Comparison of Various Object Stress Rates under Simple Shear

Abstract:

Object Stress rates to predict the behavior of material have been researched based on numerically and theoretically for researchers who study continuum mechanics due to its complexity. This study focused on the various objective stress rates which assumed the finite deformation theory. Eight object stress rates (Oldroyd, Truesdell, Cotter–Rivlin, Jaumann, Green–Naghdi, Eulerian, grangian, and logarithmic object stress rates) were introduced using continuum mechanics and analyzed to derive the numerical solution to the simple shear problem. Numerical results from each object stress rate were analyzed and compared with the results of the other stress rates. Finally, the appropriate object stress rate for the simple shear problem was determined based on the numerical results from eight objects stress rates.

• Periodical: Advanced Materials Research (Volume 650)
• Pages: 407-413
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.650.407
• Online since: January 2013
• Authors: Dong Keon Kim, Jong Wan Hu
• Keywords: Continuum Mechanics, Finite Deformation, Object Stress Rate, Simple Shear

References

[1] C. Truesdell and W. Noll: Handbook of Physics. Springer, New York, (1965).

[2] W. Prager: J. Appl. Mech. 23, (1956).

[3] J. C Nagtegaal and J.E. De Jong: Int. J. Numerical Methods in Eng., 17, (1981), 15.

[4] E. H. Lee, R. L. Mallett, and T. B. Wertheimer: J. Appl. Mech., 50, (1983), 554.

[5] Y. F. Dafalias and E. R. Popov: Acta Mechanica., 21, (1975), 173.

[6] Bruhns, H. Xiao, and A. Myers: Int. J. Solid. Struct., 38, (2001), 8701.

[7] S. Seon and J. W. Hu: J. Korean Soc. Adv. Comp. Struc., 2(3), (2011), 1.

[8] R. Lin: Z. Angew. Math. Mech., 83, (2003), 163.

[9] R. Naghdabadi, M. Yeganeh, and A. R. Saidi: Int. J. Plasticity., 21, (2005), 1546.