The primary focus in this research is on proposing a methodology for modeling of discrete crack propagation in geomaterials such as soil, rock, and concrete. Structures made of such materials may undergo damage due to several reasons. Here, mechanical loading and chemo-mechanical interactions that result in degradation of strength parameters are considered as the sources of damage initiation. Both tensile and compressive cracks are investigated. For analysis of crack propagation, two different methodologies are employed; the Constitutive Law with Embedded Discontinuity (CLED) and the Extended Finite Element Method (XFEM). The CLED approach is enhanced here to describe the discrete nature of crack propagation. This is done by coupling the CLED with explicit modeling of crack path using the Level-Set method. The XFEM is used as a verification tool to check the results from CLED analysis. An algorithm is proposed for crack initiation and propagation that results in stable and a mesh-independent solution. The CLED approach is further improved by developing the return-mapping and closest-point projection algorithms. Extensive numerical investigations are conducted that include mode I cracking in a three point bending test, mode I cracking in notched cantilever beam, mixed cracking mode in a plate subjected to shear and tension, and a mixed mode cracking in a notched beam under four point loading. For frictional interfaces, the shear band formation in a sample subjected to bi-axial compression and the shear band formation in a geo-slope are studied. The thesis also addresses the topic of the response of unsaturated cohesive soils undergoing an infiltration process. The problem is approached within the framework of Chemo-Plasticity. It is assumed that the complex chemo-mechanical interactions are the controlling factors for degradation of strength parameters during this process. A return mapping integration scheme is developed and the approach is employed to investigate the stability of a geoslope subjected to a heavy rainfall. Analysis of shear band formation is further investigated in the context of sedimentary rocks. The microstructure tensor approach is used to describe the inherent anisotropy in this class of materials. The orientation of the shear band is defined by invoking the Critical Plane approach and the closest-point projection algorithm is developed for numerical integration of the governing constitutive relations. The model is used along with CLED for analysis of the mechanical response of Tournemire argillite. It is shown that the friction between loading platens and sample can play an important role in the process of shear band formation and the associated assessment of the ultimate load. A mesh-sensitivity analysis employing the CLED framework is also conducted here. The research clearly demonstrates that the discrete representation of crack path propagation is essential for an accurate analysis of failure in various engineering structures. It is shown that if the classical smeared Constitutive Law with Embedded Discontinuity is enhanced to simulate the discrete nature of the damage process, it can yield very accurate results that are virtually identical to those obtained from discrete approaches such as XFEM. / Thesis / Candidate in Philosophy

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Constitutive laws commonly used to model friction stir welding have been evaluated, both qualitatively and quantitatively, and a new application of a constitutive law which can be extended to materials commonly used in FSW is presented. Existing constitutive laws have been classified as path-dependent or path-independent. Path-independent laws have been further classified according to the physical phenomena they capture: strain hardening, strain rate hardening, and/or thermal softening. Path-dependent laws can track gradients in temperature and strain rate characteristic to friction stir welding; however, path-independent laws cannot. None of the path-independent constitutive laws evaluated has been validated over the full range of strain, strain rate, and temperature in friction stir welding. Holding all parameters other than constitutive law constant in a friction stir weld model resulted in temperature differences of up to 21%. Varying locations for maximum temperature difference indicate that the constitutive laws resulted in different temperature profiles. The Sheppard and Wright law is capable of capturing saturation but incapable of capturing strain hardening with errors as large as 57% near yield. The Johnson-Cook law is capable of capturing strain hardening; however, its inability to capture saturation causes over-predictions of stress at large strains with errors as large as 37% near saturation. The Kocks and Mecking model is capable of capturing strain hardening and saturation with errors less than 5% over the entire range of plastic strain. The Sheppard and Wright and Johnson-Cook laws are incapable of capturing transients characteristic of material behavior under interrupted temperature or strain rate. The use of a state variable in the Kocks and Mecking law allows it to predict such transients. Constants for the Kocks and Mecking model for AA 5083, AA 3004, and Inconel 600 were determined from Atlas of Formability data. Constants for AA 5083 and AA 3004 were determined with the traditional Kocks and Mecking model; however, constants for Inconel 600 could not be determined without modification to the model. The temperature and strain rate combinations for Inconel 600 fell into two hardening domains: low temperatures and high strain rates exhibited twinning while high temperatures and low strain rates exhibited slip. An additional master curve was added to the Kocks and Mecking model to account for two hardening mechanisms. The errors for the Kocks and Mecking model predictions are generally within 10% for all materials analyzed.

