Finite and transversely isotropic elastic cylinders under compression with end constraint induced by friction

Abstract

a b s t r a c tThis paper derives an exact solution for the non-uniform stress and displacement fields within a finite, transversely isotropic, and linear elastic cylinder under compression with a kind of radial constraint induced by friction between the end surfaces of the cylinder and the loading platens. The main feature of the present work is the introduction of a general solution form for Lekhnitskii's stress function such that the governing equation and all end and curved boundary conditions of the cylinder are satisfied exactly. Two different solutions were obtained corresponding to the real or complex characteristic roots of the governing equation, depending on the combination of the elastic material constants. The solution by Watanabe [Watanabe, S., 1996. Elastic analysis of axi-symmetric finite cylinder constrained radial displacement on the loading end. Structural Engineering/Earthquake Engineering JSCE 13, 175s-185s] for isotropic cylinders under compression test can be recovered as a special case. Our numerical results show that both the non-uniform stress distribution and the difference between the apparent and the true Young's moduli of the cylinder are very sensitive to the anisotropy of Young's moduli, Poisson's ratios and shear moduli. A more distinct bulging shape of the cylinder is expected when anisotropy in shear modulus is strong, the cylinder is relatively short, and the end constraint is large. The bulging shape, however, does not depend strongly on anisotropy of either Poisson's ratio or Young's modulus.

Magnetic properties of URu2Si2under uniaxial stress by neutron scattering

“…Before going further, Table I can be only used in the case of hydrostatic pressure (column 2) or uniaxial stress along a v in the free lateral expansion conditions (column 3), as emphasized in Ref. [27] (study made in the case of isotropic crystal). The free lateral expansion condition is fulfilled only if the ratio κ 2.…”

Compression behavior of natural graphite sheet

“…Measurements of the compression modulus can be biased by the barreling effect [22]. The highly anisotropic structure of NGS was considered to be prone to this behavior as the low shear stiffness in the in-plane direction (perpendicular to the compression direction) can allow a high lateral displacement during the compression tests.…”

Characterisation and modelling of a transversely isotropic melt-extruded low-density polyethylene closed cell foam under uniaxial compression

“…To the best of the authors' knowledge, such a model has yet to be published, though steps in this direction have been taken: For the case of small strain, the linear elastic transversely isotropic compressible model 4 can provide accurate results, as demonstrated by Wei and Chau. 5 For large strain conditions which must necessarily include a nonlinear material response, alternative approaches have been devised: Isotropic elastic compressible foams can be modelled using Ogden's hyperelastic model for isotropic compressible rubber, [6][7][8] and transversely isotropic incompressible hyperelastic models have been proposed for biological materials; 9-11 the high water content of which means the incompressibility condition is appropriate. 12 To create a model for transversely isotropic compressible materials under large strain, a linear elastic followed by plastic approach has been demonstrated by Tagarielli et al 13 (for balsa wood); though beyond small strains, the deformation was modelled as irreversible and while appropriate for balsa wood is not suitable for describing the recovery of predominantly viscoelastic materials such as LDPE foam.…”