Constitutive modeling of human cornea through fractional calculus approach

Abstract

In this work, the fractional calculus approach is considered for modeling the viscoelastic behavior of human cornea. It is observed that the degree of both elasticity and viscosity is easy to describe in terms of the fractional order parameters in such an approach. Modeling of the human cornea when subjected to simple stress up to the level of 250 MPa by fractional order Maxwell model along with the Fractional Kelvin Voigt Viscoelastic Model is reported. For the Maxwell governing fractional equation, two fractional parameters α and β have been considered to model the stress–strain relationship of the human cornea. The analytical solution of the fractional equation has been obtained for different values of α and β using Laplace transform methods. The effect of the fractional parameter values on the stress-deformation nature has been studied. A comparison between experimental values and calculated values for different fractional order of the Maxwell model equation defines the parameters which depict the real-time stress–strain relationship of the human cornea. It has been observed that the fractional model converges to the classical Maxwell model as a special case for α = β = 1.