Torsion and circular shear coupling in nonlinear-elastic hollow cylinder

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

Combined torsional and circular shear of an incompressible nonlinear-elastic right-circular hollow cylinder is studied. A solution to the problem is obtained for an arbitrary elastic potential depending on the first invariant of the left Cauchy – Green deformation tensor solely (generalized neo-Hookean solid). For the Gent material, an analytical solution in closed form is obtained. A rotary damper design based on the obtained solution is proposed. Formulas for the dissipation of kinetic energy due to friction on the cylindrical surfaces of the pipe are given. For a strain softening material, a numerical solution is obtained, which is compared with experimental results.

Толық мәтін

Рұқсат жабық

Авторлар туралы

G. Sevastyanov

Institute of Machinery and Metallurgy FEB RAS

Хат алмасуға жауапты Автор.
Email: akela.86@mail.ru
Ресей, Komsomolsk-on-Amur

O. Komarov

Institute of Machinery and Metallurgy FEB RAS

Email: olegnikolaevitsch@rambler.ru
Ресей, Komsomolsk-on-Amur

A. Popov

Institute of Machinery and Metallurgy FEB RAS

Email: popov.av@live.com
Ресей, Komsomolsk-on-Amur

Әдебиет тізімі

  1. Mioduchowski A., Haddow J.B. Combined torsional and telescopic shear of a compressible hyperelastic tube // J Appl Mech-T Asme. 1979. V. 46. № 1. P. 223–226. https://doi.org/10.1115/1.3424509
  2. Fosdick R.L., MacSithigh G. Helical shear of an elastic, circular tube with a non-convex stored energy // Arch. Ration Mech. AN. 1983. V. 84. P. 31–53. https://doi.org/10.1007/BF00251548
  3. Tao L., Rajagopal K.R., Wineman A.S. Circular shearing and torsion of generalized neo-Hookean materials // IMA J Appl Math. 1992. V. 48. № 1. P. 23–37. https://doi.org/10.1093/imamat/48.1.23
  4. Zidi M. Azimuthal shearing and torsion of a compressible hyperelastic and prestressed tube // Int. J Nonlin Mech. 2000. V. 35. № 2. P. 201–209. https://doi.org/10.1016/S0020-7462(99)00008-6
  5. Zidi M. Combined torsion, circular and axial shearing of a compressible hyperelastic and prestressed tube // J Appl. Mech-T Asme. 2000. V. 67. № 1. P. 33–40. https://doi.org/10.1115/1.321149
  6. Zidi M. Finite torsion and shearing of a compressible and anisotropic tube // Int. J Nonlin Mech. 2000. V. 35. № 6. P. 1115–1126. https://doi.org/10.1016/S0020-7462(99)00083-9
  7. Horgan C.O., Saccomandi G. Helical shear for hardening generalized neo-Hookean elastic materials // Math. Mech. Solids. 2003. V. 5. № 5. P. 539–559. https://doi.org/10.1177/10812865030085007
  8. Saravanan U., Rajagopal K.R. Inflation, extension, torsion and shearing of an inhomogeneous compressible elastic right circular annular cylinder // Math. Mech. Solids. 2005. V. 10. № 6. P. 603–650. https://doi.org/10.1177/1081286505036422
  9. Zhukov B.A. Nonlinear interaction of finite longitudinal shear with finite torsion of a rubber-like bushing // Mech. Solids. 2015. V. 50. P. 337–344. https://doi.org/10.3103/S0025654415030097
  10. Sevastyanov G.M. Torsion with circular shear of a Mooney – Rivlin solid // Mech. Solids. 2020. V. 55. P. 273–276. https://doi.org/10.3103/S0025654420020156
  11. Rivlin R.S. Large elastic deformations of isotropic materials. VI. Further results in the theory of torsion, shear and flexure // Philos. TR R Soc. S-A. 1949. V. 242. № 845. P. 173–195. https://doi.org/10.1098/rsta.1949.0009
  12. Ericksen J.L. Deformations possible in every isotropic, incompressible, perfectly elastic body // Z Angew Math. Phys. 1954. V. 5. № 6. P. 466–489. https://doi.org/10.1007/BF01601214
  13. Knowles J.K. The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids // Int. J Fracture. 1977. V. 13. P. 611–639. https://doi.org/10.1007/BF00017296
  14. Gent A.N. A new constitutive relation for rubber // Rubber Chem. Technol. 1996. V. 69. № 1. P. 59–61. https://doi.org/10.5254/1.3538357
  15. Horgan C.O., Saccomandi G. Constitutive modelling of rubber-like and biological materials with limiting chain extensibility // Math. Mech. Solids. 2002. V. 7. № 4. P. 353–371. https://doi.org/10.1177/108128028477
  16. Horgan C.O., Saccomandi G. Pure azimuthal shear of isotropic, incompressible hyperelastic materials with limiting chain extensibility // Int. J Nonlin. Mech. 2001. V. 36. № 3. P. 465–475. https://doi.org/10.1016/S0020-7462(00)00048-2
  17. Anssari-Benam A., Horgan C.O. Extension and torsion of rubber-like hollow and solid circular cylinders for incompressible isotropic hyperelastic materials with limiting chain extensibility // Eur. J Mech. A-Solids. 2022. V. 92. P. 104443. https://doi.org/10.1016/j.euromechsol.2021.104443
  18. Begun A.S., Burenin A.A., Kovtanyuk L.V. Helical viscoplastic flow in a gap between rigid cylinders // Mech. Solids. 2017. V. 52. P. 640–652. https://doi.org/10.3103/S0025654417060048
  19. Lurie A.I. Nonlinear theory of elasticity. North-Holland, New York, 1990.
  20. Polyanin A.D., Zaitsev V.F., Moussiaux A. Handbook of first order partial differential equations. Taylor & Francis, London, 2002.
  21. Kut S., Ryzińska G. Modeling elastomer compression: Exploring ten constitutive equations // Materials. 2023. V. 16. № 1. P. 4121. https://doi.org/10.3390/ma161141
  22. Mullins L., Tobin N.R. Stress softening in rubber vulcanizates. Part I. Use of a strain amplification factor to describe the elastic behavior of filler-reinforced vulcanized rubber // J Appl. Polym. Sci. 1965. V. 9. P. 2993–3009. https://doi.org/10.1002/app.1965.070090906

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу
2. Fig. 1. Loading scheme of the deformable element of the damper.

Жүктеу (150KB)
Метадеректер
3. Fig. 2. Design of the rotary damper with friction: 1 – central sleeve, 2 – outer cage, 3 – elastic element, 4 – grippers.

Жүктеу (81KB)
Метадеректер
4. Fig. 3. Structural elements of a rotary damper with friction: 1 – central sleeve, 2 – outer cage, 3 – elastic element, 4 – grippers.

Жүктеу (232KB)
Метадеректер
5. Fig. 4. Simple tension, s11 in MPa. The markers are experimental data for polyurethane A83 (engineering stresses). The Ghent model with parameters E = 3m = 17 MPa, Jm = 16 (data for polyurethane A90 according to [21]). Model (3.2) with parameters E0 = 17 MPa, E1 = 1 MPa, b = 0.29, I1a – 3 = 0.107.

Жүктеу (148KB)
Метадеректер
6. Fig. 5. Torque M [N · m] when loading the rotary damper with the angle of rotation a (in degrees). Markers are experimental data. The solid line is a numerical and analytical calculation based on the elastic model (3.2). The dotted line is an analytical calculation for the Gent material with parameters E = 3m = 17 MPa, Jm = 16.

Жүктеу (98KB)
Метадеректер

© Russian Academy of Sciences, 2025