Stress tensor in the linear viscoelatsic incompressible half-space beneath axisymmetric bodies in normal contact

Abstract

We present a simple method to determine the stress state in a linear viscoelastic half-space in frictionless unilateral normal contact with an axisymmetric rigid indenter for arbitrary loading histories. The procedure consists in the superposition of elastic solutions for flat punch or parabolic contact along the line load within the framework of the method of dimensionality reduction. We provide simple expressions for all stress components and the hydrostatic pressure gradient, which is of particular interest in the biomechanical field. The method brings advantages especially in its numerical application, since no convolution in time over the entire contact history is necessary.