Double initial and caustic curves in diametrically compressed transparent discs - Application to the contact length

Abstract

General formulae for double initial and caustic curves (reflected and transmitted) are obtained in the case of smooth contact of two cylindrical elastic bodies of arbitrary radii. Namely, based on the method of reflected and transmitted caustics, the conditions for the development of double initial and contact caustic curves are established as functions of six independent para­meters, while easy-to-use closed-form expressions are given for obtaining the contact length. An experimental protocol is then implemented in the case a thin cylindrical transparent disc is compressed between the jaws of the Inter­na­tional Society for Rock Mechanics suggested device for the execution of the Brazilian-disc test. The experimental method of caustics can provide the con­tact length quite accurately, even in the case of double curves which seem that are not always a consequence of a wide contact region.