IJE TRANSACTIONS C: Aspects Vol. 27, No. 3 (March 2014) 441-448   

downloaded Downloaded: 174   viewed Viewed: 2319

M. Kadkhodayan and F. Moayyedian
( Received: April 08, 2013 – Accepted: August 22, 2013 )

Abstract    In this study a non-associated viscoplastic flow rule (NAVFR) with combining von Mises and Tresca loci in place of yield and plastic potential functions and vice verse is presented. With the aid of fully implicit time stepping scheme and discussing the other studies on plastic potential flow rules and also experimental results it is shown that the proposed NAVFR can be adopted to forecast the experimental events more accurate than the conventional associated viscoplastic flow rules (AVFR).


Keywords    Rate-Dependant Non-associated Viscoplastic Flow Rule, Fully Implicit Time Stepping Scheme, Internally Pressurized Thick Walled Cylinder.


چکیده    در این پژوهش قانون جریان ویسکوپلاستیسیته ناوابسته با ترکیب سطوح تسلیم ون مایزز و ترسکا به جای توابع تسلیم و پتانسیل پلاستیک و برعکس ارائه شده است. به کمک روش مرحله ای زمانی کاملا غیرصریح و همچنین بحث در مورد مطالعات انجام شده روی توابع پتانسیل پلاستیک ارائه شده توسط سایر مولفین و همچنین نتایج آزمایشگاهی نشان داده خواهد شد که قانون جریان ویسکوپلاستیسیته ناوابسته ارائه شده از قانون جریان وابسته مرسوم نظیر خود نتایج آزمایشگاهی را دقیق تر پیش بینی می نماید.



1.     Stoughton, T. B. and Yoon, J.-W., "A pressure-sensitive yield criterion under a non-associated flow rule for sheet metal forming", International Journal of Plasticity,  Vol. 20, No. 4, (2004), 705-731.

2.     Nukala, P. K. V., "A return mapping algorithm for cyclic viscoplastic constitutive models", Computer Methods in Applied Mechanics and Engineering,  Vol. 195, No. 1, (2006), 148-178.

3.     Ohno, N. and Wang, J., "Kinematic hardening rules for", European Journal of Mechanics, A/Solids,  Vol. 13, No. 4, (1994), 519-531.

4.     Liang, L., Liu, Y. and Xu, B., "Design sensitivity analysis for parameters affecting geometry, elastic–viscoplastic material constant and boundary condition by consistent tangent operator-based boundary element method", International Journal of Solids and Structures,  Vol. 44, No. 7, (2007), 2571-2592.

5.     Cvitanić, V., Vlak, F. and Lozina, ˇ., "A finite element formulation based on non-associated plasticity for sheet metal forming", International Journal of Plasticity,  Vol. 24, No. 4, (2008), 646-687.

6.     Stoughton, T. B. and Yoon, J. W., "Anisotropic hardening and non-associated flow in proportional loading of sheet metals", International Journal of Plasticity,  Vol. 25, No. 9, (2009), 1777-1817.

7.     Gao, X., Zhang, T., Hayden, M. and Roe, C., "Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy", International Journal of Plasticity,  Vol. 25, No. 12, (2009), 2366-2382.

8.     Mohr, D., Dunand, M. and Kim, K.-H., "Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading", International Journal of Plasticity,  Vol. 26, No. 7, (2010), 939-956.

9.     Romano, G., Barretta, R. and Diaco, M., "Algorithmic tangent stiffness in elastoplasticity and elastoviscoplasticity: A geometric insight", Mechanics Research Communications,  Vol. 37, No. 3, (2010), 289-292.

10.   Taherizadeh, A., Green, D. E. and Yoon, J. W., "Evaluation of advanced anisotropic models with mixed hardening for general associated and non-associated flow metal plasticity", International Journal of Plasticity,  Vol. 27, No. 11, (2011), 1781-1802.

11.   Gao, X., Zhang, T., Zhou, J., Graham, S. M., Hayden, M., and Roe, C., "On stress-state dependent plasticity modeling: Significance of the hydrostatic stress, the third invariant of stress deviator and the non-associated flow rule", International Journal of Plasticity,  Vol. 27, No. 2, (2011), 217-231.

12.   Voyiadjis, G. Z., Shojaei, A. and Li, G., "A generalized coupled viscoplastic–viscodamage–viscohealing theory for glassy polymers", International Journal of Plasticity,  Vol. 28, No. 1, (2012), 21-45.

13.   Voyiadjis, G. Z. and Abu Al-Rub, R. K., "Thermodynamic based model for the evolution equation of the backstress in cyclic plasticity", International Journal of Plasticity,  Vol. 19, No. 12, (2003), 2121-2147.

14.   Berga, A., "Mathematical and numerical modeling of the non-associated plasticity of soils—part 1: The boundary value problem", International Journal of Non-Linear Mechanics,  Vol. 47, No. 1, (2012), 26-35.

15.   Moayyedian, F. and Kadkhodayan, M., "A general solution in rate-dependant plasticity", International Journal of Engineering,  Vol. 26, No., (2013), 391-400.

16.   Hinton, E. and Owen, D., "Finite elements in plasticity: Theory and practice", Pineridge, Swansea, Wales,  Vol., No., (1980).

17.   de Souza Neto, E. A., Peric, D. and Owen, D. R. J., "Computational methods for plasticity: Theory and applications", John Wiley & Sons,  (2011).

18.   Simof, J. and Hughes, T., "Computational inelasticity", (2008).

19.   Zienkiewicz, O. C. and Taylor, R. L., "The finite element method for solid and structural mechanics", Butterworth-Heinemann,  (2005).

20.   Crisfield, M., Remmers, J. and Verhoosel, C., "Nonlinear finite element analysis of solids and structures", John Wiley & Sons,  (2012).

21.   Hill, R., "The mathematical theory of plasticity", Oxford university press,  Vol. 11,  (1998).

22.   Chakrabarty, J., "Theory of plasticity", Butterworth-Heinemann,  (2006).

23.   Chen, W.-F. and Zhang, H., "Structural plasticity: Theory, problems and cae software", Springer-Verlag New York, Inc.,  (1990).

24.   Huang, S., "Continuum theory of plasticity", Wiley. com,  (1995).

25.           Marcal, P., "A note on the elastic-plastic thick cylinder with internal pressure in the open and closed-end condition", International Journal of Mechanical Sciences,  Vol. 7, No. 12, (1965), 841-845. 

International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir