A plastic correction algorithm for full-field elasto-plastic finite element simulations : critical assessment of predictive capabilities and improvement by machine learning

This paper introduces a new local plastic correction algorithm developed to accelerate finite element simulations for structures with elasto-plastic constitutive laws. The proposed method belongs to the category of generalized multiaxial Neuber-type methods enabled by pointwise proportional evolution rules. The algorithm numerically integrates J2 plasticity laws as a function of the finite element elastic response of the structure, to obtain full-field 3D elasto-plastic quantities for any proportionally applied loading. Examples of the numerical capabilities of this algorithm are shown on a structure containing a distribution of pores, for monotonic and fatigue loading. The approximation errors due to the proposed local plastic correction are also investigated. As a second point of innovation, we show that the proposed local plastic correction can be accelerated when dealing with large-scale structures by employing a simple meta-model, with virtually no added errors. Finally, we develop and investigate the merits of an additional deep-learning-based corrective layer to reduce approximations errors on a subset of structures for which full elasto-plastic FE simulations are performed, the solutions of which are subsequently used as training set for a Convolutional Neural Network algorithm designed to learn the error between full FE and plastic correction approximations.