Exact solutions for elastoplastic stress distribution in functionally graded curved beams subjected to pure bending

The material of the beam is presumed to be isotropic and ideally elastic-plastic and the elastic modulus and yield limit vary radially according to power law functions. Based on Tresca's yield criterion and its associated flow rule, the expressions of the stresses and displacements in four different stress states are presented. The condition to achieve the concurrent yielding on the inner and outer surfaces is given explicitly. The position of the neutral plane and the plastic limit bending moment in a completely plastic state are determined. The distinct characteristics of elastoplastic behavior of functionally graded materials (FGMs) curved beam are shown in examples.