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On The Objective Corotational Rates of Eulerian Strain Measures

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Abstract

In the present paper, some new basis-free expressions for an arbitrary objective corotational rate of the general Eulerian strain measures are provided which are in compact form. Moreover, a complete discussion on the requirements for the continuity of the objective corotational rates are presented.

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References

  1. Dubey, R.N.: Co-rotational rates on principal axis. S. M. Arch. 10, 245–255 (1985)

    MATH  MathSciNet  Google Scholar 

  2. Dui, G.: Some basis-free formulae for the time rate and conjugate stress of logarithmic strain tensor. J. Elast. 83, 113–151 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dui, G., Ren, Q., Shen, Z.: Time rates of Hill’s strain tensors. J. Elast. 54, 129–140 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dui, G., Chen, Y.C.: Basis-free representation for the stress rate of isotropic materials. Int. J. Solids Struct. 41, 4845–4860 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gurtin, M.E., Spear, K.: On the relationship between the logarithmic strain rate and the stretching tensor. Int. J. Solids Struct. 19, 437–444 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  6. Guo, Z.H.: Rates of stretch tensors. J. Elast. 14, 263–267 (1984)

    MATH  Google Scholar 

  7. Guo, Z.H., Dubey, R.N.: Basic aspects of Hill’s method in solid mechanics. S. M. Arch. 9, 353–380 (1984)

    MATH  Google Scholar 

  8. Guo, Z.H., Lehmann, Th., Liang, H.Y.: Further remarks on rates of stretch tensors. Trans. CSME 15, 161–172 (1991)

    Google Scholar 

  9. Guo, Z.H., Lehmann, Th., Haoyun, L., Man, C.S.: Twirl tensors and tensor equation AXXA=C. J. Elast. 27, 227–245 (1992)

    MATH  Google Scholar 

  10. Hill, R.: On constitutive inequalities for simple materials. I. J. Mech. Phys. Solids 16, 229–242 (1968)

    Article  MATH  ADS  Google Scholar 

  11. Hill, R.: Aspects of invarience in solid mechanics. Adv. Appl. Mech. 18, 1–75 (1978)

    MATH  Google Scholar 

  12. Hoger, A.: The material time derivative of logarithmic strain. I. J. Solids Struct. 22, 1019–1032 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hoger, A., Carlson, D.E.: On the derivative of the square root of a tensor and Guo’s rate theorem. J. Elast. 14, 329–336 (1984)

    MATH  MathSciNet  Google Scholar 

  14. Kato, T.: A short introduction to perturbation theory for linear operators. Springer, New York (1982)

    MATH  Google Scholar 

  15. Lehmann, T., Guo, Z.H., Liang, H.Y.: The conjugacy between Cauchy stress and logarithm of the left stretch tensor. Euro. J. Mech. A/Solids 10, 395–404 (1991)

    MATH  MathSciNet  Google Scholar 

  16. Man, C.S., Guo, Z.H.: A basis-free formula for time rate of Hill’s strain tensors. I. J. Solids Struct. 30, 2819–2842 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Mehrabadi, M.M., Nemat-Nasser, S.: Some basic kinematical relations for finite deformations of continua. Mech. Mater. 6, 127–138 (1987)

    Article  Google Scholar 

  18. Meyers, A., Schiebe, P., Bruhns, O.T.: Some comments on objective rates. Acta Mech. 139, 91–103 (2000)

    Article  MATH  Google Scholar 

  19. Naghdabadi, R., Dubey, R.N., Heppler, G.R.: On material time derivative of logarithmic strain. Proceedings of CANCAM 95, 844–845 (1995)

    Google Scholar 

  20. Ogden, R.W.: Non-linear elastic deformations. Ellis Horwood, Chichester (1984)

    Google Scholar 

  21. Reinhardt, W.D., Dubey, R.N.: Eulerian strain rate as a rate of logarithmic strain. Mech. Res. Commun. 22, 165–170 (1995)

    Article  MATH  Google Scholar 

  22. Reinhardt, W.D., Dubey, R.N.: Coordinate-independent representation of spins in continuum mechanics. J. Elast. 42, 133–144 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  23. Scheidler, M.: Time rates of generalized strain tensors, part I: Component formulas. Mech. Mater. 11, 199–210 (1991)

    Article  Google Scholar 

  24. Scheidler, M.: Time rates of generalized strain tensors. Part II: Approximate basis-free formulas. Mech. Mater. 11, 211–219 (1991)

    Article  Google Scholar 

  25. Seth, B.R.: Generalized strain measures with application to physical problems. Second-order effects in elasticity, plasticity and fluid dynamics, pp. 162–172. Pergamon, Oxford (1964)

    Google Scholar 

  26. Wang, W.B., Duan, Z.P.: On the invariant representation of spin tensors with applications. Int. J. Solids Struct. 27, 329–341 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  27. Xiao, H.: Unified explicit basis-free expressions for time rate and conjugate stress of an arbitrary Hill’s strain. Int. J. Solids Struct. 32, 3327–3340 (1995)

    Article  MATH  Google Scholar 

  28. Xiao, H., Bruhns, O.T., Meyers, A.: Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mech. 124, 89–105 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  29. Xiao, H., Bruhns, O.T., Meyers, A.: Strain rates and material spins. J. Elast. 52, 1–41 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  30. Xiao, H., Bruhns, O.T., Meyers, A.: Elastoplasticity beyond small deformations. Acta Mech. 182, 31–111 (2006)

    Article  MATH  Google Scholar 

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Asghari, M., Naghdabadi, R. On The Objective Corotational Rates of Eulerian Strain Measures. J Elasticity 90, 175–207 (2008). https://doi.org/10.1007/s10659-007-9138-9

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