A Variational Multiscale Method for Material Heterogeneity of Solid Mechanics and an Investigation of Machine Learning Framework for Fracture Modeling

open_access
Open Access
Author:
Kong, Hye Eun
Graduate Program:
Civil Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
October 22, 2025
Committee Members:
Farshad Rajabipour, Program Head/Chair
Pinlei Chen, Chair, Minor Member & Dissertation Advisor
Christian Peco, Outside Unit & Field Member
Gordon Warn, Major Field Member
Kostas Papakonstantinou, Major Field Member
Keywords:
CFRP
multiscale
material heterogeneity
variational enrichment
thermomechanical
phase-field fracture
PINNs
interfacial stabilization
Abstract:
Carbon-fiber-reinforced polymer (CFRP) composites are widely used across aerospace, marine, and energy applications due to their high stiffness-to-weight ratios and superior resistance to corrosion and fatigue. However, their complex multiscale structures lead to intricate failure mechanisms, including fiber breakage, matrix cracking, and interlaminar delamination. Accurately resolving these damage phenomena remains a challenge for conventional numerical methods. For highly heterogeneous materials, these methods often require prohibitively fine meshes and high computational costs. To address these challenges, this dissertation develops a fully coupled thermomechanical variational multiscale discontinuous Galerkin formulation, referred to as the VMCF framework, to model dynamic thermoelastic behavior and embedded interfaces without introducing user-defined stabilization parameters. Building upon this foundational VMS framework, a Variational Multiscale Stabilization and Enrichment (VMSE) method is subsequently developed. By naturally deriving interfacial penalty parameters directly from the local geometry and material properties, the VMSE formulation eliminates the need for ad hoc parameter tuning while enabling accurate and efficient resolution of interfacial discontinuities and localized stress representations under mixed boundary conditions. To overcome mesh-dependent limitations and computational overhead inherent in traditional finite element methods, this work further introduces a Physics-Informed Neural Network (PINN) framework for modeling heterogeneous materials and singular stress fields. The study systematically investigates the architectural and data-related factors that govern PINN stability and accuracy. By analyzing the synergy between sparse observational data and physical regularization, the research establishes an optimal data threshold that acts as a physical low-pass filter, effectively denoising sensor-corrupted measurements and ensuring the accurate resolution of localized stress concentrations. To navigate the highly non-convex optimization landscape, a first-order mixed-variable loss formulation is shown to be essential for mitigating derivative inconsistencies in displacement-based networks across strong material discontinuities. Combined with a sequential dual-optimizer strategy and rigorous non-dimensionalization, the proposed framework achieves stable convergence while preserving traction continuity and mechanical equilibrium. Building on these developments, a Thermomechanical Phase-Field Physics-Informed Neural Network (TMPF-PINN) is proposed to model fully coupled multiphysics fracture. By directly incorporating the energy density term associated with the thermal field into the loss formulation, the method captures complex thermomechanical interactions and evolving crack behavior without reliance on mesh-based discretization. Numerical results demonstrate that thermal pre-stresses significantly influence crack initiation and load-carrying capacity. By establishing a relationship between collocation point density and the phase-field length scale, the framework accurately resolves highly localized deformation near cracks and complex internal features without requiring mesh refinement, geometric tracking, or nonlinear iterative solvers. In general, this work establishes a computational paradigm that investigates the variational multiscale formulations and physics-informed machine learning, providing a robust and efficient framework for simulating heterogeneous, multiscale, and multiphysics fracture problems.