Background We examine the mechanical response of a neo-Hookean spherical core coated with a thin coating of another neo-Hookean material within the framework of finite deformation elasticity. Specifically we consider the cases of simple shear displacement and traction boundary conditions. This problem has currently no analytical solution for finite deformation elasticity. We have determined the general form of the displacement field and pressure function in both phases. These are calculated using the incompressibility constraint, equilibrium equations, continuity of the displacement and traction at the interface, and the different boundary conditions. For the case of displacement/traction boundary condition we begin the analysis with the coating and determine the displacement/traction at the interface. Then we move on to the core and determine the traction/displacement at the interface, completing the solution in the core, before moving back to the coating and completing the solution for the coated sphere. Results We compared our analytical solution to a numerical simulation we obtained with ABAQUS finite elements code for different materials, amounts of shear and thickness of the coating. We compared the displacement, Cauchy stress and energy-density between the analytical solution and the numerical simulation along a few rays. We have found an almost perfect correspondence between our solution and the numerical simulation, for a strain of up to about 30%.
