The objective of this dissertation is to further the understanding of inelastic behavior in metallic materials. Despite the increasing use of polymeric composites in aircraft structures, high specific strength metals continue to be used in key components such as airframe, fuselage, wings, landing gear and hot engine parts. Design of metallic structures subjected to thermomechanical extremes in aerospace, automotive and nuclear applications requires consideration of the plasticity, creep and fracture behavior of these materials. Consideration of inelasticity and damage processes is also important in the design of metallic components used in functional applications such as thin films, flexible electronics and micro electro mechanical systems. Fracture mechanics has been largely successful in modeling damage and failure phenomena in a host of engineering materials. In the context of ductile metals, the Gurson void growth model remains one of the most successful and widely used models. However, some well documented limitations of the model in quantitative prediction of the fracture strains and failure modes at low triaxialities may be traceable to the limited representation of the damage microstructure in the model. In the first part of this dissertation, we develop an extended continuum model of void growth that takes into account details of the material microstructure such as the texture of the plastically deforming matrix and the evolution of the void shape. The need for such an extension is motivated by a detailed investigation of the effects of the two types of anisotropy on the materials' effective response using finite element analysis. The model is derived using the Hill-Mandel homogenization theory and an approximate limit analysis of a porous representative volume element. Comparisons with several numerical studies are presented towards a partial validation of the analytical model. Inelastic phenomena such as plasticity and creep result from the collective behavior of a large number of nano and micro scale defects such as dislocations, vacancies and grain boundaries. Continuum models relate macroscopically observable quantities such as stress and strain by coarse graining the discrete defect microstructure. While continuum models provide a good approximation for the effective behavior of bulk materials, several deviations have been observed in experiments at small scales such as an intrinsic size dependence of the material strength. Discrete dislocation dynamics (DD) is a mesoscale method for obtaining the mechanical response of a material by direct simulation of the motion and interactions of dislocations. The model incorporates an intrinsic length scale in the dislocation Burgers vector and potentially allows for size dependent mechanical behavior to emerge naturally from the dynamics of the dislocation ensemble. In the second part of this dissertation, a simplified two dimensional DD model is employed to study several phenomena of practical interest such as strain hardening under homogeneous deformation, growth of microvoids in a crystalline matrix and creep of single crystals at elevated temperatures. These studies have been enabled by several recent enhancements to the existing two-dimensional DD framework described in Chapter V. The main contributions from this research are: (i) development of a fully anisotropic continuum model of void growth for use in ductile fracture simulations and (ii) enhancing the capabilities of an existing two-dimensional DD framework for large scale simulations in complex domains and at elevated temperatures.

The focus of this dissertation is on constant displacment rate experiments on asphalt concrete and on developing continuum models in a general thermo-mechanical setting which will corroborate with the experimental results. Modeling asphalt concrete and predicting its response is of great importance to the pavement industry. More than 90 percent of the US Highways uses asphalt concrete as a pavement material. Asphalt concrete exhibits nonlinear response even at small strains and the response of asphalt concrete to different types of loading is quite different. The properties of asphalt concrete are highly influenced by the type and amount of the aggregates and the asphalt used. The internal structure of asphalt concrete keeps on evolving during the loading process. This is due to the influence of different kinds of activities at the microlevel and also due to the interaction with the environment. The properties of asphalt concrete depend on its internal structure. Hence we need to take the evolution of the internal structure in modeling the response of asphalt concrete. Experiments were carried out at different confinement pressures and displacement rates on cylindrical samples of asphalt concrete. Two different aggregates were used to make the sample -limestone and granite. The samples were tested at a constant displacement rate at a given confinement pressure. The force required to maintain this constant displacement rate is measured and recorded. The frame-work has been developed using the idea of multiple natural configurations that was introduced recently to study a variety of non-linear dissipative response of materials. By specifying the forms of the stored energy and rate of dissipation function of the material, specific models were developed using this frame work. In this work both a compressible and an incompressible model were developed by choosing appropriate forms of stored energy and rate of dissipation function. Finally the veracity of the models were tested by corroborating with the experimental results. It is anticipated that the present work will aid in the development of better constitutive equations which in turn will accurately model asphalt concrete in laboratory and in field.

