An indentation contact problem of a stamp and a bonded thin elastic layer

Abstract

An indentation contact problem between a cylinder stamp and a bonded elastic layer is investigated in this paper. Based on the Navier equation and boundary conditions, the contact problem is transformed into a governing formula, which is in the form of singular integral equation of the first kind, through Fourier transform techniques. By using dimensionless parameterization tricks, a numerical scheme for inverse contact problem is built, and the contact stresses could be obtained directly through the coupled solution of governing equation and equilibrium relationship. Thereinto, the contact pressure is approximated by Chebyshev polynomials, and the governing equation is solved numerically. The reliability of the numerical results is demonstrated through comparison with existing analytical solutions, and the influences of Poisson’s ratio and layer thickness on contact stresses are discussed. Results show that, contact pressure converges to a Hertzian type when the layer thickness increases, and both increasing Poisson's ratio and reducing the layer thickness can sharpen the contact stress.