Mechanics of Axisymmetric Indentation Revisited.

摘要

In this report, we derive new solutions to the singular integrals that appear as stress and displacement components, the Jm(n) terms, in Sneddon's solution (1) to the problem of axisymmetric indentation of an elastic half-space by a rigid flat-ended cylindrical punch. The analytical solutions are used to verify a newly developed peridynamics numerical code (2, 3). The peridynamic solutions for the normal and radial displacements of an elastic half-space under the action of a rigid cylindrical punch compare well with analytical results for these fields. Principal stress and shear trajectories in the elastic half-space under the action of a rigid cylindrical punch are determined by numerical integration of the governing equations; our results generally compare well with Sneddon's hand-drawn curves, but we find that Sneddon's sigma(1) trajectories (4) are in error outside the indentation region and near the surface of the half-space.