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Winkler boundary conditions for three-point bending tests on 1D nanomaterials.
Nanotechnology 2010; 21(22):225704N

Abstract

Bending tests with atomic force microscopes (AFM) is a common method for elasticity measurements on 1D nanomaterials. Interpretation of the force and deflection data is necessary to determine the Young's modulus of the tested material and has been done assuming either of two classic boundary conditions that represent two extreme possibilities for the rigidity of the sample-anchor interface. The elasticity results from the two boundary conditions differ by a factor of four. Furthermore, both boundary conditions ignore the effects of deflections in the anchors themselves. The Winkler model for beams on elastic foundations is developed here for three-point bending tests to provide a more realistic representation. Equations for computing sample elasticity are derived from two sets of boundary conditions for the Winkler model. Application of this model to interpret the measurement of mechanical stiffness of a silica nanowire at multiple points in a three-point bending is discussed. With the correct choice of boundary conditions, the Winkler model gives a better fit for the observed stiffness profile than the classical beam models while providing a result that differs from both by a factor of two and is comparable to the bulk elasticity.

Authors+Show Affiliations

Department of Physics, University of Idaho, Moscow, ID 83844-0903, USA.

Pub Type(s)

Journal Article
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

Language

eng

PubMed ID

20453278

Citation

Gangadean, D, et al. "Winkler Boundary Conditions for Three-point Bending Tests On 1D Nanomaterials." Nanotechnology, vol. 21, no. 22, 2010, p. 225704.
Gangadean D, McIlroy DN, Faulkner BE, et al. Winkler boundary conditions for three-point bending tests on 1D nanomaterials. Nanotechnology. 2010;21(22):225704.
Gangadean, D., McIlroy, D. N., Faulkner, B. E., & Aston, D. E. (2010). Winkler boundary conditions for three-point bending tests on 1D nanomaterials. Nanotechnology, 21(22), p. 225704. doi:10.1088/0957-4484/21/22/225704.
Gangadean D, et al. Winkler Boundary Conditions for Three-point Bending Tests On 1D Nanomaterials. Nanotechnology. 2010 Jun 4;21(22):225704. PubMed PMID: 20453278.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Winkler boundary conditions for three-point bending tests on 1D nanomaterials. AU - Gangadean,D, AU - McIlroy,David N, AU - Faulkner,Brian E, AU - Aston,D Eric, Y1 - 2010/05/07/ PY - 2010/5/11/entrez PY - 2010/5/11/pubmed PY - 2010/5/11/medline SP - 225704 EP - 225704 JF - Nanotechnology JO - Nanotechnology VL - 21 IS - 22 N2 - Bending tests with atomic force microscopes (AFM) is a common method for elasticity measurements on 1D nanomaterials. Interpretation of the force and deflection data is necessary to determine the Young's modulus of the tested material and has been done assuming either of two classic boundary conditions that represent two extreme possibilities for the rigidity of the sample-anchor interface. The elasticity results from the two boundary conditions differ by a factor of four. Furthermore, both boundary conditions ignore the effects of deflections in the anchors themselves. The Winkler model for beams on elastic foundations is developed here for three-point bending tests to provide a more realistic representation. Equations for computing sample elasticity are derived from two sets of boundary conditions for the Winkler model. Application of this model to interpret the measurement of mechanical stiffness of a silica nanowire at multiple points in a three-point bending is discussed. With the correct choice of boundary conditions, the Winkler model gives a better fit for the observed stiffness profile than the classical beam models while providing a result that differs from both by a factor of two and is comparable to the bulk elasticity. SN - 1361-6528 UR - https://www.unboundmedicine.com/medline/citation/20453278/Winkler_boundary_conditions_for_three_point_bending_tests_on_1D_nanomaterials_ L2 - https://doi.org/10.1088/0957-4484/21/22/225704 DB - PRIME DP - Unbound Medicine ER -