This paper describes the development of a fractional calculus approach to model the hysteretic behavior shown by the variation of resistance with strain in nano-composites (like MetalRubberOˆ). Experiments have been carried out on MetalRubberOˆ to study the strain-resistance variation of this material under strains varying in a triangular manner. Combined fractional derivative and integer order integral model and fractional integral model (with two sub-models) have been developed to model this behavior. Effieiency of these models has been discussed by comparison of their results with the experimental result.
A Modified Fractional Derivative Approach to Model Hysteresis
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Rabius Sunny, MM, Kapania, RK, Moffitt, RD, Mishra, A, & Goulbourne, N. "A Modified Fractional Derivative Approach to Model Hysteresis." Proceedings of the ASME 2007 International Mechanical Engineering Congress and Exposition. Volume 10: Mechanics of Solids and Structures, Parts A and B. Seattle, Washington, USA. November 11–15, 2007. pp. 389-396. ASME. https://doi.org/10.1115/IMECE2007-43747
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