Rigid Stamp Indentation on a Curvilinear Hole Boundary of an Anisotropic Elastic Body

Abstract

A general solution for the problems of rigid stamp indentation on a curvilinear hole boundary of an anisotropic elastic body is obtained by employing the Stroh formalism, the method of analytical continuation, and the technique of mapping a closed curve to a unit circle. With this general solution, two typical curvilinear holes are studied. One is an ellipse, the other is a polygon. Since the transformation functions used in our solutions are not always one to one, some of the solutions are not exact but only approximate. For example, the solutions to the problems of anisotropic plates containing an elliptic hole and isotropic plates containing a polygonal hole are exact, but the solutions to the problems of anisotropic plates containing a polygonal hole are only approximate. Because the solutions presented in this paper are new and no other analytical solution has been found in the literature, the correctness of the present results can only be checked analytically by their reduced forms such as those for isotropic media or those for the stress boundary value problems. To show the generality of our solutions and to see clearly the physical behavior of the indentation problems two numerical examples are given, and their related hoop stress and stress contour are also plotted.