Date

6-16-2025

Department

School of Engineering

Degree

Doctor of Philosophy in Engineering (PhD)

Chair

Mark Horstemeyer

Keywords

Unified Multiscale Modeling, Internal State Variable (ISV) Framework, Composite Material Systems, Organic-Inorganic Composites, Thermomechanical Constitutive Modeling, Viscoplastic-Viscoelastic Coupling, Temperature-Dependent Material Behavior, Strain Rate Sensitivity, Corotational (Lie Derivative) Rate Formulations, Kinematics and Thermodynamics of Deformation, History-Dependent Mechanical Response, Irreversible Thermodynamics, Deformation Gradient Correction, Hooke’s Law Extension, Thermal Dissipation in Materials, Objective Stress Rate, Geo-Soil Constitutive Behavior, Brain Tissue Mechanics, High-Fidelity Material Modeling, Polymeric Composite Modeling, Computational Material Science, Multiphysics Simulation, Biomechanics of Soft Tissue, Smart Composites under Thermal Load, Internal Rearrangement Dynamics, Finite Deformation Framework

Disciplines

Computational Engineering | Engineering

Abstract

This work represents a transformational milestone that addresses the complex mechanical behavior of composite material systems within a unified framework for both inorganic and organic constituents. The motivation for this research stems from the need to accurately model and predict the mechanical behavior of these complex material systems, which are widely used in various industries. These materials present a unique challenge due to the intricate interplay of inorganic and organic phases, making them ideal candidates for an Internal State Variable (ISV) multiscale modeling approach.

The proposed model is a comprehensive ISV framework that seamlessly predicts inorganic and organic material behavior. It accounts for the micro to macroscale interactions between these constituents, offering a holistic understanding of the kinematics, thermodynamics, and kinetics governing the material's response. Building upon the foundational research of Boulevard, Francis, and He, this work represents a pivotal advancement in materials science and mechanics, offering a unified approach that transcends prior boundaries.

Key contributions and advancements include:

  1. Corrected Deformation Gradient for Viscoelasticity: In a departure from traditional models, this framework incorporates a corrected deformation gradient tailored for viscoelastic materials. This correction yields an enhancement in our ability to analyze and predict the intricate mechanical behavior of various composite systems with increased accuracy.
  2. Objective Rate Form and Corotational Rates: The theory adopts an objective rate form, thoughtfully implementing (Lie derivatives) corotational rates across all rate equations. This strategic integration rectifies previous inconsistencies, presenting a comprehensive and internally consistent model for material response under varying conditions.
  3. Temperature Dependence and Strain Rate Relationship in Hooke’s Law: Extending Hooke’s Law, our framework accommodates temperature-dependent material properties and strain rate dependencies. This expanded model enhances our capacity to describe material responses across diverse thermal and loading scenarios.
  4. Robust Internal State Variable (ISV) Framework for History-Dependent Behavior:
    The framework incorporates a comprehensive ISV framework that rigorously accounts for the evolution of microstructural states and their influence on macroscopic response. This formulation ensures that the long-term effects of deformation—such as irreversible internal rearrangements and thermal dissipation—are consistently integrated into the model according to established thermodynamic principles.
  5. Application to Different Composite Systems: Beyond its application in polymers, this theory demonstrates versatility by effectively modeling inorganic and organic materials. It extends its reach to encompass geo soils and even brain tissue, presenting a novel and adaptable tool for researchers in various disciplines.

Overall, this unified framework offers a comprehensive and adaptable means to model material behavior, enabling a deeper understanding and more accurate predictions of complex material responses. It bridges the chasm between theory and practice, facilitating innovative research and technological advancements across a spectrum of applications, from geoengineering to neuroscience.

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