Indentation of solids with gradients in elastic properties .2. Axisymmetric indentors

Analytical and computational results are presented for the evolution of stresses and deformation fields due to indentation from a rigid axisymmetric indentor on an elastic substrate. The theory addresses the variations in Young's modulus, E, of the substrate as a function of depth, z, beneath the indented surface for two cases: (1) a simple power law, E = E(0)z(k), where 0 less than or equal to k < 1 is a non-dimensional exponent; (2) an exponential law, E = E(0)e(alpha z), where E-0 is Young's modulus at the surface and alpha is a length parameter. The indentor geometries for which analytic solutions are derived include flat circular punch, sphere and circular cone. The analytical results for the punch are compared with finite element simulations; the latter validate the theory and offer further insights into the effects of the variation in Poisson ratio, upsilon, with depth. (C) 1997 Elsevier Science Ltd.