Dual series solution for the standardized ISRM Brazilian disc test modelled as an advancing contact problem

A new analytical solution is found for the stress and displacement fields in a standardized ISRM Brazilian disc test with curved jaws, based on the solution of a set of dual trigonometric series. The disc is assumed to be linear elastic and isotropic and in frictionless advancing contact with the two jaws assumed as rigid, under plane stress loading conditions. Use is made of the Michell solution for an elastic disc in polar coordinates, whose coefficients are found by imposing the mixed boundary conditions along the disc rim, both along the free surface and the contact region. The problem is first reduced to a set of dual trigonometric series and then to a linear system of infinite equations, which is solved by truncation. The non-linear relations providing the contact angular extent and pressure distribution in terms of the applied load or jaw displacement, consequent to the progressive advance of the contact, are derived by using an inverse method. The obtained results are validated by comparison with previous theoretical and experimental results available in the literature. The study indicates that the method of dual series is simpler and more straightforward as compared to the analytical methods proposed in the literature for treating the Brazil disc test as an advancing contact problem.