Progress in Fractional Differentiation & Applications

Author Country (or Countries)



We consider anelastic media governed by constitutive equations with memory behavior, which depend on the physical properties of the medium itself. In this note we use a model of elasto-plastic media with two unspecified memory formalisms, which are determined by performing a single virtual experiment on a sample of the medium. As an application, using a mathematical memory formally mimicking the Caputo-Fabrizio fractional derivative, we show that, when the applied stress is asymptotically vanishing, then a shorter memory in the constitutive equation and/or a slower decay of the applied stress, generate larger asymptotic plastic residual strain. In the last part of the paper, we present a non-linear stress-strain constitutive equation, which is suitable for describing hysteresis loops with discontinuity in the first derivative of the cycle.

Digital Object Identifier (DOI)