A Review of Theories and Numerical Methods in Nanomechanics for the Analysis of Nanostructures

Mostafa Sadeghian (), Arvydas Palevicius () and Giedrius Janusas
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Mostafa Sadeghian: Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania
Arvydas Palevicius: Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania
Giedrius Janusas: Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, 51424 Kaunas, Lithuania

Mathematics, 2025, vol. 13, issue 22, 1-40

Abstract: Nanostructures, such as carbon nanotubes (CNTs), graphene, nanoplates, etc., show behaviors that classical continuum theories cannot capture. At the nanoscale, size effects, surface stresses, and nonlocal interactions become important, so new models are needed to study nanostructures. The main nanomechanics theories that are used in recently published papers include nonlocal elasticity theory (NET), couple stress theory (CST), and nonlocal strain gradient theories (NSGTs). To solve these models, methods such as finite elements, isogeometric analysis, mesh-free approaches, molecular dynamics (MD), etc., are used. Also, this review categorizes and summarizes the major theories and numerical methods used in nanomechanics for the analysis of nanostructures in recently published papers. Recently, machine learning methods have enabled faster and more accurate prediction of nanoscale behaviors, offering efficient alternatives to traditional methods. Studying these theories, numerical models and data driven approaches provide an important foundation for future research and the design of next generation nanomaterials and devices.

Keywords: nanomechanics theories; numerical methods; nanostructures; machine learning; review (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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