Homogenization requires a description of the microstructure by means of inclusion models and inclusion-matrix interaction laws. In geomechanics, inclusions are often defined as cracks, pores, crystals or grains, because these microstructure features can be identified experimentally by imaging. However, there is no guarantee that these physical features are the most relevant to the properties that are being homogenized - typically, the stiffness tensor. Additionally, physical features are altered by localizations, e.g., when cracks coalesce or when pores collapse, which makes it impossible to define a Representative Elementary Volume (REV) that can hold for any loading path. The overarching goal of this research is to design Artificial Intelligence (AI) algorithms to determine the microstructure features that are the most significant to describe the mechanical behavior of a material REV.

In the first part of this presentation, we benchmark a pruned VGG19 model subjected to Axial Coronal Sagittal (ACS) convolutions and a custom VGG16 model to predict 3D fabric descriptors from a set of 2D images. The data used for training and testing are extracted from a set of 600 3D biphase microstructures created numerically. Fabric descriptors calculated from the 3D microstructures constitute the ground truth, while the input data are obtained by slicing the 3D microstructures in each direction of space at regular intervals. Increasing the number of slices improves the performance of the custom VGG16 model, but becomes cost ineffective beyond 3 images per direction. For both models, the aggregate volume fraction is predicted with less accuracy than higher order descriptors, which is attributed to the bias given by the loss function towards highly-correlated descriptors. Both models perform better to predict means than standard deviations, which are noisy quantities. The custom VGG16 model predicts the second and third invariants of the orientation matrix, which suggests that the model can predict orientation descriptors regardless of the orientation of the input images.

In the scond part of the talk, we present a prototype deep learning model to detect the features that control the mechanical behavior of 2D composites made of a solid matrix, aggregates and cracks. Several loading paths are simulated with the Finite Element Method (FEM), and stress maps are extracted at several loading steps. A prototype Variational Encoder (VAE) is designed to encode these stress maps as vectors of latent features. The decoder that reciprocates the VAE is used to reconstruct stress map series to augment the input data set. The series of latent feature vectors are analyzed to detect any change in feature components or ranking during the loading paths. Detecting these microstructure transitions will be useful to understand the stress regimes that call for different inclusion models in the homogenization theory. Furthermore, we iteratively seek the physical fabric descriptors that best correlate with the latent feature vectors identified by the VAE. This will allow us to determine the fabric tensor variations that are the most significant to explain the variations of the stress tensor in the microstructure. We also propose a strategy to encode time/loading sequences of latent vectors (i.e., latent vectors obtained at consecutive loading steps during the FEM simulations) to gain a more fundamental understanding of the precursors of microstructure transformation upon mechanical loading.