This paper proposes the macroscopic model which enables us to evaluate partially-plastic states in a cross section of the Bernoulli-Euler beam. In this paper, the basic equations (the yield function, the plastic flow rule, and the hardening rule) in the form of resultant stresses are exactly derived from the assumed ones in the form of stresses. The Helmholtz free energy for the cross section in the form of resultant stress involves additional potential due to partially-plastic states besides the elastic stored energy and the hardening potential. The thermodynamic forces derived from this additional potential describe the post-yielding behavior from partially-plastic states to fully-plastic states. The constraint conditions (the yield function) and the plastic flow rule are also modified to characterize the evolution of plastic regions without the direct evaluation of microscopic behavior. Then, a numerical scheme to calculate resultant stress under cyclic loading is proposed. Finally, the proposed macroscopic model is applied to the beam element and some numerical examples are shown to examine the validity of the present method.
