Indentation of axisymmetric rigid punch: Model implementation by a Python Algorithm

We present a computationally efficient Python algorithm based on the Boundary Element Method (BEM) for frictionless linear elastic axisymmetric contact of coated solids. The algorithm solves indentation problems using conical, spherical, and cylindrical flat indenters, with results also reported for flat punch indentation on a soft-coated substrate. To validate BEM, we implement Finite Element Method (FEM) simulations, analyzing soft layers with Poisson ratios of 0.25, 0.4, and 0.49, aspect ratios from 0.25 to 10, and modulus mismatches of 10 and 100. BEM and FEM show good agreement for compressible soft layers but diverge as incompressibility increases. For Poisson’s ratio of 0.4999, BEM fails due to confinement effects. We verify FEM results using the Poker-chip test, confirming accuracy in highly confined, nearly incompressible cases. For compressible soft layer and large aspect ratios, we found good agreement between BEM and analytical result of Poker-chip test applicable in that regime.