Hyper-reduced predictions for lifetime assessment of elasto-plastic structures

Abstract

Finite element (FE) elasto-plastic or elasto-viscoplastic simulations of complex components can still be prohibitive for lifetime predictions. There is a need for fast estimation methods of plasticity in a given region of interest, where a crack could be initiated. Some rules are already available for fast predictions of elasto-plastic stress and strain, by using elastic simulations. Furthermore, as shown by the Herbland’s model, inclusion theory can be incorporated in simplified rules to improve their accuracy. Recent advances in model reduction methods for nonlinear mechanical models give access to fast elasto-plastic or elasto-viscoplastic predictions having both accuracy and computational complexity in between usual FE predictions and these simplified rules. Hyper-reduction performs quite well in the simplification of elasto-plastic or elasto-viscoplastic models. Similarly to Herbland’s model, we show in this paper a first attempt to improve hyper-reduced models by the recourse to a virtual inclusion placed in the region of interest. In the proposed numerical example, a finite element model involving 5000 degrees of freedom is reduced to 12 variables. The mesh is also reduced to 550 elements over a total of 900 elements for the original mesh. The approximation error on the predicted plastic strains and stresses is lower than 3 % and the computational time is reduced up to a factor 5.