Analysis of the tilted flat punch in couple-stress elasticity

In the present paper we explore the response of a half-plane indented by a tilted flat punch with sharp corners in the context of couple-stress elasticity theory. Contact conditions arise in a number of modern engineering applications ranging from structural and geotechnical engineering to micro and nanotechnology. As the contact scales reduce progressively the effects of the microstructure upon the macroscopic material response cannot be ignored. The generalized continuum theory of couple-stress elasticity introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying material microstructure. The problem under investigation is interesting for three reasons: Firstly, the indentor's geometry is simple so that benchmark results may be extracted. Secondly, important deterioration of the macroscopic results may emerge in the case that a tilting moment is applied on the indentor inadvertently or in the case that the flat punch itself is not self-aligning so that asymmetrical contact pressure distributions arise on the contact faces. Thirdly, the voluntary application of a tilting moment on the flat punch during an experiment gives rise to potential capabilities of the flat punch for the determination of the material microstructural characteristic lengths. The solution methodology is based on singular integral equations which have resulted from a treatment of the mixed boundary value problem via integral transforms and generalized functions. The results show significant departure from the predictions of classical elasticity revealing that valuable information may be deducted from the indentation of a tilted punch of a microstructured solid.