A concise treatment of indentation problems in transversely isotropic half-spaces

Abstract

A concise treatment of a class of indentation problems in elastic transversely isotropic half-spaces is presented. The half-space is deformed either by a prescribed surface traction or by the indentation of a rigid punch that includes frictionless normal indentation, sliding contact and adhesive punch problems. The complete solution in the half-space is obtained by integrating the elastic displacement due to point loads with appropriate distribution functions over the contact area. The point load on the contact area is the linear superposition of the normal and tangential point forces, and the centers of compression. The point load distribution is the same as the surface traction distribution, but for a sign difference and is either prescribed or determined from the surface deformation due to the indentation. The governing equations for the surface deformation and the surface traction are the same for the isotropic and the transversely isotropic half-spaces. For a given punch, the surface tractions on either half-spaces have the same spatial distribution but with different magnitudes. The profiles of the deformed boundary surfaces for either half-spaces are the same.