Progress in Fractional Differentiation & Applications

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Plastic media have the particular property to exhibit non zero strain at a vanishing applied stress and are modeled by a variety of possible constitutive memory equations. In this note using laboratory data we compare the results based on the constitutive equations of Polycrystalline Halite (PH) which include the Caputo and Caputo-Fabrizio fractional derivatives to model the plastic properties of this medium. Based on this finding we suggest that a variety of different mathematical memory formalisms is needed to model all phenomena and media with memory. We suggest a method to obtain these mathematical formalisms with laboratory experiments which leads to determine the plastic properties of PH showing that its strain memory is much longer than that of stress.

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