The problem of damage accumulation in laminated composite materials hasreceived much attention due to their widespread application in the aerospace, automotive,civil, and sports industries. In the aerospace industry, composites are usedto make light weight and efficient structural components. In the Boeing 787, forexample, more than 50% of the structure is made of composite materials. Althoughthere have been significant developments in analyzing cross-ply laminates, none ofthe present approaches provides reasonable predictions for multidirectional laminatesin which intralaminar cracks may form in multiple orientations. Nevertheless, theprediction of damage accumulation and its effect on structural performance is a verydifficult problem due to complexity of the cracking processes.This study presents a synergistic damage mechanics (SDM) methodology to analyzedamage behavior in multidirectional composite laminates with intralaminarcracks in plies of multiple orientations. SDM combines the strengths of micro-damagemechanics (MDM) and continuum damage mechanics (CDM) in predicting the stiffness degradation due to these cracks. The micromechanics is performed on a representativeunit cell using a three-dimensional finite element analysis to calculate thecrack opening displacement accounting for the influence of the surrounding plies, theso-called constraint effect. This information is then incorporated in the CDM formulationdealing with laminates containing cracks in different ply orientations through a `constraint parameter'. Following CDM, a separate damage mode is defined for eachtype of crack and the expressions for engineering moduli of the damaged laminateare then derived in terms of crack density and the constraint parameter. The SDMmethodology is implemented for [0m/±θn/0m/2]s laminates containing cracks in ±θplies. It is then extended to [0m/±θn/90r]s and [0m/90r/±θn]s laminates with cracksadditionally in the 90°-plies. The predictions agree well with published experimentaldata as well as independent FE computations. Limited parametric studies areperformed to show usability of SDM for more general laminates.To predict the initiation and growth of intralaminar cracks, an energy basedmodel is proposed in which these cracks initiate and multiply when the work requiredto form new set of cracks exceeds a laminate dependent critical energy release rate.The approach requires determination of average crack opening and sliding displacementsat varying crack spacing. This task is performed through a suitable 3-D FEanalysis. In case of off-axis ply cracking, a mixed mode fracture criterion is utilized,where the critical energy release rates in normal and shear modes are determinedby fitting the damage model with the experimental data for a reference laminate.The predictions from the model for [0/± θ4/01/2]s and [0/90/ ± 45]s laminates showremarkable agreement with the experimental results.The methodology and the results covered in this dissertation will be of interest tomechanics of materials researchers as well as to engineers in industry where compositematerials for structural applications are of interest.

This thesis presents a continuum model for asphalt concrete incorporating non- linear viscoelasticity, viscoplasticity, mechanically-induced damage and moisture- induced damage. The Schapery single-integral viscoelastic model describes the nonlinear viscoelastic response. The viscoplastic model of Perzyna models the time- dependent permanent deformations, using a Drucker-Prager yield surface which is modified to depend on the third deviatoric stress invariant to include more complex dependence on state of stress. Mechanically-induced damage is modeled using continuum damage mechanics, using the same modified Drucker-Prager law to determine damage onset and growth. A novel moisture damage model is proposed, modeling moisture-induced damage using continuum damage mechanics; adhesive moisture- induced damage to the asphalt mastic-aggregate bond and moisture-induced cohesive damage to the asphalt mastic itself are treated separately. The analytical model is implemented numerically for three-dimensional and plane strain finite element analyses, and a series of simulations is presented to show the performance of the model and its implementation. Sensitivity studies are conducted for all model parameters and results due to various simulations corresponding to laboratory tests are presented. In addition to the continuum model, results are presented for a micromechanical model using the nonlinear-viscoelastic-viscoplastic-damage model for asphalt mastic and a linear elastic model for aggregates. Initial results are encouraging, showing the strength and stiffness of the mix as well as the failure mode varying with moisture loading. These initial results are provided as a an example of the model's robustness and suitability for modeling asphalt concrete at the mix scale.

