Research Overview

The modeling of fracture and damage in materials undergoing coupled physical processes remains a fundamental challenge in computational mechanics. Our work focuses on the development of thermodynamically consistent constitutive frameworks that describe the interaction between deformation, damage evolution, and transport phenomena in porous and heterogeneous materials. Particular emphasis is placed on poromechanical systems, where fracture processes are governed by the coupling between solid deformation, pore-pressure evolution, and evolving permeability. Within this setting, damage and transport are treated as coupled processes embedded within an energy-based formulation, allowing for a consistent representation of material degradation and fluid flow . A central aspect of this research is the formulation of non-local and multi-length-scale models that regularize strain localization and enable the representation of distributed fracture processes, with distinct length scales associated with mechanical damage and transport to capture hierarchical crack networks and their influence on macroscopic response . Extensions to time-dependent and inelastic behavior incorporate viscoelasticity and damage–plasticity coupling, allowing for the analysis of transient and progressive failure in geomaterials, while energy-based analyses are employed to quantify the partitioning of energy during fracture processes, including elastic storage, viscous dissipation, and damage evolution. Ongoing work extends these formulations to chemomechanical characterization and modeling, with the goal of capturing the role of chemical processes, such as mineral dissolution/precipitation and reactive transport, in driving material degradation and fracture evolution.
Key highlights:

• Thermodynamically consistent formulations for coupled deformation–damage–transport processes 
• Non-local and gradient-based regularization of strain localization in damage mechanics 
• Multi-length-scale frameworks for representing coupled damage and transport interactions 
• Poro-damage-viscoelastic and damage–plasticity models for time-dependent and inelastic response 
• Energy-based formulations for analyzing fracture and dissipation mechanisms 
• Numerical frameworks for nonlinear solution of coupled multiphysics systems 
• Calibration strategies for identification of constitutive model parameters 
• Applications in geomechanics, geoenergy systems, and infrastructure-related materials

Our work in scientific machine learning focuses on the development of hybrid formulations that integrate machine learning models within established numerical methods, with an emphasis on preserving the structure, stability, and interpretability of physics-based solvers. A central contribution is the Integrated Finite Element Neural Network (IFENN) framework, in which neural networks are embedded within finite element formulations to approximate auxiliary fields or internal variables, thereby reducing the number of coupled unknowns while maintaining numerical robustness . This framework has been extended to nonlinear and multiphysics problems—including non-local damage, thermoelasticity, and phase-field fracture—using architectures such as physics-informed convolutional and temporal convolutional networks to capture spatial and history-dependent behavior . In parallel, we develop operator learning approaches based on DeepONets and their variants, including multiple-input formulations (MIONet) and physics-informed loss functions that enforce equilibrium and energy consistency for structural and multiphysics systems . Recent advances explore alternative operator representations, such as DeepOKAN for enhanced expressivity and NCDE-based operator learning for continuous-time modeling of transient systems, addressing limitations of discrete-time sequence models . Ongoing efforts extend these ideas toward foundation models for computational mechanics, agentic AI for adaptive simulation workflows, and systematic analysis of error convergence, stability, and hyperparameter sensitivity in physics-informed and hybrid learning frameworks.

 Key highlights:

• Development of Integrated Finite Element Neural Networks (IFENN) for hybrid physics–ML simulation
• Embedding neural networks within FEM to reduce coupled unknowns and computational cost
• Use of physics-informed CNNs and TCNs for spatial and history-dependent multiphysics problems
• Integration of DeepONet and MIONet for operator learning in parametric systems
• Physics-informed operator learning with stiffness- and energy-based loss formulations
• Introduction of DeepOKAN for improved operator expressivity
• Development of NCDE-based operator learning for continuous-time and history-dependent systems
• Analysis of error convergence, stability, and hyperparameter sensitivity in PINNs and hybrid solvers
• Ongoing work on foundation models and agentic AI for scientific computing

Our work on subsurface processes focuses on the development of thermodynamically consistent constitutive and computational frameworks for reservoir geomaterials, with an emphasis on coupled deformation, fracture, and fluid transport in porous media. Central to this effort are non-local damage and damage–plasticity formulations, which regularize strain localization and enable physically meaningful representation of fracture process zones, permeability evolution, and fluid-driven failure mechanisms. These models capture the strong coupling between mechanical deformation and fluid flow governed by Darcy-type transport, allowing for the simulation of hydraulic fracture, fracture–permeability interactions, and evolving flow pathways in reservoir systems. Energy-based formulations further provide a quantitative description of energy storage and dissipation during fluid-driven fracturing, offering insight into fracture propagation and transport efficiency in subsurface environments .

In parallel, we develop computational strategies for accelerating multiphysics reservoir simulations, addressing the significant cost of coupled THM and chemo-mechanical problems. The Integrated Finite Element Neural Network (IFENN) framework enables efficient solution of these systems by embedding neural network surrogates within finite element formulations, reducing the number of coupled unknowns while preserving numerical stability and physical consistency . Extensions to transient and history-dependent processes using temporal convolutional networks and operator learning demonstrate the ability to capture load-history-dependent fracture and transport behavior with reduced computational effort . While current developments focus on constitutive and component-scale modeling, ongoing efforts aim to enable integration within large-scale reservoir simulators (e.g., GEOS) through collaboration with national laboratories, providing a pathway toward scalable, high-fidelity modeling of subsurface systems for geoenergy applications.

 Key highlights:

• Development of non-local damage and damage–plasticity models for reservoir geomaterials
• Modeling of fluid-driven fracture and fracture–permeability interactions
• Coupled mechanics–flow processes governing transport in fractured reservoirs
• Energy-based frameworks for quantifying fracture propagation and dissipation mechanisms
• Use of mixed finite element formulations for multiphysics reservoir problems
• Use of IFENN to accelerate coupled THM and multiphysics simulations
• Extension to history-dependent processes via TCNs and operator learning
• Focus on component-scale models with strong physical interpretability
• Pathway toward integration with reservoir simulators (e.g., GEOS)
• Ongoing efforts toward collaborations with national laboratories