Prediction of creep and stress-relaxation for cornea using fractional Maxwell model

Farrahi, Mohammadnabi; Domiri Ganji, Davood; Jalili, Payam

doi:10.24200/sci.2026.67132.10442

Prediction of creep and stress-relaxation for cornea using fractional Maxwell model

Articles in Press

Document Type : Research Article

Authors

Mohammadnabi Farrahi ¹

Davood Domiri Ganji ¹

Payam Jalili ²^{, 3}

¹ Department of Mechanical Engineering, Babol Noshirvani University of Technology, P.O. Box 484, Babol, Iran.

² Department of Mechanical Engineering, NT.C., Islamic Azad University, Tehran, Iran.

³ Research Center for Modern Energy Technologies, North Tehran Branch, Islamic Azad University, Tehran, Iran.

10.24200/sci.2026.67132.10442

Abstract

In this work, fractional calculus is used to model the viscoelastic behavior of the human cornea. The corneal response under simple stress conditions up to 5 MPa is described using a fractional-order Maxwell model. Two fractional parameters, α and β, are introduced to represent the stress–strain relationship, creep, and stress relaxation. The governing equation is transformed to the Laplace domain, and the time-domain response is recovered numerically by the Gaver–Stehfest method. The effects of α and β on the stress–strain, creep, and stress-relaxation responses are examined. At α = 0.8 and β = 0.6, the model results closely agree with the experimental data. These calibrated parameters are then used to predict the creep and stress-relaxation behavior of the human cornea. The agreement between the predicted deformation and the experimental response supports the accuracy of the proposed model.

Keywords

Viscoelasticity

Corneal biomechanics

Creep test

Stress-relaxation test

Subjects