Numerical implementation of a multiaxial cyclic plasticity model for the Local Strain method in low cycle fatigue

•Numerical implementation of a simple cyclic plasticity model for multiaxial fatigue.•General return mapping algorithm for ABAQUS/UMAT subroutine of facile implementation.•Integration scheme has strong impact on simulations of neutral non-proportional loads.•Implicit integration is mandatory in simulations with neutral load segments.

Very often computations on structural elements or machine components subjected to variable loading require the use of an advanced finite element model. This paper reports the numerical implementation of a model for multiaxial cyclic elasto-plastic behaviour, developed to extend the tools of the Local Strain method to fatigue under multiaxial conditions. A basic computer code for axial–torsional loads was developed with the commercial software MATLAB and a more sophisticated one, for general multiaxial loads, was developed as a UMAT subroutine in ABAQUS. Stress integration was introduced in the two usual forms: implicitly and explicitly. A comparison of the results obtained with the implicit and explicit formulations revealed that, under certain loading conditions, the outcome of the process depends very much on the particular integration scheme used.