An analytical model of the mechanical behaviour of elastic adhesively bonded joints

Contact and adhesion between two elastic solids bonded by a thin elastic adhesive are considered. The peculiar case of a rigid flat cylindrical punch being adhered to an elastic layer is considered. In order to evaluate the influence of adhesive thickness on the mechanical behaviour of the bonded solids, an approximate solution of the contact problem is derived, using the Ritz method. Comparison of the analytical solution with FE calculations shows a good convergence towards the asymptotic value when the ratio of the punch radius to the layer thickness is greater than 4. Numerical simulation reveals a strong effect of the adhesive compressibility, for a thin adhesive. This effect is assessed quantitatively from a double asymptotic expansion of the analytical solution. Lastly, the rupture stress is evaluated as a function of the adhesive thickness, from the knowledge of the solution of the contact problem; the asymptotic value for a very thin adhesive is determined independently.