A local isotropic damage coupled hyperelastic-plastic framework is formulated in principal axes where thermo-mechanical extensions are also addressed. It is shown that, in a functional setting, treatment of many damage growth models, including ones originated from phenomenological models (with formal thermodynamical derivations), micro-mechanical models or fracture criteria, proposed in the literature, is possible. Quasi-unilateral damage evolutionary forms are given with special emphasis on the feasibility of formulations in principal axes. Local integration procedures are summarized starting from a full set of seven equations which are simplified step by step initially to two and finally to one where different operator split methodologies such as elastic predictor-plastic/damage corrector (simultaneous plastic-damage solution scheme) and elastic predictor-plastic corrector-damage deteriorator (staggered plasticdamage solution scheme) are given. For regularization of the post peak response with softening due to damage and temperature, Perzyna type viscosity is devised. Analytical forms accompanied with algorithmic expressions including the consistent material tangents are derived and the models are implemented as UMAT and UMATHT subroutines for ABAQUS/Standard, VUMAT subroutines for ABAQUS/Explicit and UFINITE subroutines for MSC.Marc. The subroutines are used in certain application problems including numerical modeling of discrete internal cracks, namely chevron cracks, in direct forward extrusion process where comparison with the experimental facts show the predicting capability of the model, isoerror map production for accuracy assessment of the local integration methods, and development two novel necking triggering methods in the context of a damage coupled environment.

Purpose of this work is to provide a comprehensive picture of thin film (interconnect) and solid droplet surface evolution under the several external applied forces with anisotropic physical properties so that one can eventually be able to predict main reasons and conditions under which stability of surface is defined. A systematic study based on the self-consistent dynamical simulations is presented for the spontaneous surface evolution of an thin film and isolated thin solid droplet on a rigid substrate, which is driven by the surface drift diffusion induced by the anisotropic diffusivity, the anisotropic capillary forces (surface stiffness) and mismatch stresses under electron winding. The effect of surface free energy anisotropies (weak and strong (anomalous)) on the development kinetics of the Stranski-Krastanow island type morphology are studied. Although, various tilt angles and anisotropy constants were considered during simulations, the main emphasis was given on the effect of rotational symmetries associated with the surface Helmholtz free energy topography in 2D space. The investigations of dynamics of surface roughness on concurrent actions of the appliedelasto- and electro- static fields clearly indicate that applied misfit stress level is highly important effect on resultant surface form which may be smooth wave like or crack like. The droplet simulations revealed the formation of an extremely thin wetting layer during the development of the bell-shaped Stranski-Krastanow island through the mass accumulation at the central region of the droplet via surface drift-diffusion. The developments in the peak height, in the extension of in the wetting layer beyond the domain boundaries, and the change in triple junction contact angle, one clearly observes that these quantities are reaching certain saturation limits or plateaus, when the growth mode turned-off. Islanding differences for weak anisotropy constant levels and the strong (anomalous) anisotropy constant domains are discussed.

Existing macroscopic models for the flow of traffic treat traffic as a continuum or employ techniques similar to those used in the kinetic theory of gases. Spurious two- way propagation of disturbances that are physically unacceptable are predicted by continuum models for the flow of traffic. The number of vehicles in a typical section of a freeway does not justify traffic being treated as a continuum. It is also important to recognize that the basic premises of kinetic theory are not appropriate for the flow of traffic. A model for the flow of traffic that does not treat traffic as a continuum or use notions from kinetic theory is developed in this dissertation and corroborated with traffic data collected from the sensors deployed on US 183 freeway in Austin, Texas, USA. The flow of traffic exhibits distinct characteristics under different conditions and reflects the congestion during peak hours and relatively free motion during off-peak hours. This requires one to use different governing equations to describe the diverse traffic characteristics, namely the different traffic flow regimes of response. Such an approach has been followed in this dissertation. An observer based on extended Kalman filtering technique has been utilized for the purpose of estimating the traffic state. Historical traffic data has been used for model calibration. The estimated model parameters have consistent values for different traffic conditions. These esti- mated model parameters are then subsequently used for estimation of the state of traffic in real-time. A short-term traffic state forecasting approach, based on the non-continuum traffic model, which incorporates weighted historical and real-time traffic information has been developed. A methodology for predicting trip travel time based on this approach has also been developed. Ten and fifteen minute predictions for traffic state and trip travel time seem to agree well with the traffic data collected on US 183.

This work presents a three dimensional elastic-plastic model for two hemispherical bodies sliding across one another under various preset vertical interferences. In particular, steel-on-steel and aluminum-on-copper contact situations are considered. A finite element analysis is used for the model and the parameters to investigate include stresses, deformations, contact areas, and energy loss in sliding. Both frictional and frictionless sliding are investigated. In addidition to structural loads, electromagnetic loads are considered and a framework for a electromagneticlly, structurally, and thermally coupled model is investigated.

