On the general solution for torsion of polar elastic media

Stojanović, Rastko; Blagojević, Djordje

doi:10.1016/0020-7683(69)90062-6

Cited by 1 publication

(2 citation statements)

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“…We note that (100)1 was first derived by Stojanovic and Blagojevic [5], but they made no connection of the result with any of the theories considered here. It may be of interest to mention that these properties are typical of the behavior of a helically oriented, fiber structured material.…”

Section: The Linearized Theorymentioning

confidence: 95%

“…In §7, however, the problem is solved completely for the incompressible form of the linearized equations, which are found to agree with equations derived by Aero and Kuvshinskii [4], and certain additional peculiar aspects of the solution for this case are illustrated. We shall show clearly that the analysis of the pure torsion of an incompressible, hemitropic Cosserat cylinder presented by Stojanovic and Blagojevic [5], which is based on the ad hoc assumption that the strain energy function depends only on a certain set of three scalar invariants, is incomplete. Their formula for the normal force needed to affect a pure infinitesimal torsion is derived as a special case from more general results in §7 wherein the Kelvin-Poynting type coupling between the normal force, the torsional moment and the elastic moduli of the linearized theory is exhibited as an effect of first order in the amount of twist per unit length of the cylinder.…”

Section: Introductionmentioning

confidence: 99%

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Extension, torsion and expansion of an incompressible, hemitropic Cosserat circular cylinder

Cheverton

Beatty

1981

J Elasticity

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Constitutive equations for the stress and couple stress on an incompressible, hemitropic, constrained Cosserat material are derived, and the theory is applied to study the problem of finite extension, torsion and expansion of a circular cylinder. As in the theory of isotropic simple elastic materials, it is found that the deformation is controllable by application of only a normal force and a tosional moment at the cylinder ends. It is shown that in general the well known universal relation between the torsional stiffness and the axial force for incompressible, isotropic simple materials in the limit as the twist goes to zero does not exist for incompressible, hemitropic Cosserat materials. However, for a special and unusual class of hemitropic materials, the same universal formula is found to hold for a certain reduced torsional stiffness. The main problem is solved completely for incompressible, hemitropic, linearly elastic, Cosserat materials; and certain additional special features of the Kelvin-Poynting. type, which here appear to the first order in the amount of twist of the cylinder, are derived and discussed in relation to experimentally observed composite material behavior.

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Section: The Linearized Theorymentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%