Related Experiment Video
Updated: Mar 14, 2026

Conducting Elevated Temperature Normal and Combined Pressure-Shear Plate Impact Experiments Via a Breech-end Sabot Heater System
Published on: August 7, 2018
Stress concentration in periodically rough Hertzian contact: Hertz to soft-flat-punch transition
R Ledesma-Alonso1, E Raphaël2, L Léger3
1Laboratoire de Physico-Chimie Théorique, UMR CNRS 7083 Gulliver, ESPCI ParisTech, PSL Research University, 10 Rue Vauquelin, 75005 Paris, France; Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, 91400 Orsay, France.
Abstract:
We report on the elastic contact between a spherical lens and a patterned substrate, composed of a hexagonal lattice of cylindrical pillars. The stress field and the size of the contact area are obtained by means of numerical methods: a superposition method of discrete pressure elements and an iterative bisection-like method. For small indentations, a transition from a Hertzian to a soft-flat-punch behaviour is observed when the surface fraction of the substrate that is covered by the pillars is increased. In particular, we present a master curve defined by two dimensionless parameters, which allows one to predict the stress at the centre of the contact region in terms of the surface fraction occupied by pillars. The transition between the limiting contact regimes, Hertzian and soft-flat-punch, is well described by a rational function. Additionally, a simple model to describe the Boussinesq-Cerruti-like contact between the lens and a single elastic pillar, which takes into account the pillar geometry and the elastic properties of the two bodies, is presented.
Related Concept Videos
Stress Concentrations
Stress Concentrations
The stress...
Stress Concentrations in Circular Shafts
Stress: General Loading Conditions
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
Circular Shaft - Stresses in Linear Range
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

