Models of Solid Mechanics in the Problems of Ophthalmology

This paper presents a very brief review of models constructed in cooperation with ophthalmologists, namely, for the change in the stress-strain state of the eye membrane after vision-correction operations and the change in the intraocular pressure after the injection of drugs into the vitreous body. The mathematical models describing the process of measuring the true intraocular pressure (IOP) by applanation methods are discussed. The models of eye biomechanics provide the possibility to obtain a series of new results in solid mechanics, i.e., to solve the problem of the stability of a spherical shell under a concentrated force and inner pressure and the stability of an axisymmetric equilibrium state of inhomogeneous annular orthotropic plates under a uniformly distributed normal load. The problems of the deformation of transversally isotropic spherical and cylindrical layers under inner and outer pressure are analyzed and the solutions obtained within the framework of the three-dimensional theory are compared with those found by the non-classical theories of shells. This comparison makes it possible to estimate the precision of some theories.