Transient finite element method for structural elastoplastic analysis under low cycle fatigue loading

In the early study the transient cyclic stress-strain relation curve (CSSR) was denoted by segment polygonal line with Jhansale model for transient FEM under low cycle fatigue loading([1]). In this study the cyclic stress-strain relation field (SSRF) was founded and the discretization criterion of the field mesh was studied. The CSSR was modified according to the stress level and the stress history of the element or Gauss point after every reversion, so the element curves are different after the first reversion. This generates a field of stress-strain relation. In transient FEM one material type was set up for one element, the number of the material types will be very large as the structural complexity and the FEM mesh refining. Actually the SSRF mesh was as same as the FEM mesh. Under fatigue loading usually the number of local elements entering plastic is small; the most area of the structure keeps elastic. It is founded that coarsening the SSRF mesh of the elastic area would affect the results indistinctively. The FEM elements never entering plastic were divided into several regions. The element stress-strain relation curves in one region were averaged and the average curve is used for all elements in this region. The average processes were not in one reversion, but add up all the element curves in the former reversions, so the material characteristic history can be reflected. The SSRF mesh is transient according to the stress level and stress history for every reversion. The examples show the proposed method can reduce the number of material type remarkably. In the example of a plate with a hole consist of 64 FEM elements the number of material types was decreased about 87%, the relative error keep under 0.0004.