Elasticity Theory on Curved Surfaces*

The challenge of determining the elastic structure constrained within a curved topology arises in various scientific disciplines and has been approached through different methods. In a recent study, using effective defect interaction models, we developed a unified elasticity theory that successfully addressed the limitations of the linear theory. In this study, we expand our approach to encompass general geometries with rotational symmetry. Using numerical techniques, we have examined the surface morphology and elastic deformation in the presence and absence of a central disclination. Our findings are then compared to predictions made by linear theory.