NDLI: Using the logarithmic strain measure for solving torsion problems

Content Provider	Springer Nature Link
Author	Pav, A. D. Shumaev, V. V.
Copyright Year	2012
Abstract	The problems of free and constrained torsion of a rod of solid circular cross-section are solved numerically using a tensor linear constitutive relation written in terms of the energy compatible Cauchy stress and Hencky logarithmic strain tensors. The only function used to determine the properties of the isotropic incompressible material of the rod is a power-law function that approximates the shear diagram and corresponds to an elastoplastic material with power-law hardening. The solution obtained shows that, despite the tensorial linearity of the state law, the use of the logarithmic strain measure allows one to describe qualitatively the effect of significant elongation of the rod in free torsion (the Poynting effect) as well as the arising normal longitudinal, radial, and circumferential stresses, whose values are commensurable, at large deformations, with the maximum tangential stresses in the cross-section. Computational dependences of the torsional moment on the angle of twist in free and constrained torsion are obtained. These dependences are found to be significantly different from each other; the limitmoment and the correspondingmaximum angle of twist for free torsion are found to be considerably lower than those for constrained torsion. It follows that the shear strength, which is traditionally calculated from the maximum torsional moment, becomes indeterminate. For constrained torsion, the dependence of the longitudinal compressive force on the angle of twist is obtained.Summing up and generalizing the computational results, one can conclude that using the logarithmic strain measure as well as the material shear diagram and the corresponding tensor linear constitutive relation allows one to describe, at large deformations, effects that usually require applying different tensor nonlinear constitutive relations of nonlinear elasticity, including elastic constants of the second and third orders.
Starting Page	71
Ending Page	78
Page Count	8
File Format	PDF
ISSN	00256544
Journal	Mechanics of Solids
Volume Number	47
Issue Number	1
e-ISSN	19347936
Language	English
Publisher	Allerton Press, Inc.
Publisher Date	2012-04-05
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	torsion shear diagram strain measure torsional elongation constitutive relations nonlinear effects Mechanics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mechanics of Materials

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