| Contact and reattachment of two types of layered structures are examined. In the first part of the dissertation, a constrained patched structure subjected to uniform temperature change with edge damage is studied. Geometric nonlinearities and shear deformation are included in the mathematical model, and the effects of shear deformation are examined. The formulation is based on the calculus of variations with propagating boundaries, and yields the governing equations, boundary conditions, matching conditions and transversality condition. Results are compared with previously published results with transverse shear deformation neglected. The effects of shear deformation on the recently discovered instabilities referred to as 'sling-shot 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, the shear moduli) on the afforementioned thermo-mechanical instabilities are elucidated.;In the second part, a representative mathematical model of the eye encircled by a scleral buckle in the vicinity of the equator is developed. The effects of the buckle on the mechanical behavior of the eye, and then on closing posterior retinal detachment are both studied. Both problems are formulated using variational methods. Closed form analytical solutions of the coupled differential equations are obtained. Results of numerical simulations are presented and critical phenomena are unveiled. The effects of material and geometric parameters (radius, width, thickness and Young's modulus) of the scleral buckle, as well as of the ocular pressure, on the deformation of the eye are studied. Volume changes for each case are evaluated as well. It is seen that the radius of the buckle is the dominant parameter with regard to mechanical behavior of the eye. In the final major chapter, the effect of the scleral buckle on closure and reattachment of posterior retinal detachment is studied. It is seen that as the radius of the scleral buckle reduces, the distance between the detached segment of retina and the retinal pigment epithelium decreases, thus encouraging reattachment between the two surfaces. This, evidently, has ramifications with regard to treatment of posterior retinal detachment. |
