Axisymmetric deformation of compressible, nearly incompressible, and incompressible thin layers between two rigid surfaces

TL;DR

This paper develops accurate asymptotic solutions for axisymmetric deformation of thin layers between rigid surfaces, applicable across all Poisson's ratios, distinguishing among different compressibility states based on material and geometric parameters.

Contribution

It introduces a unified asymptotic approach for thin layer deformation that is valid for all Poisson's ratios, using Saint-Venant's principle and layer thinness assumptions.

Findings

Solutions valid for entire Poisson's ratio range

Distinguishes compressible, nearly incompressible, and incompressible layers

Applicable to layers between rigid plates or spheres

Abstract

Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed using Saint-Venant's principle and the layer thinness as the only assumptions. The solutions are valid in the entire range of Poisson's ratios, and allow one to distinguish among compressible, nearly incompressible, and incompressible layers. That classification involves both material and geometric parameters.