A novel rapid method of purely elastic solution correction to estimate multiaxial elastic-plastic behaviour

In structural analysis, it is of paramount importance to assess the level of plasticity a structure may experience under monotonic or cyclic loading as this may have a significant impact, particularly in fatigue analysis for singular areas. For efficient design analyses, it is often searched for a compromise in accuracy that consists in correcting a purely elastic analysis, generally simpler and faster to obtain compared to a full non-linear Finite Element (FE) analysis involving elastic-plastic behaviour, to estimate the actual elastic-plastic solution. There exists a great number of correction techniques in the literature among which the most famous and commonly used are Neuber and ESED energy-based methods. Nonetheless, both of them are known to provide respectively upper and lower bounds of the exact solution in most cases, with a relative deviation depending on the level of multiaxiality and on the amount of stress redistribution due to yielding. The new methodology presented in this paper is based on the well-known multiaxial Radial Return Method (RRM) revisited using effective parameters approach. By essence, it is fast and can be applied either to analytical elastic problems or to more complex three-dimensional elastic FE analyses. The accuracy of the proposed method is assessed by direct comparison with results from Neuber and ESED methods on various examples. It is also shown for each of them that this new method is very good agreement with the exact elastic-plastic solution.