A mechanics based mathematical model for the behavior of an eye encircled by a scleral buckle, a procedure used by surgeons to correct retinal detachment, is developed. Closed form analytical solutions are obtained, and results of numerical simulations based on those solutions are presented. The effects of material and geometric parameters of the scleral buckle, as well as of the ocular pressure, on the deformation and volume change of the eye are studied. Critical behavior is identified, and correlations are drawn with regard to the properties of the buckle, the associated deformation of the eye, and the ocular pressure. The results indicate that a judicious choice of the buckle parameters is advisable for planning surgery. In particular, the initial (undeformed) radius of the buckle is seen to have the dominant influence with regard to deformation of the eye, while the thickness (height) and width, and hence the shape, of the buckle are seen to have minimal influence and may be chosen for other reasons, such as to maximize the comfort of the patient.
A mechanics-based mathematical model of an eye possessing a posterior retinal detachment is presented for the case where an encircling scleral buckle (a cerclage) is sutured around the equator of the eye. The mechanical behaviour of the retina and the globe, both before and after applying the cerclage, is studied. An energy formulation yields the self-consistent equations of equilibrium and boundary conditions of the ocular system, and analytical solutions are established for the scleral buckle, for the globe and for the detached segment of the retina. Results of numerical simulations based on the solutions unveil characteristic behaviour of the ocular system, and demonstrate the influence of the scleral buckle, as well as of the pressure difference between the vitreous cavity and the subretinal space, on the deformation of the eye and on closing the region of retinal detachment. The results indicate that a scleral buckle encircling the equator, normally used for closing retinal tears and associated retinal detachments in the immediate vicinity of the buckle, can have a marked influence on bringing the detached segment of neurosensory retina back into contact with the retinal pigment epithelium, even for detachments at the posterior of the eye.
The problem of a patched structure under uniform thermal loading is studied, where geometric nonlinearity and shear deformation are considered. The formulation is based on the calculus of variations with propagating boundaries, and yields the governing equations, boundary conditions, matching conditions and transversality condition. Closed form analytical solutions are obtained in terms of an (unknown) membrane force parameter, the angle of rotation due to bending and the transverse displacement. Results of numerical simulations based on those solutions are presented and critical phenomena of the composite structure are unveiled. Results of the current work are compared with previously published results where transverse shear deformation was neglected. It is seen that shear deformation plays an important role in certain situations. In particular, the effects of shear deformation on the phenomena of "slingshot buckling" and "buckle trapping" are demonstrated and discussed. The influence of the relative size of the detached region and of the difference between the material properties of the base plate and of the patch (in particular, shear moduli) on the thermomechanical instabilities are elucidated.
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