Mathematical model of the eye cornea with account for an exponential nonlinearity of its elastic properties under the assumption of geometric smallness of strains

A method is proposed for taking into account the nonlinearity of the elastic behavior of the cornea of the eye, which makes it possible to effectively evaluate the influence of this factor on the results of experiments and clinical measurements. The cornea is modeled by a homogeneous isotropic momentless elastic surface. Its elastic properties are determined by a nonquadratic dependence of the strain energy on the components of the strain tensor. Strains are assumed tobe small. For the simplest exponential form of this function, a single additional parameter appears in comparison with the linear case. The model is tested on the problem of inflating the cornea with pressure, which corresponds to experiments with an isolated cornea. Predictions of the linear model do not agree with experimental data, whereas the proposed exponential model describes them well. The model allows us to consider the nonlinear behavior of the cornea, taking into account its real mechanical properties and the minimum number of parameters. The use of the nonlinear model is advisable in those cases where in the process under consideration the intraocular pressure and the stressed state of the cornea vary significantly, as a result of which the linearization of the constitutive relation can lead to noticeable errors.