Two topics involving irradiation damage in alpha-iron have been considered. First, damage cascades representative of those that would be induced by radiation have been simulated using molecular dynamics (MD). The number and type of defects produced are compared for pure iron and iron with a small hydrogen concentration. Second, the inter- action energy between point defects and line dislocations has been calculated for a number of configurations, using both molecular statics methods and calculations based on linear elastic continuum theory and the dipole force tensor. Results from both methods are com- pared. Results from these two topics are relevant for predicting macroscopic behaviors such as creep and plasticity in reactor structural materials.

This work begins by establishing the necessary and sufficient conditions for hygrothermal stability of composite laminates. An investigation is performed into the range of coupling achievable from within all hygrothermally stable families. The minimum number of plies required to create an asymmetric hygrothermally stable stacking sequence is found to be five. Next, a rigorous and general approach for determining designs corresponding to optimal levels of coupling is established through the use of a constrained optimization procedure. Couplings investigated include extension-twist, bend-twist, extension-bend, shear-twist, and anticlastic. For extension-twist and bend-twist coupling, specimens from five- through ten-ply laminates are manufactured and tested to demonstrate hygrothermal stability and achievable levels of coupling. Nonlinear models and finite element analysis are developed, and predictions are verified through comparison with test results. Sensitivity analyses are performed to demonstrate the robustness of the hygrothermal stability and couplings to deviations in ply angle, typical of manufacturing tolerances. Comparisons are made with current state-of-the-art suboptimal layups, and significant increases in coupling over previously known levels are demonstrated.

For decades, epitaxy is used in nanotechnologies and semiconductor fabrications. So far, it's the only affordable method of high quality crystal growth for many semiconductor materials. Heterostructures developed from these make it possible to solve the considerably more general problem of controlling the fundamental parameters inside the semiconductor crystals and devices. Moreover, as one newly arising study and application branch of epitaxy, selective area growth (SAG) is widely used to fabricate materials of different thicknesses and composition on different regions of a single wafer. All of these new and promising fields have caught the interests and attentions of all the researchers around the world. In this work, we will study the stress and strain analysis of epitaxy in nano-scale materials, in which we seek a methodology to bridge the gap between continuum mechanical models and incorporate surface excess energy effects, which can be obtained by molecular dynamical simulations. We will make a brief description of the elastic behavior of the bulk material, covering the concepts of stress, strain, elastic energy and especially, the elastic constants. After that, we explained in details about the definitions of surface/interface excess energy and their characteristic property tensors. For both elastic constants and surface excess energy, we will use molecular dynamic simulations to calculate them out, which is mainly about curve-fitting the parabola function between the total strain energy density and the strain. After this, we analyzed the stress and strain state in nanoisland during the selective area growth of epitaxy. When the nanoisland is relaxed, the lattice structure becomes equilibrated, which means the total strain energy of system need to be minimized. Compared to other researcher's work, our model is based on continuum mechanics but also adopts the outcome from MD simulations. By combining these microscopic informations and those macroscopic observable properties, such as bulk elastic constants, we can provide a novel way of analyzing the stress and strain profile in epitaxy. The most important idea behind this approach is that, whenever we can obtain the elastic constants and surface property tensors from MD simulations, we can follow the same methodology to analyse the stress and strain in any epitaxy process. This is the power of combining atomistic simulations and continuum method, which can take considerations of both the microscopic and macroscopic factors.

Two multiscale continuum models for simulating protein dynamics are developed which allow for resolution of protein peptide planes in a beam-like finite element. A curvature and strain based finite element formulation is utilized. This formulation is advantageous in simulating proteins since amino acid chains may be described by a single element, even when the protein segment considered exhibits large curvature and twist such as the alpha-helical shapes prominent in many proteins. Specifically, concurrent and hierarchical multiscale models are developed for the curvature and strain based beam formulation. The hierarchical multiscale continuum model utilizes a novel shooting method to calculate the deformed configuration of the protein. An optimization algorithm determines the requisite stiffness parameters by varying the beam stiffness used in the shooting method until deformed configurations of test cases correspond to those produced by the LAMMPS molecular dynamics software. Additionally, a concurrent multiscale method is detailed for evaluating protein inter-atomic potential parameters from the curvature and strain degrees of freedom employed in the model. This allows internal forces and moments to be calculated using nonlinear protein potentials. Proof of concept testing and model verification for both models includes comparing the multiscale techniques to all-atom molecular dynamics solutions. Specifically, the models are verified by simulating a polypeptide in a vacuum and comparing the predicted results to those computed using LAMMPS.