A semi-analytical approach to the contact of thin elastic layers

摘要

As half-space theory is inapplicable to thin contacting elements, an adequate interference equation is derived in this paper and solved using a robust contact solver based on the conjugate gradient method. Due to geometric and loading symmetry of the problem, the arrangement of a thin elastic layer compressed between 2 identical indenters is modelled by the contact between one indenter and a half-thick layer laying without friction on a rigid flat foundation. The Green function for the thin layer is found by superimposing a supplementary displacement field to the half-space solution, so that their sum satisfies all linear elasticity requirements (boundary conditions, force balance equation, biharmonicity, and asymptotic behaviour). The principle of uniqueness of solutions in elastostatics guarantees that this solution is the required one. The superposition principle further allows numerical computation of displacements and stresses produced by a digitised pressure distribution, thus yielding the solution for the contact problem involving thin layers.