The determination of the deformation diagram of a material with a falling branch using the torsion diagram of a cylindrical sample

We present a method for constructing the deformation diagram of a material with a falling branch purely shearing along the torsion diagram of a solid cylindrical sample. The problem reduces to a Volterra integral equation of the first kind, and so it belongs to the class of ill-posed problems arising in attempts to determine physical quantities using measurement results. We show that for an arbitrary torsion diagram the solution to the Volterra equation leads to a sawtooth-shaped broken line in the diagram of the material. We regularize the solution using a trial-and-error method, which yields satisfactory results.