Large deformation analysis of fully incompressible hyperelastic curved beams

•A nonlinear formulation for large deformation of elastic curved beams is developed.•The incompressibility constraint is exactly satisfied.•The formulation models moderately thick as well as thin hyperelastic beams.•A Total Lagrangian FE formulation is developed to solve the nonlinear equations.•The element based on the present formulation does not suffer from shear locking. The aim of this contribution is to develop a nonlinear formulation for modelling the large deformation of elastic curved beams made of fully incompressible hyperelastic materials. The basic idea is to apply the incompressibility constraint besides the plane stress assumption in the directions perpendicular to the centreline of the beam. Accordingly, a system of three nonlinear algebraic equations for the hydrostatic pressure as well as normal strain components in the beam cross section are obtained. By solving the system of equations, either analytically or numerically, it is possible to propose constitutive equations for the force and moment resultants present in the formulation. The main advantage of this strategy is that it allows for using three-dimensional incompressible constitutive equations. Due to highly nonlinear nature of the differential equations, a Total Lagrangian finite element formulation is developed. Performance and accuracy of the formulation are investigated through several numerical examples.