Closed-form solutions for elastoplastic pure bending of a curved beam with material inhomogeneity

The elastoplastic pure bending problem of a curved beam with material inhomogeneity is investigated based on Tresca's yield criterion and its associated flow rule. Suppose that the material is elastically isotropic, ideally elastic-plastic and its elastic modulus and yield limit vary radially according to exponential functions. Closed-form solutions to the stresses and radial displacement in both purely elastic stress state and partially plastic stress state are presented. Numerical examples reveal the distinct characteristics of elastoplastic bending of a curved beam composed of inhomogeneous materials. Due to the inhomogeneity of materials, the bearing capacity of the curved beam can be improved greatly and the initial yield mode can also be dominated. Closed-form solutions presented here can serve as benchmark results for evaluating numerical solutions.