International Journal of Materials Engineering and Technology

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PURE AXIAL SHEAR OF A PSEUDO-ELASTIC LONG CIRCULAR CYLINDRICAL TUBE

Authors

  • Rajesh Kumar

Keywords:

pseudo-elasticity, homogeneous, residual strain.

DOI:

https://doi.org/10.17654/0975044423002

Abstract

We apply the theory of pseudo-elasticity developed by Ogden and Roxburgh to a problem related to non-homogeneous deformation, namely pure axial shear of a pseudo-elastic long circular cylindrical tube. Loading, affected by application of a specified rotation of the outer surface of the tube relative to the inner one, is described by an isotropic elastic strain-energy function. Here we have shown that if the maximum applied shear stress is below a certain critical value, then there is no residual strain after the shearing stress is removed, while if it is greater than a second critical value, then there is residual strain throughout the tube. In this paper, residual strain is calculated explicitly in context of a particular material model. The stress softening effect of the shear stress on unloading is numerically compared with the loading.

Received: March 1, 2023
Accepted: March 28, 2023

References

R. W. Ogden and D. G. Roxburgh, A pseudo-elastic model for the Mullins effect in filled rubber, Proc. R. Soc. London A 455 (1999a), 2861-2877.

R. W. Ogden, Stress softening and residual strain in the azimuthal shear of a pseudo-elastic circular cylindrical tube, Internat. J. Non-Linear Mech. 36 (2001), 477-487.

K. A. Lazopoulos and R. W. Ogden, Nonlinear elasticity theory with discontinuous internal variables, Math. Mech. Solids 3 (1998), 29-51.

A. Hoger, On the determination of residual stress in an elastic body, J. Elasticity 16 (1986), 303-324.

B. E. Johnson and A. Hoger, The use of strain energy to quantify the effect of residual stress on mechanical behavior, Math. Mech. Solids 3 (1998), 447-470.

M. F. Beatty and S. Krishnaswamy, A theory of soft softening in incompressible isotropic elastic materials, J. Mech. Phys. Solids 48 (2000), 1931-1965.

S. Krishnaswamy and M. F. Beatty, The Mullins effect in compressible solids, Int. J. Engg. Sci. 38 (2000), 1397-1414.

R. S. Rivlin, Large elastic deformations of isotropic materials. VI. Further results in the theory of torsion, shear and flexure, Philos. Trans. Roy. Soc. London Ser. A 242 (1949), 173-195.

R. W. Ogden, Non-linear Elastic Deformations, Dover, New York, 1997.

X. Jiang and R. W. Ogden, Some new solutions for the axial shear of a circular cylindrical tube of compressible elastic material, Internat. J. Non-Linear Mech. 35 (2000), 361-369.

Kuldeep Kumar and Rajesh Kumar, Pure azimuthal shear in an elastic dielectric material, Mathematical Sciences Quarterly Journal 4(1) (2000), 107-124.

C. O. Horgan and G. Saccomandi, Pure azimuthal shear of isotropic incompressible nonlinearly elastic materials with limiting chain extensibility, Internat. J. Non-Linear Mech. 36 (2001a), 465-475.

J. G. Simmonds and P. W. Warne, Azimuthal shear of compressible or incompressible rubber like polar orthotropic tubes of infinite extent, Internat. J. Non-Linear Mech. 27 (1992), 447-464.

L. M. Kanner and C. O. Horgan, Inhomogeneous shearing of strain-stiffening rubber-like hollow circular cylinders, Int. J. Solids and Structures 45 (2008), 5464-5482.

Q. Jiang and J. K. Knowles, A class of compressible elastic materials capable of sustaining finite anti-plane shear, J. Elasticity 25 (1991), 193-201.

D. A. Polignone and C. O. Horgan, Axisymmetric finite anti-plane shear of compressible nonlinearly elastic circular tubes, Quart. Appl. Math. 50 (1992), 323-341.

Q. Jiang and M. F. Beatty, On compressible materials capable of sustaining axisymmetric shear deformation. I. Anti-plane shear of isotropic hyperelastic materials, J. Elasticity 39 (1995), 75-95.

C. O. Horgan and G. Saccomandi, Pure axial shear of isotropic incompressible non linearly elastic materials with limiting chain extensibility, J. Elasticity 57 (1999b), 307-319.

C. O. Horgan, G. Saccomandi and I. Sgura, A two-point boundary value problem for the axial shear of hardening isotropic incompressible nonlinearly elastic materials, SIAM J. Appl. Math. 62 (2002), 1712-1727.

A. S. Wineman, Some results for generalized neo-Hookean elastic materials, Internat. J. Non-Linear Mech. 40 (2005), 271-279.

G. A. Holzapfel, Nonlinear Solid Mechanics, Wiley, Chichester, 2000.

X. Jiang and R. W. Ogden, On azimuthal shear of a circular cylindrical tube of compressible elastic material, Quart. J. Mech. Appl. Math. 51 (1998), 143-158.

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Published

2023-06-02

Issue

Vol. 22 No. 1 (2023)

Section

Articles

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How to Cite

PURE AXIAL SHEAR OF A PSEUDO-ELASTIC LONG CIRCULAR CYLINDRICAL TUBE. (2023). International Journal of Materials Engineering and Technology, 22(1), 7-22. https://doi.org/10.17654/0975044423002