Transfer learning for enhancing the homogenization-theory-based prediction of elasto-plastic response of particle/fiber-reinforced composites

Abstract

We recently proposed the adaptive incrementally affine method as a novel homogenization scheme that enables accurate prediction of the nonlinear mechanical response of particulate-reinforced composites under cyclic or multiaxial loading conditions. However, being a mean-field homogenization method that relies on the solution of Eshelby’s inclusion problem, the aforementioned method does not provide accurate predictions when the shape of the reinforcement has a high aspect ratio or the interaction among reinforcements becomes significant. Herein, we propose a combined theoretical and data-driven approach in which the homogenization method is followed by transfer learning to enhance the prediction of the nonlinear mechanical response of particle/fiber-reinforced composites. We trained a deep neural network (DNN) with a massive stress-strain curve dataset of a composite subjected to uniaxial loading in the elasto-plastic regime based on the adaptive incrementally affine homogenization method; then, we fine-tuned the pre-trained DNN via transfer learning with a relatively small dataset based on time-consuming three-dimensional (3D) finite element analyses (FEA). The transfer learning approach exhibited better predictive performance than the DNN directly trained only with the FEA dataset did, for a wide range of reinforcement volume fractions and shapes. With transfer learning, the DNN exploits the knowledge learned from the homogenization theory to perform a new learning task on a small dataset from 3D FEA. The combined theoretical and data-driven approach proposed herein can be extended to other composite analyses when experiments or simulations require excessive time and cost for a large dataset and the applicability of the homogenization theory is limited.