Influence of nonlinearity of the elastic properties of the cornea on its deformation when loading the eye with a Schiotz tonometer

The effective model previously developed by the authors for a nonlinear elastic cornea of the eye is applied to the study of the cornea stress-strain state when loaded with a concave stamp and the Schiøtz tonometer, the structure composed of independently moving concave stamp and rod (plunger). It is shown that in both cases the condition of geometrical smallness of strains is satisfied. Allowance for nonlinearity leads to a significant increase in the minimum values of tensile stresses: the possibility of the appearance of compressive stresses becomes less likely. The effect of nonlinearity on the relationship between the directly measured characteristic of corneal deformation, the depth of the impression produced on the cornea by the plunger, and the pressure under the tonometer (tonometric pressure) is studied. It turned out that at sufficiently high tonometric pressures, nonlinearity practically does not affect this dependence; however, neglecting the nonlinearity leads to a noticeable underestimation of the tonometric pressure from the impression depth for low pressures (below 20-25 mm Hg). This is the case regardless of the stiffness of the cornea. Allowance for nonlinearity, as well as an increase in stiffness, slightly shifts the pressure-depth curve towards the dependence that is commonly used in the processing of measurement results. This convergence is more noticeable for the lighter plunger weight.