Plane strain indentation on finite thickness bonded layer in couple stress elasticity

Abstract

Contact of flat, cylindrical and wedge indenter on a finite thickness layer obeying couple stress elasticity and bonded to a rigid base under plane strain conditions is solved. The method of stress functions and Fourier transforms is employed to reduce the mixed boundary value contact problem to a singular integral equation in terms of the unknown contact pressure and contact size. For a given load on the indenter, the solution is obtained iteratively through numerical inversion of the integral equation and the effect of layer thickness and intrinsic length inherent in couple stress elastic material on the contact pressure and contact size is studied. Finally a map described in terms of the intrinsic length and layer thickness is proposed which can be used as a guiding tool to decide appropriate combination of geometry i.e. layer or half space and material behavior i.e. classical elasticity or couple stress elasticity to obtain accurate indentation response for a given system.