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

Fabien Amiot 1
1 MECANIQUE APPLIQUEE
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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [13 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00783801
Contributor : Christine Froidevaux <>
Submitted on : Friday, February 1, 2013 - 4:41:26 PM
Last modification on : Monday, September 3, 2018 - 11:30:08 AM
Long-term archiving on : Thursday, May 2, 2013 - 4:10:09 AM

File

phil_mag_letter_ccsd.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

333

Files downloads

666