Progress in Fractional Differentiation & Applications
Abstract
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)
http://dx.doi.org/10.18576/pfda/040102
Recommended Citation
Caputo, Michele and Fabrizio, Mauro
(2018)
"Deformations in Elasto-Plastic Media with Memory: the Inverse Problem,"
Progress in Fractional Differentiation & Applications: Vol. 4:
Iss.
1, Article 2.
DOI: http://dx.doi.org/10.18576/pfda/040102
Available at:
https://digitalcommons.aaru.edu.jo/pfda/vol4/iss1/2