Nonlinear bending of elastoplastic functionally graded ceramic-metal beams subjected to nonuniform distributed loads

Nonlinear bending of elastoplastic functionally graded (FG) ceramic-metal beams subjected to nonuniform distributed loads is investigated by the finite element method. A bilinear stress-strain relation with isotropic hardening is assumed for elastoplastic behavior of metal, and the elastoplastic properties of the FG ceramic-metal material are evaluated by using Tamura-Tomota-Ozawa (TTO) model. Based on Euler-Bernoulli beam theory, a nonlinear finite element formulation, taking the effect of plastic deformation into account, is derived and used in the investigation. The formulation employing nonlinear von Kámán strain-displacement relationship is derived by using the physical neutral surface as reference plane. An incremental-iterative procedure based on Newton-Raphson method, in which the plastic equation is solved at Gauss points for updating the stress and evaluating the element formulation, is employed to solve nonlinear equilibrium equations. The elastoplastic behavior is illustrated for a FG beam composed of TiB and Ti. The numerical results show that yielding in the FG beam occurs at the layer near the ceramic surface earlier than it does at the layer near the metal surface. The effect of the material distribution, plastic deformation on the nonlinear behavior of the beam with various end conditions is investigated in detail. The formation and propagation of plastic zone inside the beam during the loading process is also examined and highlighted.