Statistics

Algorithm

Machine learning

Physics

Geology

Engineering

Surrogate model

Finite element method

Aerospace engineering

Recurrent neural network

Paleontology

Artificial intelligence

Range (aeronautics)

Scale (ratio)

Context (archaeology)

Mathematics

Computer science

Artificial neural network

Quantum mechanics

Structural engineering

Stochastic process

Computer Methods in Applied Mechanics and Engineering

An artificial Neural Network (NNW) is designed to serve as a surrogate model of micro-scale simulations in the context of multi-scale analyses in solid mechanics. The design and training methodologies of the NNW are developed in order to allow accounting for history-dependent material behaviors. On the one hand, a Recurrent Neural Network (RNN) using a Gated Recurrent Unit (GRU) is constructed, which allows mimicking the internal variables required to account for history-dependent behaviors since the RNN is self-equipped with hidden variables that have the ability of tracking loading history. On the other hand, in order to achieve accuracy under multi-dimensional non-proportional loading conditions, training of the RNN is achieved using sequential data. In particular the sequential training data are collected from finite element simulations on an elasto-plastic composite RVE subjected to random loading paths. The random loading paths are generated in a way similar to a random walking in stochastic process and allow generating data for a wide range of strain-stress states and state evolution. The accuracy and efficiency of the RNN-based surrogate model is tested on the structural analysis of an open-hole sample subjected to several loading/unloading cycles. It is shown that a similar accuracy as with a FE2 multi-scale simulation can be reached with the RNN-based surrogate model as long as the local strain state remains in the training range, while the computational time is reduced by four orders of magnitude.

A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths