In this paper, the elasto-plastic pre- and post-buckling behavior of beams made of functionally graded materials subjected to mechanical loading is investigated. A continuum-based finite element formulation is developed to determine the major characteristics of buckling. The arc-length algorithm is employed to analyze the stability problem. A plane stress von Mises model with isotropic hardening is utilized for the elasto-plastic nonlinear analysis of the beam. Basic idea in geometric and material nonlinear analysis of functionally graded material beams is to use the plasticity capacity of metal phase as a ductile material during loading. The influences of number of axial modes, material index, geometrical parameters and boundary conditions on the critical buckling point, pre- and post-buckling paths, plastic bifurcation point and stress distribution are fully studied. A good agreement between generated results and existing data in the literature is observed.
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