Microstructure-based constitutive modeling of corneal nonlinear anisotropic rheology and modulus

Abstract

The cornea, as a soft transparent fiber-reinforced composite, exhibits nonlinear anisotropic rheology affecting its optical performance, crucial for clinical refractive correction. However, there is still lacking of constitutive models that accurately predict the cornea’s time-dependent anisotropic mechanical response. Inspired by the corneal fiber-matrix microstructure, a nonlinear anisotropic rheological model is developed under the thermodynamics framework. Firstly, through multiplicative deformation gradient decomposition, the fluid-like matrix phase is described by molecular chain reptation-based nonlinear viscoplasticity, while the solid-like fiber phase is modeled with quasilinear viscoelasticity. Then based on the rheological model, the anisotropic modulus of the cornea is numerically derived for the first time. The model is validated using experimental relaxation data of the cornea from in-plane tension and out-of-plane compression tests. The calculated relaxation modulus reveals distinct anisotropic decay patterns absent in current corneal constitutive models: the transverse direction recovers to 100.01 % of baseline, while the fiber direction retains substantial residual stiffness at 375.01 % of baseline. At last, the constitutive model is applied to study the three-dimensional corneal creep under cylindrical indentation, which is related to refractive correction using contact lens. Compared to existing models, our model predicts a 19.8 % larger flattened area and a viscous deformation that accelerates from 16.7 % to 100.9 % of elastic deformation. The nonlinear fluid-like viscous deformation of the matrix enables greater and faster morphology change of cornea, which is meaningful for improving refractive correction precision.