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Elastic-plastic analysis of a circular pipe turned inside out
- Authors: Sevastyanov GM.1
-
Affiliations:
- Institute of Machinery and Metallurgy, KhFRC FEBRAS
- Issue: No 3 (2024)
- Pages: 34–50
- Section: Articles
- URL: https://bakhtiniada.ru/1026-3519/article/view/273703
- DOI: https://doi.org/10.31857/S1026351924030039
- EDN: https://elibrary.ru/uiilgm
- ID: 273703
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Abstract
The paper presents an analytical solution to the problem of a circular pipe turned inside out in a rigid gasket. Formulas were obtained for the magnitude of the radial stress, which is responsible for the adhesion between the pipe and the gasket. The solution is obtained for an arbitrary incompressible hyperelastic material with a hyperelastic potential that depends only on the first invariant of the left Cauchy – Green deformation tensor (various generalizations of the neo-Hookean solid) or on the second invariant of the logarithmic Hencky strain tensor (various generalizations of the incompressible Hencky material). The solution takes into account the occurrence of plastic flow in areas adjacent to the lateral surfaces of the pipe. Both ideally plastic and isotropically hardening materials of a general type are considered. For the latter, a solution scheme is given; in the particular case of a linearly hardening material, a closed-form solution is obtained. For the perfect plasticity model, a closed-form solution was obtained for the neo-Hookean solid, for an incompressible Hencky material, and for the Gent material.
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About the authors
G M. Sevastyanov
Institute of Machinery and Metallurgy, KhFRC FEBRAS
Author for correspondence.
Email: akela.86@mail.ru
Russian Federation, Komsomolsk-on-Amur
References
- Rivlin R.S. Large elastic deformations of isotropic materials. VI. Further results in the theory of torsion, shear and flexure // Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1949. Vol. 242. P. 173–195. https://doi.org/10.1098/rsta.1949.0009
- Gent A.N., Rivlin R.S. Experiments on the mechanics of rubber. I: Eversion of a tube // Proceedings of the Physical Society. Section B. 1952. Vol. 65 (2). P. 118–121. https://doi.org/10.1088/0370-1301/65/2/305
- Lurie A.I. Nonlinear theory of elasticity. North Holland, New York, 1990.
- Ericksen J.L. Inversion of a perfectly elastic spherical shell // ZAMM. 1955. V. 35 (9–10). P. 382–385. https://doi.org/10.1002/zamm.19550350909
- Orr A. The eversion and bifurcation of elastic cylinders. PhD Thesis. University of Glasgow, 1995.
- Baaser H., Nedjar B., Martin R.J., Neff P. Eversion of tubes: Comparison of material models. In: Constitutive Models for Rubber X. CRC Press, 2017. http://dx.doi.org/10.1201/9781315223278-20
- Gao X.-L., Atluri S.N. An exact finite deformation elasto-plastic solution for the outside-in free eversion problem of a tube of elastic linear-hardening material // IMA Journal of Applied Mathematics. 1997. Vol. 58. P. 259–275. https://doi.org/10.1093/imamat/58.3.259
- Shufen R., Dixit U.S. A review of theoretical and experimental research on various autof-rettage processes // Journal of Pressure Vessel Technology. 2018. V. 140. № 5. 050802. https://doi.org/10.1115/1.4039206
- Levitas V.I. Large deformation of materials with complex rheological properties at normal and high pressure. Nova Science Publishers, New York. 1996
- Burenin A.A., Kovtanyuk L.V. Large irreversible deformations and elastic aftereffects. Dal’nauka, Vladivostok, 2013 (in Russian)
- Burenin A.A., Kovtanyuk L.V., Panchenko G.L. Modeling of large elastoviscoplastic deformations with thermophysical effects taken into account // Mechanics of Solids. 2010. V. 45. P. 583–594. https://doi.org/10.3103/S0025654410040084
- Feng B., Levitas V.I., Hemley R.J. Large elastoplasticity under static megabar pressures: Formulation and application to compression of samples in diamond anvil cells // International Journal of Plasticity. 2016. Vol. 84. P. 33–57. https://doi.org/10.1016/j.ijplas.2016.04.017
- Burenin A.A., Kovtanyuk L.V., Polonik M.V. The forming of one-dimensional residual strain field in the vicinity of a cylindrical continuum defect in an elastic-plastic medium // Journal of Applied Mathematics and Mechanics. 2003. V. 67 (2). P. 315–325 (in Russian)
- Aleksandrov S.E., Goldstein R.V. Calculation of the wall thickness of a pipeline under internal pressure with an arbitrary hardening law // Deformation and Fracture of Materials. 2011. P. 15–20 (in Russian)
- Aleksandrov S.E., Goldstein R.V. Stress-strain state in an elastoplastic cylindrical tube with free ends. I. General solution // Mechanics of Solids. 2013. V. 48. P. 537–545. https://doi.org/10.3103/S0025654413050099
- Sevastyanov G.M. Adiabatic heating effect in elastic-plastic contraction / expansion of spherical cavity in isotropic incompressible material // European Journal of Mechanics – A/Solids. 2021. V. 87. 104223. https://doi.org/10.1016/j.euromechsol.2021.104223
- Gent A.N. A new constitutive relation for rubber // Rubber Chemistry and Technology. 1996. V. 69 (1). P. 59–61. https://doi.org/10.5254/1.3538357
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