An Euler-Bernoulli second-strain gradient beam theory for cantilever sensors

Fabien Amiot 1
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
Abstract : This paper derives an Euler-Bernoulli beam theory for isotropic elastic materials based on a second strain gradient description. As such a description has been proved to allow for the definition of surface tension for solids, the equations satisfied by a beam featuring a through-thickness cohesion modulus gradient are established in order to describe the behavior of micro-cantilever sensors. Closed-form solutions are given for mechanical and chemical loadings. It is then shown that the involved material parameters seem virtually identifiable from full-field measurements and that the shape of the displacement field resulting from a chemical loading depends on the cantilever's thickness as well as on the material parameters. This makes such a theory potentially able to explain some of the experimental results found in the literature.
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Submitted on : Friday, February 1, 2013 - 4:41:26 PM
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Fabien Amiot. An Euler-Bernoulli second-strain gradient beam theory for cantilever sensors. Philosophical Magazine Letters, Taylor & Francis, 2013, ⟨10.1080/09500839.2012.759294⟩. ⟨hal-00783801⟩



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