Geometry-Based Thermodynamic Homogenization for Porous Media, with Application to Resilience Prediction and Gyroscopic Sustainability

Abstract

Understanding and predicting the behavior of porous media holds unexpected potential for technological advances toward resilience and sustainability. Indeed, these materials are ubiquitous and exhibit a rich palette of processes, both multiphysics and multiscales, which are potential sources of inspiration for engineering design. Along these lines, the intended outcomes of this dissertation are twofold: 1) predicting the resilience of porous media and 2) enhancing behaviors of interest in these materials that could inspire sustainable metamaterials design. Geomaterials, a particularly complex subclass of porous media, will be the primary focus.This program starts by laying down a general theoretical framework, based on non-equilibrium thermodynamics and differential geometry. A generalized relaxation equation is derived to ensure systematic satisfaction of the second law of thermodynamics. This is associated with a variational framework, based on Fermat's principle, that generalizes that of Onsager, in order to reckon with gyroscopic forces - that is, nondissipative but nonconservative forces. This framework is then applied to modeling the microstructure of porous media, upon which the behavior of these materials largely depends. To that aim, phase-field modeling is employed to capturing the exact microstructural geometry, in association with digital rock physics based on microtomographic imaging. This effort is required to model processes too complex to be described by a unique constitutive law, such as pressure solution, as studied first in this dissertation. Therein, a microstructural viscosity is derived to capture the kinetics of processes, which is crucial for modeling geomaterials, since the associated timescales span from the engineering to the geological times. Upon narrowing down the complexity of porous media processes, it is possible to extract the necessary and sufficient microstructural information through morphometry. From running phase-field simulations on a large variety of synthetic microstructures, a general morphometric strength law is inferred, which builds upon seminal works on metals and ceramics. This morphometric framework is applied to predicting the strength of various porous materials, including rocks and bones, from their microstructural geometry.