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The purpose of this study is to show how gradual strength degradation of metal beams under cyclic bending up to fatigue failure is simulated based on a new elastoplasticity model free of any yield criterion.

A new approach is proposed toward accurately and explicitly prescribing evolution of non-uniform stress distribution on beam cross-section under cyclic bending and, as such, gradual degradation of the bending strength can be directly determined.

Explicit results for the bending response in a whole cyclic process up to fatigue failure are obtained and the fatigue characteristic curve is for the first time simulated directly between the curvature amplitude and the cycle number to failure.

First, explicit and accurate determination of the non-uniform stress distribution on beam cross-section is achieved with asymptotic softening effects. Second, degradation of the bending strength can be directly deduced cycle by cycle. Finally, the relationship between the bending moment and the curvature is calculated using new and efficient numerical algorithms, thus bypassing usual time-consuming calculations with finite element procedures. Numerical results are presented and in good agreement with experimental data.