All materials are heterogeneous at various scales of observation. The influence of material heterogeneity on nonuniform response and microstructure evolution can have profound impact on continuum thermomechanical response at macroscopic "engineering" scales. In many cases, it is necessary to treat this behavior as a multiscale process. This research developed a hierarchical multiscale approach for modeling microstructure evolution. A theoretical framework for the hierarchical homogenization of inelastic response of heterogeneous materials was developed with a special focus on scale invariance principles needed to assure physical consistency across scales. Within this multiscale framework, the second gradient is used as a nonlocal kinematic link between the response of a material point at the coarse scale and the response of a neighborhood of material points at the fine scale. Kinematic consistency between two scales results in specific requirements for constraints on the fluctuation field. A multiscale internal state variable (ISV) constitutive theory is developed that is couched in the coarse scale intermediate configuration and from which an important new concept in scale transitions emerges, namely scale invariance of dissipation. At the fine scale, the material is treated using finite element models of statistical volume elements of microstructure. The coarse scale is treated using a mixed-field finite element approach. The coarse scale constitutive equations are implemented in a finite deformation hyperelastic inelastic integration scheme developed for second gradient constitutive models. An example problem based on an idealized porous microstructure is presented to illustrate the approach and highlight its predictive utility. This example and a few variations are explored to address the boundary-value-problem dependent nature of length scale parameters employed in nonlocal continuum theories. Finally, strategies for developing meaningful kinematic ISVs, free energy functions, and the associated evolution kinetics are presented. These strategies are centered on the goal of accurately representing the energy stored and dissipated during irreversible processes.

L'activité constitutive est une propriété pharmacologique que possèdent de nombreuxrécepteurs couplés aux protéines G. Cependant, son rôle biologique reste largement inconnu.Nous avons étudié les relations entre la pharmacologie et le trafic intracellulaire du récepteurcannabinoïque CB1, un récepteur abondamment exprimé dans le cerveau qui possède uneactivité constitutive avérée. Exprimé dans les cellules HEK-293, l'activité constitutive durécepteur CB1 provoque un cycle continu d'endocytose et de recyclage du récepteur entre lamembrane plasmique et les endosomes intracellulaires : à l'équilibre, le récepteur CB1 estmajoritairement présent dans les endosomes. Le cycle fait intervenir une endocytose par puitsrecouverts de clathrine et un trafic intracellulaire dépendant de Rab5 et de Rab4, mais pas deRab11. Dans les neurones d'hippocampe en culture, ce cycle d'endocytose/recyclage durécepteur CB1 est limité au compartiment somatodendritique, et le récepteur est stable à lasurface de l'axone. Ce cycle dépend de l'activité constitutive du récepteur CB1 etl'endocytose sélective du récepteur dirige l'établissement de l'expression axonale durécepteur CB1 à la surface du neurone.

