Abstract
As at the nanoscale the surface-to-volume ratio may be comparable with any characteristic length, while the material properties may essentially depend on surface/interface energy properties. In order to get effective material properties at the nanoscale, one can use various generalized models of continuum. In particular, within the framework of continuum mechanics, the surface elasticity is applied to the modelling of surface-related phenomena. In this paper, we derive an expression for the effective bending stiffness of a laminate plate, considering the Steigmann–Ogden surface elasticity. To this end, we consider plane bending deformations and utilize the through-the-thickness integration procedure. As a result, the calculated elastic bending stiffness depends on lamina thickness and on bulk and surface elastic moduli. The obtained expression could be useful for the description of the bending of multilayered thin films.
Highlights
Nowadays, it is well established that the usual material properties at the nanoscale, such asYoung’s modulus, may significantly differ from what is observed at the macroscale
Unlike the Gurtin–Murdoch model, this model explicitly takes into account the surface bending stiffness
The derived formula contains various contributions related to the elastic response in the bulk, the influence of the surface Lamé moduli and of the surface bending stiffness moduli
Summary
It is well established that the usual material properties at the nanoscale, such as. In addition to tensional stiffness, there exist various other stiffness parameters such as bending and torsional stiffnesses, known from textbooks on the strength of materials These parameters may characterize the behaviour of thin structures of nanometer size. The aim of this paper is to discuss the bending stiffness of layered nanosized plates. To this end, we consider the classic linear elasticity as a model for material properties in the bulk and the Steigmann–Ogden surface elasticity [9,10] for the modelling of plate faces and interfaces between layers. Let us note tat the surface elasticity models can be treated as a singular case of nonlocality related to the appearance of boundary layers near shell faces.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
