Accelerated offline setup of homogenized microscopic model for multi‐scale analyses using neural network with knowledge transfer

Abstract

AbstractThe FE computational homogenization method is a predictive multi‐scale method without the need for constitutive assumptions and/or potential function postulates at the macro engineering scale. Instead, the effective micro‐structural responses are extracted directly from a representative volume element (RVE) underlying each macro point. However, the FE method is still computationally too expensive for most practical uses, since the micro‐macro FE coupling is done at each loading step/iteration for the entire domain. To this end, the machine learning method has been utilized in the literature for the offline training of a surrogate model to predict the RVE homogenized response for general loading conditions. In this contribution, the neural network (NN) is incorporated into the macro finite element framework in a non‐intrusive manner. This is termed as the FE‐NN framework, in analogy to the FE method. In general, online simulations in the FE‐NN method is very efficient, with predictions matching closely to those obtained from reference direct numerical simulations (DNS). A bottleneck with the FE‐NN framework, however, is the high computational cost associated with the data generation for offline NN model setup. In this paper, focusing on the FE‐NN multi‐scale framework for non‐linear elastic deformation of heterogeneous materials, a sequential training strategy with knowledge transfer is proposed, to enable an efficient offline microscopic NN model setup. For a given target RVE, we first consider a simplified source RVE, where data can be generated rapidly, for the NN pre‐training of surrogate model. The pre‐trained network parameters are next downloaded to initialize the target NN surrogate model, followed by a fine‐tuning training process, using only a small dataset generated by the computationally expensive high‐fidelity RVE. The efficiency of the proposed sequential learning method over the conventional NN training, as well as, its excellent predictive capability for multi‐scale analyses, are demonstrated for a multi‐phase composite material. The proposed FE‐NN‐KT approach can be implemented easily without complicated pre‐processing procedures, since the data generation only involves the standard extraction of effective responses from RVEs, together with a standard NN architecture.