{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T03:13:45Z","timestamp":1778210025279,"version":"3.51.4"},"reference-count":95,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2015,11,11]],"date-time":"2015-11-11T00:00:00Z","timestamp":1447200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Sensors"],"abstract":"<jats:p>Experiments on micro- and nano-mechanical systems (M\/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke\u2019s law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M\/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale.<\/jats:p>","DOI":"10.3390\/s151128543","type":"journal-article","created":{"date-parts":[[2015,11,12]],"date-time":"2015-11-12T03:46:55Z","timestamp":1447300015000},"page":"28543-28562","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":85,"title":["Modelling the Size Effects on the Mechanical Properties of Micro\/Nano Structures"],"prefix":"10.3390","volume":"15","author":[{"given":"Amir","family":"Abazari","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran"},{"name":"Advanced NEMS Group, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne CH-1015, Switzerland"}]},{"given":"Seyed","family":"Safavi","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5243-3199","authenticated-orcid":false,"given":"Ghader","family":"Rezazadeh","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Urmia University, Urmia 57561-51818, Iran"}]},{"given":"Luis","family":"Villanueva","sequence":"additional","affiliation":[{"name":"Advanced NEMS Group, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), Lausanne CH-1015, Switzerland"}]}],"member":"1968","published-online":{"date-parts":[[2015,11,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1038\/nnano.2012.119","article-title":"Single-protein nanomechanical mass spectrometry in real time","volume":"7","author":"Hanay","year":"2012","journal-title":"Nat. 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