Geodesic
The determination of the deformation diagram of a material with a falling branch using the torsion diagram of a cylindrical sample
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 138-144 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, Volterra equation of the first kind, trial-and-error method, regularization.
Mots-clés : torsion diagram 
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V. V. Struzhanov. The determination of the deformation diagram of a material with a falling branch using the torsion diagram of a cylindrical sample. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 138-144. http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a13/

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