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Fracture in porous materials is a complex process in which several non-linear and multiphysical processes contribute to the microcrack network nucleation and growth to the formation of macroscale damage. In this research, several challenges are sought to be tackled: a) the need to model sub-scale long-range mechanical and fluid-flow interactions, b) the need to understand the energy budget and quantify the energy stored versus the energy dissipated in solid fracture and fluid flow, and c) the need to address the extremely elevated computational cost of the non-linear Multiphysics models.

To address these challenges, we present a non-local damage and transport model that can represent long-range sub-scale crack networks and long-range capillary fluid networks. The model is originated from a thermodynamically consistent framework and implemented within a mixed finite element setup. The model is successfully used to represent various loading conditions including 1d and 2d consolidation, slope stability, and fluid driven fracturing; the latter is also extended to analyze the interactions with pre-existing fractures. The thermodynamic basis allows for the derivation of the pertinent expressions of energy storage and dissipation, which are also calculated numerically using the finite element setup. In hydraulic fracturing, the calculation of energy quantities provides valuable insights about the ratio of the applied work that gets utilized to increase the stimulated reservoir volume versus that spent in fluid-viscous flow. This framework can be extended to serve as a basis for hydraulic fracturing optimization based on the energy budget. To address the elevated computational cost of the proposed model, and other expensive models in this research area, we propose a new approach named Integrated Finite Element Neural Network (I-FENN). This approach utilizes the rapidly evolving ML tools within the FEM setup to limit the computational expense of coupled problems; this is achieved through pre-training a network to predict one of the coupled processes and using the network within the FEM setup to predict a map of the coupled variable. The I-FENN setup has been applied to several classes of problems and is showing promising computational gains.

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