Affiliation:
1. Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 8 Kliment Ohridsky, blvd., 1756 Sofia, Bulgaria
Abstract
The energies of the classical Maxwell mechanical model of viscoelastic behavior have been studied as a template with a variety of relaxation kernels in light of a causal formulation of the force–displacement relationship. The starting point uses the Lorenzo–Hartley model with the time-fractional Riemann–Liouville derivative. This approach has been reformulated based on critical analysis, allowing for the application of a variety of relaxation (memory) functions mainly based on the Mittag-Leffler family, in order to meet the need for broader modeling of viscoelastic behavior. The examples provided include cases of the types of forces used by Lorenzo and Hartley as well as a new family of force approximations such as a general power-law ramp, polynomials, and the Prony series.
Subject
Fluid Flow and Transfer Processes,Computer Science Applications,Process Chemistry and Technology,General Engineering,Instrumentation,General Materials Science
Reference44 articles.
1. Findley, W.N., Lai, J.S., and Onaran, K. (1976). Creep and Relaxation of Nonlinear Viscoelastic Materials, North Nolland Publishing.
2. Application of fractional calculus to the theory of viscoelasticity;Koeller;J. Appl. Mech.,1984
3. Relaxation and retardation functions of the Maxwell model with fractional derivatives;Friedrich;Rheol. Acta,1991
4. Fractal rheological models and fractional differential equations for viscoelastic behavior;Heymans;Rheol. Acta,1994
5. On the thermodynamics of fractional damping elements;Lion;Continum Mech. Thermodyn.,1997