Self-learning FEM/NMM approach to identification of equivalent material models for plane stress problem

Abstract

The autoprogressive and cumulative algorithms, basing on 'on line' formulation of patterns and the training of NMM (Neural Material Model), are evaluated to be comparable in case of uniaxial stress state problems. It is shown in the paper that for the plane stress boundary value problems the autoprogressive algorithm, in which NMM is trained for each load increment, is superior to the cumulative algorithm. In order to formulate a small NMM and accelerate the convergence of the iteration of computed equilibrium paths to the monitored paths, a smaller number of inputs NMM is discussed and a modified selection of the training patterns is applied. A new approach is proposed with respect to the designing of NMMs, combining the 'on line' and 'off line' training of neural networks. The discussed problems are illustrated with two study cases. They are related to the formulation of NMMs for the identification of equivalent materials in plane trusses made of the Ramberg-Osgood material and for elasto-plastic plane stress boundary value problems.