On geometrical interpretation of the fractional strain concept

• Autorzy: Sumelka W.

Identyfikatory

DOI

10.15632/jtam-pl.54.2.671

• Języki publikacji: EN

Abstrakty

EN

In this paper, for the first time, the geometrical interpretation of fractional strain tensor components is presented. In this sense, previous considerations by this author are shown in a new light. The fractional material and spatial line elements concept play a crucial role in the interpretation.

Słowa kluczowe

EN

fractional strain; fractional calculus; non-local models

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2016
• Tom: Vol. 54 nr 2
• Strony: 671--674
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Sumelka W.

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

Bibliografia

• 1. Atanackovic T.M., Stankovic B., 2009, Generalized wave equation in nonlocal elasticity, Acta Mechanica, 208, 1/2, 1-10
• 2. Carpinteri A., Cornetti P., Sapora A., 2011, A fractional calculus approach to nonlocal elasticity, European Physical Journal Special Topics, 193, 193-204
• 3. Drapaca C.S., Sivaloganathan S., 2012, A fractional model of continuum mechanics, Journal of Elasticity, 107, 107-123
• 4. Klimek M., 2001, Fractional sequential mechanics – models with symmetric fractional derivative, Czechoslovak Journal of Physics, 51, 12, 1348-1354
• 5. Lazopoulos K.A., 2006, Non-local continuum mechanics and fractional calculus, Mechanics Research Communications, 33, 753-757
• 6. Pecherski R.B., 1983, Relation of microscopic observations to constitutive modelling for advanced deformations and fracture initiation of viscoplastic materials, Archives of Mechanics, 35, 2, 257-277
• 7. Podlubny I., 2002, Geometric and physical interpretation of fractional integration and fractional differentiation, Fractional Calculus and Applied Analysis, 5, 4, 367-386
• 8. Sumelka W., 2014a, A note on non-associated Drucker-Prager plastic flow in terms of fractional calculus, Journal of Theoretical and Applied Mechanics, 52, 2, 571-574
• 9. Sumelka W., 2014b, Application of fractional continuum mechanics to rate independent plasticity, Acta Mechanica, 255, 11, 3247-3264
• 10. Sumelka W., 2014c, Thermoelasticity in the framework of the fractional continuum mechanics, Journal of Thermal Stresses, 37, 6, 678-706
• 11. Sumelka W., Zaera R., Fernandez-S ´ aez J. ´ , 2015, A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics, Meccanica, 50, 9, 2309-2323

Uwagi

EN

Short Research Communication

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.