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One of the important factors determining the lifetime of polymer electrolyte membrane fuel cells (PEMFCs) is membrane degradation and failure. The lack of effective mitigation methods is largely due to the currently very limited understanding of the underlying mechanisms for mechanical and chemical degradations of fuel cell membranes. In order to understand degradation of membranes in fuel cells, two different experimental approaches were developed; one is fuel cell testing under open circuit voltage (OCV) with bi-layer configuration of the membrane electrode assemblies (MEAs) and the other is a modified gas phase Fenton's test. Accelerated degradation tests for polymer electrolyte membrane (PEM) fuel cells are frequently conducted under open circuit voltage (OCV) conditions at low relative humidity (RH) and high temperature. With the bi-layer MEA technique, it was found that membrane degradation is highly localized across thickness direction of the membrane and qualitatively correlated with location of platinum (Pt) band through mechanical testing, Infrared (IR) spectroscopy, fluoride emission, scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy dispersive spectroscopy (EDS) measurement. One of the critical experimental observations is that mechanical behavior of membranes subjected to degradation via Fenton's reaction exhibit completely different behavior with that of membranes from the OCV testing. This result led us to believe that other critical factors such as mechanical stress may affect on membrane degradation and therefore, a modified gas phase Fenton's test setup was developed to test the hypothesis. Interestingly, the results showed that mechanical stress directly accelerates the degradation rate of ionomer membranes, implying that the rate constant for the degradation reaction is a function of mechanical stress in addition to commonly known factors such as temperature and humidity. Membrane degradation induced by mechanical stress necessitates the prediction of the stress distribution in the membrane under various conditions. One of research focuses was on the developing micromechanism-inspired continuum model for ionomer membranes. The model is the basis for stress analysis, and is based on a hyperelastic model with reptation-inspired viscous flow rule and multiplicative decomposition of viscoelastic and plastic deformation gradient. Finally, evaluation of the membrane degradation requires a fuel cell model since the degradation occurs under fuel cell operating conditions. The fuel cell model included structural mechanics models and multiphysics models which represents other phenomena such as gas and water transport, charge conservation, electrochemical reactions, and energy conservation. The combined model was developed to investigate the compression effect on fuel cell performance and membrane stress distribution.

<p dir="ltr">Defects in composite manufacturing often lead to compromised structural integrity and reduced performance of the final product. A robust constitutive modeling framework is needed to efficiently and accurately predict the deformation responses of dry fabrics and pre-impregnated fibers, paving the way for defect simulation. This thesis presents a comprehensive study on the development and application of a novel constitutive model of fabric preforms and pre-impregnated fibers during composite manufacturing processes.</p><p dir="ltr">This work proposes an integrated constitutive study for textile fabrics in the aspects of mesoscale tow and macroscale fabric behavior. First, a textile architecture-based discrete modeling approach was developed to predict and visualize fiber tow and fabric deformation. The fabrics consist of interlacing virtual fiber tows which are represented by Timoshenko beams joined by translational and rotational springs and rotary dashpots, which are used to capture the energy dissipation during in-plane shear deformation. Second, an anisotropic hyper-viscoelastic model was developed using the strain energy density function of a homogenized unit cell to predict the fabric deformation as a continuous field. A Maxwell model consisting of one Maxwell element and an additional spring is used to consider the nonequilibrium stresses generated during in-plane shear, transverse shear, and through-thickness compaction deformations. Both approaches were experimentally characterized and applied to a hemisphere draping model in the commercial Finite Element Analysis (FEA) software, Abaqus, to demonstrate the predictive capabilities.</p><p dir="ltr">Then, the robust hyper-viscoelastic model is extended to predict prepreg compaction and bending behavior. In the compaction aspect, a coupling term of energy that captures the effect of squeezing flow and a highly nonlinear transverse compression energy are proposed to predict the compaction response of prepreg with liquid and rubbery resin. The viscoelastic parameters were characterized by a Computational Fluid Dynamics (CFD) model for liquid resin and a discrete micromechanics model for rubbery resin. The method was applied to stepwise compaction simulation at different temperatures in Abaqus and compared to experiments for validation. In the bending aspect, the effective shear modulus is expressed as a function of the second-order gradient of deformation. Modeling parameters were characterized by an analytical model that captures the underlying fiber and matrix deformation mechanism. Parametric study was conducted to illustrate the influence of each parameter and the capability to enhance the accuracy of bending prediction.</p>

