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Applied Math Seminar: Frictionless indentation of a rigid stamp into a half-space

Speaker: Lauren White (K-State)

Abstract: Investigation of material behavior at a nanoscale has shown that material properties differ when compared to larger scales. Surfaces have a non-negligible influence on the behavior of nanomaterials. Due to this, contact problems at a nanoscale must consider surface energy. In this talk, we consider an isotropic half-space subjected to nanoscale contact with a rigid punch. The Steigmann-Ogden model of surface elasticity is used to model the surface while linear elasticity is used to model the bulk of the material. The nanoindentation problem is solved using Boussinesq’s displacement potentials and Hankel integral transforms. The problem is reduced to a single integral equation. This equation is further transformed into a Fredholm integral equation of the first kind. Numerical methods of solution to the corresponding Fredholm equation using Chebyshev–Gauss quadrature are presented.

Zoom link will be sent out on Wednesday (Oct 7)

Thursday, October 8, 2020 at 4:00pm to 4:50pm

Event Type

Lecture, Colloquia, Seminar

Mathematics, Department of
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