A generalised fractional derivative model to represent elastoplastic behaviour of metals

In this paper, a one-dimensional elastoplastic model based on fractional calculus is presented. This model is conceived for metal deformation. First, a brief introduction about fractional calculus is exposed. Then, a fractional calculus based general model is proposed, build-up as a series of fractional derivatives. The particular cases of one, two and three terms are discussed. Finally, these three particular cases of the general model are fitted to experimental data and compared with the classical Hollomon and Ramberg–Osgood models. As a result, a model capable of representing the elastoplastic behaviour more precisely than the Hollomon and Ramberg–Osgood models is obtained, despite numerical efforts are enlarged.

► A one-dimensional general elastoplastic model based on fractional calculus is developed.
► Particular cases of one, two and three terms are discussed.
► Three particular cases of the general model are fitted to 6082O aluminium alloy.
► Experimental data and compared with the classical Hollomon and Ramberg–Osgood models.
► The result shows the developed model reach to 45% the square error among model and data provided by truly used Hollomond model.