This dissertation investigates the rhetorical constitution of a religio-political social collective which has come to be understood as Christian Reconstruction (CR). CR is guided by conservative Calvinism (Reformed theology) and upholds the ideas of theonomy, postmillennialism, and presuppositional apologetics. Some of the leaders associated with CR are R. J. Rushdoony, Gary North, Gary DeMar of American Vision and Doug Phillips of Vision Forum. A few of its key practices are homeschooling, the father ‘returning home,’ and having as many children ‘as God will allow,’ (a vision aligned with the Quiverfull movement). It is primarily a national movement within the United States, not limited to a singular geographical location or denomination. This study provides a comprehensive overview of CR, illustrating how the grammars of CR are animated, embodied, and upheld in peoples’ lives and practices. Through the observation of conferences and events, and the collection and examination of media materials, this analysis takes a constructivist approach to piecing together the discursive fragments that constitute CR. CR grammar is richly embedded in a web of interaction, media, technology, images, bodily adornment, performance, music, games, and consumer culture. My theoretical framework utilizes the work of critical cultural theorists (Gramsci, 1971; Butler, 1990; Hall, 1976, Laclau, 2005) in combination with theories of constitutive (Burke, 1950; Charland, 1987; McGee, 1975) and visual rhetoric and display (Olson, Finnegan & Hope, 2008; Prelli, 2006; Selzer & Crowley, 1999) to examine the types of social, cultural, and political subjectivities, practices and institutions that are constituted within the CR community. It focuses primarily on the patriarchal identities within CR families as well as the focus on nationalistic teaching about Christian American history as methods for changing the culture of America. I consider the hegemonic machinations of CR grammars in constituting these identities. Finally, this study makes available a methodology and method for the study of dispersed “peoples” and their discursive lives. I demonstrate that multi-sited ethnography, combined with the theories of constitutive and visual rhetorics and critical cultural studies provides a systematic heuristic with which to inquire into a people, its culture, activities, identities, and how they constitute themselves.

There has been an increasing interest in fundamental and applied research on emerging geotechnical and geoenvironmental engineering applications that pose multi-physics problems involving non-isothermal processes in unsaturated soils. Properly studying these problems requires the development of analytical models to describe the constitutive behavior of unsaturated soils under non-isothermal conditions. However, major gaps remain in the development of unified models that can properly represent the temperature dependency of unsaturated soil behavior. The effects of temperature on the stability of slopes, lateral earth pressure, and pile resistance in unsaturated soils are also not well understood. The main objective of this study is to provide new insight and robust tools to characterize and model the temperature-dependent behavior of unsaturated soils. For this purpose, novel unified models are developed for soil water retention curve, effective stress, thermal conductivity function, and small-strain shear modulus for unsaturated soils at elevated temperatures. The models are proposed by establishing or extending the unified model at isothermal conditions to nonisothermal conditions. The fundamental and main variable in all unified models is capillary pressure (also referred to as matric suction). The effect of temperature is considered on adsorption and capillarity as a function of water-air surface tension, soil-water contact angle, and enthalpy of immersion. The proposed models are verified by comparing them with experimental data reported in the literature and measurements made in this study. Overall results of the proposed models show an excellent predictive capability. Furthermore, the parametric study is conducted to understand the effect of different parameters such as soil type, temperature, drainage conditions, and among others on hydraulic and mechanical properties of unsaturated soil. Finally, the proposed models are incorporated into geotechnical applications such as slope stability, lateral earth pressure, and pile resistance involving unsaturated conditions and elevated temperatures. The variation of temperature in unsaturated soils for these applications can be notable and cannot be ignored in the design and analysis. The proposed formulations can also be readily incorporated into analytical solutions and numerical simulations of thermo-hydro-mechanical processes in unsaturated soils. The findings of the study can facilitate using numerical models to simulate various non-isothermal applications including geo-energy systems and soil-atmospheric interaction problems.