On Radial Deformation of Incompressible Cylindrical Mooney-Rivlin Materials under Internal Pressure: Application of Collocation and Shooting Methods

Abstract

Abstract: In order to solve the radial deformation of incompressible Mooney-Rivlin isotropic synthetic rubber-like materials under various pressure regimes, this study compares the collocation and firing numerical approaches. Using the Mooney-Rivlin constitutive law to describe the complicated material response, the study tackles the nonlinear boundary value problems resulting from thick-walled cylinders exposed to moderate (0.1 MPa), high (1 MPa), and extremely high (10 MPa) internal pressures. The study measures the accuracy, convergence, and robustness of each approach across the pressure ranges under investigation by utilizing the collocation method, which is renowned for its effectiveness and stability with stiff nonlinear equations, and the shooting method, which converts the boundary value problem into an initial value framework. The collocation approach offers quicker and more dependable convergence, particularly at higher pressure regimes, despite the fact that both approaches can precisely resolve massive deformations and associated stress distributions, as shown by numerical simulations. The findings provide information for failure analysis and pressurized hyperelastic structure design optimization by highlighting the sensitivity of radial deformation and stress concentration close to the inner wall to both the applied pressure and material model parameters. The study and design of pipelines, pressure vessels, biomedical balloons, and other rubber-like components that are subjected to high internal loads can all benefit from these discoveries.