A note on non-associated Drucker-Prager plastic flow in terms of fractional calculus

• Autorzy: Sumelka W.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we consider a special case of the general fractional plastic flow rule, namely the one which is equivalent to the classical non-associated Drucker-Prager (D-P) plasticity model. Fractional plastic flow is obtained from the classical flow rule by generalisation of the classical gradient of a plastic potential with a fractional gradient operator. It is important that, contrary to the classical models, non-associativity of fractional flow appears without introduction of the additional potential. The classical associative D-P plasticity is obtained as a special case. The discussion on objectivity of the fractional gradient is also presented also.

Słowa kluczowe

EN

fractional calculus; plastic flow; non-normality

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2014
• Tom: Vol. 52 nr 2
• Strony: 571--574
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Sumelka W.

• Poznan University of Technology, Institute of Structural Engineering, Poznań, Poland

Bibliografia

• 1. Agrawal O., 2007, Fractional variational calculus in terms of Riesz fractional derivatives, Journal of Physics A, 40, 24, 6287-6303
• 2. Diethelm K., Ford N., Freed A., Luchko Y., 2005, Algorithms for the fractional calculus: a selection of numerical methods, Computer Methods in Applied Mechanics and Engineering, 194, 743-773
• 3. Frederico G., Torres D., 2010, Fractional Noether’s theorem in the RieszCaputo sense, Applied Mathematics and Computation, 217, 1023-1033
• 4. Kilbas A., Srivastava H., Trujillo J., 2006, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam
• 5. Leszczyński J., 2011, An Introduction to Fractional Mechanics, Monographs No. 198, The Publishing Office of Czestochowa University of Technology
• 6. Lubliner J., 1990, Plasticity Theory, Macmillan Publishing, New York
• 7. Odibat Z., 2006, Approximations of fractional integrals and Caputo fractional derivatives, Applied Mathematics and Computation, 178, 527-533
• 8. Podlubny I., 1999, Fractional Differential Equations, Vol. 198 of Mathematics in Science and Engineering, Academin Press
• 9. Samko S., Kilbas A., Marichev O., 1993, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Amsterdam
• 10. Sumelka W., 2014, Fractional viscoplasticity, Mechanics Research Communications, 56, 31-36