Department of Mathematics & Statistics / Indian Institute of Technology Kanpur / Kanpur-208016, Uttar Pradesh, India.

Title: Indentation of Heterogeneous Media

Abstract: Indentation of materials is a classical and important engineering problem. Historically, investigations into this problem have been carried out mostly for homogeneous, elastic media. At the same time, the ubiquity and importance of heterogeneous materials, such as composites, soil and biological tissue is self-evident. This necessitates a thorough investigation of indentation of heterogeneous materials.

I will present the study of indentation of a layered half-space – an instance of a heterogeneous material. Layered materials are composed of two homogeneous, isotropic materials stacked periodically along the normal to the free surface. Rapid spatial variation of material parameters in a layered material with layers of small thickness makes its numerical investigation hard. We introduce three problems each involving a smooth, rigid indenter indenting a layered half-space but for the purpose of the talk consider only the analysis of  indentation of a layered, elastic half-space by a long, cylindrical rigid indenter.