One-step SelfSim algorithm: Formulating material models from measured strain fields with machine learning

This article introduces a method to formulate material models from measured strain fields using machine learning, termed One-step SelfSim. Unlike the original SelfSim algorithm, which requires two simulations—one with measured displacements and another with measured loads—One-step SelfSim only performs the simulation with the measured loads. The training dataset is created by coupling the simulation’s stress results with a measured strain field.

The method is applied to an elastoplastic problem, using a recurrent neural network initially trained on linear elastic data to model the behaviour of a steel plate undergoing elastoplastic deformation. Results demonstrate that the machine learning model effectively captures the elastoplastic behaviour, with good agreement between simulation outcomes and expected data, particularly for the displacement field. The model is further tested on a plate with a hole, confirming its applicability in scenarios distinct from the training phase.

Two additional contributions are presented. First, the SelfSim algorithm is implemented within a finite volume framework, extending its application beyond finite element simulations. Second, a recurrent neural network is employed to represent history-dependent behaviour, replacing the nested modular neural networks commonly used in earlier studies.