Instability and Wrinkles in the Bending of elastic sector with analytical WKB method

In this paper, We purpose to analyze the large bending of elastic curved structures that found in the engineering, science and nature. We investigated large bending of an open sector circular cylindrical tube into a complete circular cylindrical tube such that the solid is modeled via an incompressible, homogenous and isotropic hyperelastic material. According to the finite deformation of the structure, in the compressed side of bended beam wrinkles and local buckling may appear. We interpret the onset this instability by using the theory of incremental deformation superimposed on the finite deformation and analytical WKB method for Mooney-Rivilin strain energy function is utilized and boundary loads are defined for bending analysis. Moreover, the instability and numbers of wrinkles is studied in detail. The main results are that the obtained bending conditions are depended on the sector angles before and after deformation, exterior traction and the numbers of wrinkles per surface area. The trend of changes and dependence of these geometric parameters are examined by drawing diagrams