The North Carolina Journal of Mathematics and Statistics

The Hereditary Approach to Time Dependent Modeling with Fractional Exponential Function

Irina Viktorova, Sophia Alekseeva, Lauren K. Holden, Michael A. Bates, Hannah Maeser

Abstract


For polymer based composites, the creep and relaxation parameters are examined using the hereditary approach to time dependent mechanical behavior. Specifically, methods of optimization are utilized to determine the optimal parameter estimates for the fractional exponential functions. The relative advantages of the Rabatnov kernel over the Abel kernel have been examined. Finally, the results of this parameter estimation using the Rabatnov kernel (i.e. fractional exponential) are compared to results obtained from experimental data.


Keywords


Hereditary mechanics; stress,strain; viscoelasticity; Volteraa integral equation; creep; relaxation

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