Homogenization Enhanced by AI for Geomechanics

Abstract: 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 challenging to define a Representative Elementary Volume (REV) that can hold for all loading paths. 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 polycrystals.

Two example homogenization models are presented to illustrate the complexity of chemo-mechanical inclusion/matrix interactions in rock. First, mass transfer is modeled indirectly through an eigenstrain to predict the propagation of microcracks due to biotite weathering. It is shown that crack growth and stress redistribution are far more sensitive to biotite weathering than to topographic or regional stresses, which suggests that biotite weathering can dominate the development of bedrock damage. Second, diffusion properties are homogenized by using imperfect interfaces to study the counter-acting effects of dislocation and pressure solution in halite. Simulations show that grain boundary healing accelerates specimen compaction, while precipitation in the pores controls the evolution of effective diffusivity.

To assess the feasibility of deploying AI strategies to optimize inclusion models in homogenization schemes, a deep learning model is proposed to detect the features that control the mechanical behavior of 2D solids with embedded cracks. Stress maps are extracted at several loading steps simulated with the Finite Element Method. A Variational Encoder (VAE) is designed to encode these stress maps as vectors of latent features. The performance of the VAE is assessed from measures of reconstruction error, linear and non-linear latent feature correlations, and stress concentration prediction accuracy. The VAE captures stress concentrations, especially when enhanced disentanglement is emphasized during training. Distances between sequences of crack graph descriptors and stress latent features are measured by Dynamic Time Warping to analyze the temporal sequences, and Earth Mover’s Distance calculations to track the dynamic shifts in tensors across the loading steps. Results show that the VAE can capture fabric transitions and highlight the statistical descriptors of the crack pattern that best explain the stress field, which suggests that AI may be used to optimize the inclusion/matrix representation of the REV in the homogenization theory.

An alternative to the interpretation of latent features is the analysis of error propagation from a given microstructure parameter to the effective stiffness tensor. This strategy is briefly discussed through a comparison of rock avatars built under different microstructure constraints. One could expect that the governing microstructure features change as localization or phase transition phenomena occur. This can inform the representation of the microstructure used in homogenization models, resulting in an adaptive homogenization scheme, that can predict mechanical response in the presence of multi-scale phenomena.

Bio: Chloé Arson is a Professor in the School of Civil and Environmental Engineering (CEE) at Cornell University. Prior to Cornell, she was a faculty member at the Georgia Institute of Technology (2012-2023) and at Texas A&M University (2009-2012). She earned her Ph.D. at Ecole Nationale des Ponts et Chaussées (France) in 2009. Dr. Arson’s expertise is in computational geomechanics, with a particular focus on damage and healing mechanics of polycrystalline materials, multi-scale modeling of porous media, and bio-inspired geotechnical design. Her group developed modeling approaches that have allowed a fundamental understanding of synergetic micro-mechanisms in rocks, the prediction of instabilities in geomaterials, and the simulation of concurrent fracture propagation at multiple scales. Homogenization, computational mechanics, Artificial Intelligence (AI) and network dynamics are the pillars of Arson’s work. Inter-disciplinary collaborations have enabled her group to deploy modeling strategies for civil engineering, Earth sciences, material sciences, robotics, and biology. Dr. Arson received the CAREER and BRITE awards from the U.S. National Science Foundation (NSF), in 2016 and 2021 respectively.

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