Difference-based deep learning framework for stress predictions in heterogeneous media

Abstract

Stress analysis of heterogeneous media, like composite materials, using Finite Element Analysis (FEA) has become commonplace in design and analysis. However, determining stress distributions in heterogeneous media using FEA can be computationally expensive in situations like optimization and multi-scaling. To address this, we utilize Deep Learning for developing a set of novel Difference-based Neural Network (DiNN) frameworks based on engineering and statistics knowledge to determine stress distribution in heterogeneous media, for the first time, with special focus on discontinuous domains that manifest high stress concentrations. The novelty of our approach is that instead of directly using several FEA model geometries and stresses as inputs for training a Neural Network, as typically done previously, we focus on highlighting the differences in stress distribution between different input samples for improving the accuracy of prediction in heterogeneous media. Our DiNN framework consists of three main modules: 1) a sample processing module that calculates the difference geometry and stress contours of each sample with respect to a reference contour extracted from the training samples, 2) an Encoder-Decoder module that predicts stress difference contours using geometry difference contours as input, and 3) a stress prediction module that combines the stress difference contours with the reference contour to construct the final prediction of stress contours. We evaluate the performance of DiNN frameworks by considering different types of geometric models that are commonly used in the analysis of composite materials, including volume fraction and spatial randomness. Results show that the DiNN structures significantly enhance the accuracy of stress prediction compared to existing structures, especially for composite models with random volume fraction when localized high stress concentrations are present.