Dynamic analysis of single and cyclic indentation of an elastic–plastic multi-layered medium by a rigid fractal surface

Abstract

Dynamic indentation of an elastic–plastic multi-layered medium by a rigid rough surface that exhibits fractal behavior was analyzed with the finite element method. A sufficiently large mesh was used to avoid the effects of the faster propagating dilatation waves after they were reflected from the artificial mesh boundaries. Single-indentation results illustrate the significance of the thickness of the surface layer and the indentation speed on the contact pressure distribution and subsurface stresses and strains. The initiation of yielding and the development of plasticity are interpreted in the context of results for the von Mises equivalent stress and equivalent plastic strain obtained during the loading and unloading phases of an indentation cycle. Cumulative plasticity and elastic shakedown are discussed in light of results revealing the evolution of deformation in the multi-layered medium due to cyclic indentation. The analysis provides insight into the importance of indentation speed, layer thickness, surface topography, and indentation cycle on the mechanical response of a multi-layered medium in dynamic contact with a rough surface exhibiting multi-scale (fractal) roughness.