi.org/10.1098/rspa.2011.0662