On Saint-Venant Principle for Carbon Nanotubes
| Saint-Venant Principle (SVP), a central principle in both elasticity theory and structural mechanics, states that localized self-equilibrating loads create stress and strain fields that decay with distance from the loaded region. However, while well established for macroscopic homogeneous structures, its relevance at the nanoscale is less certain. Carbon nanotubes (CNTs)—with their exceptional mechanical properties and slender cylindrical shape provide a unique framework to examine the validity of SVP for elastic structures at the nanoscale. This research studies the validity of SVP in CNTs subjected to localized axial loading. Analysis is within the framework of linear elastic stability theory in conjunction with the nature of nanoscale response. Mathematical models are developed for representative configurations such as concentric CNT-like beams embedded in elastic media, systems with unequal radii, and simultaneous buckling of multilayer arrangements. Findings indicate that localized self-equilibrating loads applied to CNT systems induce axially decaying (exponentially) stress and strain fields, though the rate and nature of axial decay depend strongly on geometry, constitutive response, and interlayer interactions. These observations suggest that a modified version of SVP applies at the nanoscale, advancing our understanding of stress transfer in nanostructures and paving the way to future research. |
Light refreshments will be served before the lecture
