Abstract
A problem for a nano-sized material surface attached to the boundary of an elastic isotropic semi-plane is considered. The semi-plane and the material surface are assumed to be in a plane strain state under the action of a normal external tractions applied to the material surface. The material surface is modeled using the Steigmann–Ogden form of surface energy. The problem is solved using integral representations of stresses and displacements. With the help of these representations, the problem can be reduced to either a system of two singular integral equations or a single singular integral equation. Two types of material surface tip conditions are considered: tip conditions with an uncompensated surface prestress (free tip conditions) and tip conditions with a compensated surface prestress term. The numerical solution of the system of singular integral equations is obtained by expanding each unknown function into a series based on the Chebyshev polynomials. Then, the approximations of the unknown functions can be obtained from a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical examples for different values of the surface energy parameters are considered. It is shown that both the surface parameters and the type of tip conditions have significant influence on the behavior of the material system.
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.