Granular materials exist in many forms in nature ranging from space debris to sand dunes and from breakfast cereals to pharmaceutical tablets. They can behave like a solid or a viscous fluid or a gas. The gas-like nature of granular materials in rapid flows allows the use of models based on kinetic theory thus revealing in depth complex physics and phenomena. However unlike conventional fluids here the energy balance requires additional dissipation terms as a consequence of inelasticity. The complexity of their interaction and diversity in application has led to numerous studies using experimental methods and numerical simulations in order to determine the most appropriate constitutive relationships for granular gases. With large dissipation the form of the constitutive relationship becomes particularly important, especially in the presence of non-equipartition and anisotropy. This thesis is focused on constitutive models of simple granular flows. A vibrated bed is often used as an idealisation of granular flows, providing a convenient approximation to the simplest type of flow: binary and instantaneous collisions with no rotations. Using finite element method (FE) based COMSOL modules we solve conservation of mass, momentum and energy resulting from granular kinetic theory in axi-symmetric form to generate time and spatial resolved solutions of packing fraction, velocity and granular temperature and compare the predictions to numerical simulation and experiment. At first we show the comparison for two closure sets, one based on a simple near elastic approach while the second based on revised Enskog theory for dense inelastic flows. The results for the second approach show good agreement with the results of previously validated near elastic models and experimental results. The observed differences between the two closure sets are small except for the observation of temperature upturn in a dilute region of the cell away from base. One cause of this is the presence of additional constitutive terms in the balance equations and are a consequence of inelasticity. The models also consider time varying effects at low frequency of excitation. These solutions show existence of wave-like effects in the cell with associated temperature upturn within the hydrodynamic applicability region. Presence of instantaneous cyclic rolling is also seen in both approaches. Evidence from MD simulations and experiments qualitatively support the findings of hydrodynamic models in phase resolved as well as time average behaviour. Subsequently, the frequency of vibration was varied to unlink the wave motion from the bulk temperature. Lack of agreement between experiment and the model predictions are shown to be due to lack of separation of time scale between the grain-base interaction and the base frequency. A sharp decrease of heat flux is measured showing that the energy input is frequency dependent. Analysis of the bulk behaviour shows that at high frequency, hard sphere based models are able to capture the steady state behaviour reasonably well. Further investigations that modulate the driving with a low frequency amplitude change revealed the dynamic nature of flow with the low frequency component. No significant influence of high frequency signal is noted except the reduction of base heat flux. Independent analysis of bulk behaviour for modulated wave excitation using MD simulations and hydrodynamic models showed wave motion in a pattern similar to non-modulated low frequency vibration. A one-dimensional inviscid model was used to determine the underlying scaling relationships for near elastic granular flows. A form of non-dimensionalisation predicts scaling behaviour for the granular flow. The predictions show good results for the dilute flows using hard sphere MD simulations. Results from MD simulations confirm dilute limit scaling of base temperature, packing fractions and heat flux coefficients. At higher inelasticity and loading condition the model fails to capture the real physics suggesting the need for a more accurate model. This simplified model does, however, set the basis for describing the main scalings for vibrofluidized granular beds, and in the future we anticipate that effects of further inelasticity and enhanced density could be incorporated.

Deregulation of platelet-derived growth factor receptor (PDGFR) signaling is a driving event in glioblastoma, promotes tumor progression epithelial to mesenchymal transition (EMT) in multiple cancers, modulates the tumor stroma to facilitate tumorigenesis and reduces tumor uptake of chemotherapeutics. Previous studies identified the 105 kDa isoform of ankyrin3 (Ank105) as a binding partner of the PDGFR signaling machinery and demonstrated that expression of Ank105 promoted PDGFR degradation (Ignatiuk et al., 2006)(Ignatiuk et al., 2006)(Ignatiuk et al., 2006). Receptor tyrosine kinases are targeted for degradation via endocytosis and ubiquitin-dependent trafficking to the lysosome. It was hypothesized that Ank105 promoted the constitutive degradation of the PDGFR and attenuation of PDGFR signaling by facilitating endocytosis of the PDGFR and targeting the PDGFR for lysosomal degradation via an ubiquitin-dependent mechanism. The studies in this thesis characterized the effects of Ank105 expression on PDGFR signaling and protein expression levels, determined the endocytic pathways involved in Ank105-mediated PDGFR degradation and studied the role of ubiquitin binding in Ank105 function. The most robust effect of Ank105 expression on the PDGFR was constitutive degradation as PDGFR protein expression levels in Ank105-expressing cells were significantly reduced compared to NIH 3T3 cells in the absence of PDGF ligand. Low constitutive PDGFR levels resulted in attenuated pro-proliferative AKT and mitogen-activated protein kinase (MAPK) signaling in response to ligand stimulation. To determine the endocytic requirements for Ank105-mediated constitutive PDGFR degradation, a constitutive PDGFR degradation assay was developed and the effects of several small molecule endocytosis inhibitors were evaluated. Additionally, the small molecule endocytosis inhibitors were validated by determining the effects of these inhibitors on low density lipoprotein (LDL) uptake and ligand-induced PDGFR degradation in Ank105-expressing cells. Both LDL uptake and ligand induced PDGFR degradation are known to proceed by a clathrin and dynamin dependent mechanism of endocytosis. In Ank105-expressing cells, both LDL uptake and ligand incuded PDGFR degradation were dependent upon clathrin and dynamin function. Interestingly, constitutive PDGFR degradation in Ank105-expressing cells was not dependent upon CME, but required dynamin activity. Expression of Ank105 may promote clathrin-independent, dynamin-dependent, constitutive endocytosis of the PDGFR. Additionally, acute inhibition of either lysosomal or proteasomal degradation strongly impaired constitutive PDGFR degradation, whereas ligand-induced PDGFR degradation was less sensitive to protein degradation inhibitors, while LDL uptake was unaffected. It was unclear if PDGFR was degraded in the proteasome or if the proteasome was involved in sorting of PDGFR to the lysosome for degradation. Ubiquitination of receptors is required to target them for degradation. Ank105 was assayed for the ability to interact with ubiquitin and ubiquitinated proteins. Interestingly, Ank105 bound ubiquitin in vitro via the spectrin binding domain and co-immunoprecipitated with several ubiquitinated proteins, suggesting a role for Ank105 in the sorting of ubiquitinated proteins for degradation. Furthermore, Ank105 co-immunoprecipitated with a number of high and low molecular weight proteins in the absence of PDGF stimulation. Identification of Ank105 binding partners would provide further insight in the mechanism of Ank105-mediated constitutive PDGFR degradation. In summary, Ank105 promoted the attenuation of PDGFR signaling via alteration of constitutive PDGFR endocytosis and targeting of constitutive PDGFR for degradation, potentially through interaction with ubiquitin and ubiquitinated proteins. Reduction of constitutive PDGFR levels in cancers with PDGFR driver mutations, acquired PDGF responsiveness and stromal expression of PDGFR, could significantly reduce tumor proliferation, tumorigenesis and increase effectiveness of chemotherapeutics.

