A new method for theoretical analysis of static indentation test

A new mathematical method was developed to study the indentation problem of an infinite elastic layer overlaid on a rigid foundation. Rigid, flat-ended cylindrical or spherical indenters are pressed onto the upper surface of the elastic layer causing a small deformation mode. Shear stresses between the indenter and the layer are assumed negligible and the layer is assumed to be either bonded or unbonded to the rigid foundation. The problem is equivalent to a mixed boundary-value problem of the theory of elasticity. Instead of using the Fredholm integral equation reported in the literature, the new approach obtained closed-form solutions through an infinite series. Convergence can be achieved using less than 10 terms of the series.