Exploring the Limits of Euler–Bernoulli Theory in Micromechanics
In this study, the limits of the Euler–Bernoulli theory in micromechanics are explored. Raman spectroscopy, which is extremely accurate and reliable, is employed to study the bending of a microbeam of a length of 191 μm. It is found that at the micro-scale, the Euler–Bernoulli theory remains an exac...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/3/142 |
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| author | Chrysoula K. Manoli Styliani Papatzani Dionysios E. Mouzakis |
| author_facet | Chrysoula K. Manoli Styliani Papatzani Dionysios E. Mouzakis |
| author_sort | Chrysoula K. Manoli |
| collection | DOAJ |
| description | In this study, the limits of the Euler–Bernoulli theory in micromechanics are explored. Raman spectroscopy, which is extremely accurate and reliable, is employed to study the bending of a microbeam of a length of 191 μm. It is found that at the micro-scale, the Euler–Bernoulli theory remains an exact and consistent tool, and, possibly, other elasticity theories (such as micropolar theory, gradient elasticity theory, and couple stress theory) are not always required to study this phenomenon. More specifically, good correlation was achieved between the theoretical and experimental results, the former acquired via the theoretical equations and the latter obtained with the use of atomic force microscopy and Raman spectroscopy. The exact predicted strain of an atomic force microscope microbeam under bending, by Euler–Bernoulli equations is confirmed by Raman spectroscopy. |
| first_indexed | 2024-03-09T13:51:32Z |
| format | Article |
| id | doaj.art-da9b018cd5984a8d826c614765c85dd7 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T13:51:32Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-da9b018cd5984a8d826c614765c85dd72023-11-30T20:50:30ZengMDPI AGAxioms2075-16802022-03-0111314210.3390/axioms11030142Exploring the Limits of Euler–Bernoulli Theory in MicromechanicsChrysoula K. Manoli0Styliani Papatzani1Dionysios E. Mouzakis2Laboratory of Mechanics, Department of Mathematics and Engineering Sciences, Hellenic Army Academy, Evelpidon Avenue, Vari, 166 72 Attica, GreeceLaboratory of Mechanics, Department of Mathematics and Engineering Sciences, Hellenic Army Academy, Evelpidon Avenue, Vari, 166 72 Attica, GreeceLaboratory of Mechanics, Department of Mathematics and Engineering Sciences, Hellenic Army Academy, Evelpidon Avenue, Vari, 166 72 Attica, GreeceIn this study, the limits of the Euler–Bernoulli theory in micromechanics are explored. Raman spectroscopy, which is extremely accurate and reliable, is employed to study the bending of a microbeam of a length of 191 μm. It is found that at the micro-scale, the Euler–Bernoulli theory remains an exact and consistent tool, and, possibly, other elasticity theories (such as micropolar theory, gradient elasticity theory, and couple stress theory) are not always required to study this phenomenon. More specifically, good correlation was achieved between the theoretical and experimental results, the former acquired via the theoretical equations and the latter obtained with the use of atomic force microscopy and Raman spectroscopy. The exact predicted strain of an atomic force microscope microbeam under bending, by Euler–Bernoulli equations is confirmed by Raman spectroscopy.https://www.mdpi.com/2075-1680/11/3/142Euler–Bernoulli beam theorymicrobeam bendingRaman spectroscopyAFMsmall deformations |
| spellingShingle | Chrysoula K. Manoli Styliani Papatzani Dionysios E. Mouzakis Exploring the Limits of Euler–Bernoulli Theory in Micromechanics Axioms Euler–Bernoulli beam theory microbeam bending Raman spectroscopy AFM small deformations |
| title | Exploring the Limits of Euler–Bernoulli Theory in Micromechanics |
| title_full | Exploring the Limits of Euler–Bernoulli Theory in Micromechanics |
| title_fullStr | Exploring the Limits of Euler–Bernoulli Theory in Micromechanics |
| title_full_unstemmed | Exploring the Limits of Euler–Bernoulli Theory in Micromechanics |
| title_short | Exploring the Limits of Euler–Bernoulli Theory in Micromechanics |
| title_sort | exploring the limits of euler bernoulli theory in micromechanics |
| topic | Euler–Bernoulli beam theory microbeam bending Raman spectroscopy AFM small deformations |
| url | https://www.mdpi.com/2075-1680/11/3/142 |
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