Pile foundations that support offshore structures are required to resist not only static loading, but also dynamic loading from waves, wind and earthquakes. The purpose of this study is to gain a better understanding of the behavior of offshore piles under cyclic or dynamic loading using the finite element approach. To achieve this goal, an appropriate constitutive model is required to simulate the behavior of soils and interfaces. The DSC constitutive model is developed for saturated interfaces to study the behavior under severe shear deformation at the soil-pile interface. Monotonic and cyclic simple shear experiments are conducted on Ottawa sand-steel interfaces under drained and undrained conditions using the Cyclic-Multi-Degree-of-Freedom shear device with porewater pressure measurement (CYMDOF-P). The effect of various parameters such as normal stress, surface roughness of steel, type of loading, and the amplitude and frequency of the applied displacement in two-way cyclic loading are investigated. The data from the simple shear tests on saturated interfaces are used to calculate the parameters in the DSC model. The resulting parameters are then used to verify the DSC model by back predicting tests from which parameters are determined and independent tests that are not used in parameters determination. The model predictions, in general, were found to provide a highly satisfactory correlation with the observations. In the context of DSC, the concept of critical disturbance is developed to identify initiation of liquefaction in saturated Ottawa sand-steel interfaces. This method is based on using microstructural changes in material as an indication of liquefaction identification. The finite element method, along with DSC constitutive model, is used to investigate the response of offshore piles to dynamic loading. These include cyclic loading of axially loaded instrumented pile in clay and full-scale laterally loaded pile in sand. The DSC model is used to model the nonlinear behavior of saturated soils and interfaces. A nonlinear dynamic finite element program DSC-DYN2D based on the DSC modeling approach and the theory of nonlinear porous media is used for this purpose. Results from numerical solutions are compared with field measurements. Strong agreement between numerical predictions and field measurements are an indication of the ability to solve challenging soil-structure interaction problems.Based on the results of this research, it can be stated that the finite element-DSC model simulation allows realistic prediction of complex dynamic offshore pile-soil interaction problems, and is capable of characterizing behavior of saturated soils and interfaces involving liquefaction.

In the present study, a computational method was developed, validated and applied for the determination of parameters of a constitutive model for a ceramic material. An optimization algorithm, based on a direct search method, was applied to the determination of the load-displacement response of the specimen, and for the identification of the parameters of the constitutive model.A one-dimensional nonlinear initial-boundary value problem of wave propagation in a composite bar made of dissimilar materials was formulated and solved numerically. Convergence of the numerical scheme was studied, and range of convergence was established. Numerical scheme was validated for a number of benchmark problems with known analytical solutions, and for the problems solved using finite element method. Investigation of the accuracy of the displacement and strain responses was conducted; known limitations of the Kolsky's method for split Hopkinson pressure bar were revealed. For numerical examples considered in the present study, comparison of performance of the optimized finite-difference solver and of the finite element code LS-DYNA showed that the finite-difference code is about 10 times faster.Developed method and solutions were applied for the identification of the parameters of the Johnson-Holmquist constitutive model for five sets of experimental data for aluminum oxide AD995. Results of analysis revealed significant sensitivity of stress response to variation of fractured strength model parameters and damage model parameters.For the determined values of parameters, detailed parametric study of stress field, damage accumulation, and velocity field, was conducted with the help of the finite element method.It was found that the accuracy of the simulation using the JH-2 constitutive model changes with the rate of damage accumulation in the ceramic material.The damage patterns and history of damage development, obtained numerically, agreed qualitatively with the fracture history and its patterns, observed in the recovered Macor ceramics available in the literature.A method for image analysis of the photographic images of the lateral sides of the recovered specimen was proposed. It was used to quantify density of the damage in the specimen and to establish a better integral approach to predict amount of damage inside the specimen.

