Plastic deformation of a tube during bending

The objective of this study is to develop an analytical approach to calculate the relationship between the axial curvature of a bent tube and the resulting deformation of the cross-section. The model accounts for both geometrical and material nonlinearities. An approximate expression in trigonometric form is introduced for the displacement field, which reflects the change of wall thickness and neutral axis shift during bending. The total deformation theory is employed as a constitutive relation. The solution is found using a minimization approach and the energy principle. A better approach for springback prediction might be obtained from the deformation model, which predicts a more accurate moment of inertia change during bending.