This article is cited in 2 papers

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

V. V. Struzhanov

Institute of Machine Engineering UB RAS, Ekaterinburg, RUSSIA

Abstract: 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.

Keywords: pure shear diagram, falling branch, torsion diagram, Volterra equation of the first kind, trial-and-error method, regularization.

UDC: 539.3

Received: 25.03.2011