Abstract: The microstructural geometry of porous media critically influences their mechanical behavior across a broad spectrum of materials, from geomaterials and biomaterials to engineered structures. Recent developments in imaging techniques, such as X-ray microcomputed tomography, alongside advanced modeling approaches, enable precise characterization of complex morphometries. However, traditional continuum theories often only partially capture this microstructural influence. To address this gap, we propose a unifying framework that leverages Minkowski functionals, as per Hadwiger's theorem, to quantitatively relate microstructural features to material strength. By conducting qualitative 2D phase-field simulations on synthetic microstructures, we derive a morphometric strength law expressed as an exponential function of the microstructural descriptors, effectively generalizing existing models for metals, ceramics, and geological materials. This relationship demonstrates promising predictive capacity when extended to real porous media, including rocks, bones, and ceramics. Complementing the morphometric approach, machine learning (ML) and deep learning (DL) techniques are employed to accelerate and enhance the assessment of porous media's mechanical properties. Using scalar morphological descriptors derived from microstructure, a fully automated methodology predicts stress-strain curves from uniaxial compression tests, providing rapid and accurate strength evaluations. To mitigate the reliance on extensive datasets, a novel two-step learning framework--learning latent hardening (LLH)--integrates domain-specific knowledge into deep neural networks, improving predictions in data scarce scenarios. Comparative analysis of six ML/DL models with and without microstructural insight highlights the significant performance gains achieved through domain integration, emphasizing the importance of combining expert knowledge with data-driven methods in material modeling. Furthermore, the evolution of digital rock physics now enables detailed numerical simulations of mechanical behavior at the microstructural level, including elasto plastic deformation and strength estimation. Through comprehensive parametric studies on cemented granular materials, we assess the impact of cementation volume, Young's modulus, friction, and cohesion on the yield surface of rocks, validated against experimental data. This approach allows us to go beyond semi-analytical criteria, providing a full numerical characterization of the strength and failure behavior of porous materials under various stress paths. Collectively, these advancements foster a deeper understanding of porous media mechanics and open new pathways for the AI-assisted design of materials with tailored properties for structural applications.

Bio: Manolis Veveakis is a Professor in the Department of Civil and Environmental Engineering, Duke University and the outgoing Editor-in-Chief of the journal Geomechanics for Energy and the Environment (Elsevier). Before joining Duke University he was a Senior Lecturer at UNSW's School of Petroleum Engineering and a Research Scientist in CSIRO's Division of Earth Sciences and Resource Engineering. Veveakis holds a Diploma in Applied Mathematics and Physics, a MEng in Materials Engineering, an MSc in Applied Mechanics and a PhD in Geomechanics, all from the National Technical University of Athens (Greece).