A combined analytic and experimental study of the displacement field in a circular ring

An analytic solution for the displacement field developed in an elastic homogeneous circular ring is described assuming that the ring is subjected to diametral pressure which is not constant but rather it varies according to a parabolic law along the contact arcs. The solution is achieved by using Kolosov's-Muskhelishvili's complex potentials method. The length of the contact arcs, which is of crucial importance for the application of the analytic solution, is experimentally determined with the aid of a recently introduced modified version of the reflected caustics technique. The overall validity of the solution is experimentally assessed by comparing its predictions against the respective results obtained experimentally using the Digital Image Correlation (DIC) technique. For the implementation of both experimental protocols the device suggested by the International Society for Rock Mechanics (ISRM) for the standardized realization of the Brazilian-disc test was used. The agreement between theory and experiment is found satisfactory as long as the linearity assumption is not violated. The same is true for the comparison between the experimental data obtained from the Reflected Caustics method with those obtained by the DIC technique concerning the length of the contact arc. Based on the analytic solution some critical aspects of the ring test (proposed as a potential substitute of the Brazilian-disc test almost half a century ago by Hobbs) are explored by studying the variation of the displacements along some strategic paths of the ring.