The disturbed state concept (DSC) based constitutive model is the focus of this research. It is applied for characterizing two problems; thermomechanical reliability analysis of electronic packages, and prediction of glacial motion. A new procedure for construction of static yield surface for materials is proposed. Further, a modified DSC model to include effect of rate of loading on material behavior is proposed.The DSC is applied to characterize the behavior of Sn-3.9Ag-0.6Cu (SAC) lead free solder alloy used in electronic packages. Proposed procedure of construction of static curve and rate dependent DSC model is applied for prediction of creep and rate dependent behavior of the SAC alloy. Laboratory test data is adopted from the literature and material parameters are determined. The DSC model is validated using the derived material parameters. A finite element analysis of the BGA 225 package is performed under cyclic thermomechanical loading. Analysis results are compared with available test data. A failure criterion for prediction of number of cycles to failure for BGA 225 is then derived.The second application of DSC discussed in this work is prediction of glacial motion. Mechanical behavior of glacial till and its contribution to overall ice movement is characterized using DSC. Two regionally significant tills are chosen and samples are collected from field. A series of laboratory tests are conducted on samples. Tests results are used for model calibration and validation. A numerical simulation of an idealized ice - till system under gravity loading is performed. Two such analyses are performed with DSC and Mohr Coulomb models and the results are compared.The DSC predicts failure when a significant portion of the material reaches a critical disturbance whereas the Mohr Coulomb model predicts failure based on peak stress. DSC predicts a gradual progression to failure whereas the Mohr Coulomb model predicts early catastrophic failure. According to DSC, the material undergoes considerable plastic strains before it reaches failure whereas the Mohr Coulomb predicts failure at very low elastic strains. In general the DSC is considered to provide a more realistic and general constitutive model for glacial tills.

The occurrence of hot tearing during solidification is one of the major factors influencing both the quality and productivity of aluminum castings. In order to reduce the formation of hot tears, quantitative information regarding both hot tearing formation and semi-solid deformation is essential. In this study, the mechanisms of hot tearing and semi-solid deformation have been investigated via two novel techniques: x-ray micro-tomography on material deformed in the semi-solid region, and development of a three phase microstructural model based on a geometry derived from a Voronoi diagram with rounded corners and porosity. Numerical techniques were utilized to quantify both the size evolution and orientation of internal damage relative to void growth. In order to conduct the above research, a new semi-solid tensile deformation methodology was devised which uses a two thermocouple control technique to enable accurate measurement of semi-solid tensile strength and ductility. The experimental work was conducted on the aluminum – magnesium alloy AA5182 in the as-cast and hot isostatic pressing (HIP) states. The x-ray micro-tomography technique was used to observe that semi-solid deformation is accommodated by internal damage via growth of as-cast porosity and the nucleation of new damage-based voids. As the volume fraction of damage increases, the growth of voids occurs in an orientation perpendicular to the loading direction, both through expansion within the grain boundary liquid and via coalescence between voids. The damage then localizes, causing failure. The finite element semi-solid microstructural model was used to explore the effects of fraction solid, fraction porosity, and grain size on semi-solid constitutive behaviour. The simulations revealed that increased grain size and fraction porosity lead to a reduction in flow stress for a given fraction solid. Furthermore, local strain accumulation was linked to hot tearing, since strain localizes in the liquid very early in the deformation process. Based on the model predictions, a new constitutive relationship was developed over the range 0.75 < fs < 0.95. Together, these two techniques have provided powerful new insight, such as the critical role played by as-cast porosity, on the phenomena of hot tearing and semi-solid deformation in aluminum alloys.