Transversely isotropic half-spaces subject to surface pressures

• Published in: International journal of solids and structures Vol. 104-105; pp. 35 - 49
• Main Authors: Marmo, Francesco, Toraldo, Ferdinando, Rosati, Luciano
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.01.2017; Elsevier BV
• Subjects: Analytical solution; Displacement; Half spaces; Half-space; Indentation; Materials elasticity; Proving; Singularities; Stress concentration; Stress state; Transversely isotropic; Analytical solution; Transversely isotropic; Half-space
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2016.11.001

We outline a general methodology for proving the equivalence between several solutions available in the literature for the elastic problem of transversely isotropic materials. The proposed methodology is mathematically supported by a novel solution strategy yet arriving at the same expression of the displacement field contributed by Ding et al. (2006). We further show how to address the case of transversely isotropic half-spaces subject to linearly distributed vertical pressures applied over arbitrary regions of the half-space boundary. In the significant case of polygonal regions, displacements and stresses at arbitrary points of the half-space are evaluated analytically and the relevant singularities are properly accounted for. The proposed approach has been numerically validated by first solving a basic indentation problem for which an analytical expression of the displacements on the half-space surface is available. Furthermore, the displacement and stress fields induced in a half-space by a polygonal indenter of arbitrary shape subject to a prescribed vertical displacement is illustrated by means of representative contour plots.