MACHINE-LEARNING-BASED ASYMPTOTIC HOMOGENIZATION AND LOCALIZATION OF SPATIALLY VARYING MULTISCALE CONFIGURATIONS MADE OF MATERIALS WITH NONLINEAR ELASTIC STRESS-STRAIN RELATIONSHIPS

This article aims to propose a general method in support of efficient and reliable predictions of both the global and local behaviors of spatially varying multiscale configurations (SVMSCs) made of materials bearing nonlinear history- independent stress-strain relationships. The framework is developed based on a complementary approach that integrates asymptotic analysis with machine learning (ML). The use of asymptotic analysis is to identify the homogenized constitutive relationship and the implicit relationships that link the local quantities of interest, say, the site where the maximum von Mises stress (MVMS) lies, with other on-site mean-field quantities. As for the implementation of the proposed asymptotic formulation, the aforementioned relationships of interest are represented by neural networks (NNs) using training data generated following a guideline resulting from asymptotic analysis. With the trained NNs, the desired local behaviors can be quickly accessed at a homogenized level without explicitly resolving the microstructural configurations. The efficiency and accuracy of the proposed scheme are further demonstrated with numerical examples, and it is shown that even for fairly complex multiscale configurations, the predicting error can be maintained at a satisfactory level. Implications from the present study to speed up classical computational homogenization (CH) schemes are also discussed.