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A fundamental study of the mechanics at the molecular scale and bridging it to the continuum level through multiscale modeling is the focus of this work. This work investigates how the material properties of nanoscale systems are influenced by the nonbonded interactions and molecular conformations. The molecular model is then bridged with the finite element model to link mechanics at nanoscale with the continuum scale. This work provides an unprecedented insight into how the interactions at the molecular scale influence mechanical properties at higher scales. Two materials are considered for the molecular modeling study: bone and Na-montmorillonite swelling clay. Bone is composed of composed of collagen molecules and hydroxyapatite in the molecular scale, which are organized into collagen fibril. The molecular dynamics study is carried out to study the nature of collagen-hydroxyapatite interface and the mechanics of collagen in bone. Furthermore, the molecular model of full-length collagen is built for the first time to show the differences in its conformation and deformation mechanism during pulling as compared to the short molecules, upon which the current understanding of is based. The mechanics of collagen is explained with the help of three-tier helical hierarchy not seen in short molecules. Two mechanisms of deformation and conformational stability of collagen are proposed: (i) interlocking gear analogy, and (ii) interplay between level-1 and level-2 hierarchies, the hydrogen bonds acting as an intermediary. The multiscale model of collagen fibril is developed by bridging nanomechanical molecular properties of collagen into the finite element model. This model shows that the molecular interactions between collagen and mineral significantly affect the mechanical response of collagen fibril. The deformation mechanism of collagen fibril and the effect of collagen crosslinks are also elucidated in this study. In recent years Na-montmorillonite has been proposed for bone regenerative medicine, besides other existing engineering applications. The molecular dynamics study of Na-montmorillonite at different levels of hydration is carried out to understand the role played by molecular interactions in the swelling behavior of Na-montmorillonite. This study greatly adds to our understanding of clay swelling, and provides important insights for modeling exfoliation and particle breakdown in clay. / NDSU Presidential Doctoral Graduate Fellowship / ND EPSCoR Doctoral Dissertation Assistantship

La magnétorésistance anisotrope (AMR) des matériaux ferromagnétiques est largement utilisée comme le phénomène de base pour la mesure ou la détection de champ magnétique. En raison de la relation entre la configuration en domaines magnétiques et la résistivité macroscopique, l'application d'un champ magnétique externe modifie la résistivité des matériaux ferromagnétiques. Bien que cet effet soit largement utilisé dans des applications industrielles, certains aspects fondamentaux du comportement AMR sont encore assez mal compris. Par exemple, le rôle de la texture cristallographique dans le comportement effectif n'est pas décrit avec précision par les outils classiques de modélisation. En raison de ce lien direct entre la microstructure en domaines et l'effet AMR, les modèles de description de l'effet AMR reposent généralement sur des calculs micromagnétiques. Pour ces calculs, le nombre de degrés de liberté et d'interactions peuvent se multiplier rapidement si on recherche à décrire un comportement macroscopique (cas des polycristaux par exemple).La thèse porte sur la modélisation numérique de l'effet de magnétorésistance anisotrope des matériaux ferromagnétiques. Ce nouvel outil de modélisation 3D peut remédier à cet inconvénient majeur des approches micromagnétiques. Un modèle permettant de décrire les effets de couplage magnéto-élastique en utilisant une approche micro-macro est disponible au laboratoire GeePs. Sur la base des mêmes principes de la modélisation micro-macro, un outil de simulation de l'effet AMR en fonction de la contrainte mécanique et de la texture cristallographique des matériaux a été développé.La stratégie de modélisation est la suivante:Trois échelles de description du comportement sont introduites: le Volume Elémentaire Représentatif (VER) polycristallin (échelle macro), le monocristal ou grain, et enfin le domaine magnétique (échelle micro).Une première étape dite de localisation permet de déterminer le chargement magnéto-mécanique (champ magnétique et contrainte mécanique) à l'échelle d'un grain en fonction du chargement extérieur appliqué. L'introduction de variables internes et des lois d'évolution correspondantes permet de décrire de façon statistique l'évolution de la microstructure en domaines magnétiques sous l'influence de ce chargement local. Toujours à cette échelle, l'utilisation du modèle phénoménologique de Doring permet, pour chaque domaine, de calculer la résistivité en fonction de l'orientation relative entre aimantation locale et courant électrique. Une fois cette résistivité locale connue, une étape dite d'homogénéisation s'appuyant sur le modèle de Bruggeman permet de déterminer la résistivité macroscopique du VER polycristallin. Il est ainsi possible de prédire la variation de la résistivité entre un état initial désaimanté et un état sous chargement magnéto-mécanique quelconque.Les résultats obtenus par cette démarche ont été comparés avec succès à des résultats expérimentaux extraits de la littérature portant sur des polycristaux de Nickel, de Fer pur ou encore de Permalloy.Ensuite des simulations reproduisant les conditions de fonctionnement des capteurs AMR ont été effectuées. Ces simulations permettent de conclure qu'il est possible d'améliorer la sensibilité des capteurs AMR en générant une contrainte résiduelle biaxiale. / The anisotropic magnetoresistance (AMR) of ferromagnetic materials is widely used as the basic phenomenon for measuring or detecting magnetic field. Owing to the relationship between magnetic domain configuration and macroscopic resistivity, the application of an external magnetic field changes the resistivity of ferromagnetic materials. Although this effect is widely used in industrial applications, some basic aspects of AMR behavior are still unsufficiently understood. For example, the role of crystallographic texture is not accurately described by conventional modeling tools. As a consequence of the direct relationship between microstructure and AMR, models for AMR effect are generally based on micromagnetic calculations. For these calculations, the number of degrees of freedom and interactions can grow exponentially when investigating macroscopic behavior (case of polycrystals for example).The thesis deals with the numerical modeling of AMR effect in ferromagnetic materials. This new 3D modeling tool can overcome this major drawback of micromagnetic approaches. A model to describe the effects of magneto-elastic coupling using a micro-macro approach is available at the laboratory GeePs. Based on the same principles of micro-macro modeling, an AMR effect simulation tool has been developed including the effect of mechanical stress and the role of crystallographic texture of materials.The modeling strategy is as follows:Three scales of description of the behavior are introduced: the Representative Volume Element (RVE) of polycrystals (macro scale), the single crystal or grain, and finally the magnetic domain (micro scale).A first step, named localization, determines the magneto-mechanical loading (magnetic field and mechanical stress) within a grain depending on the external applied load. The introduction of internal variables and corresponding evolution laws allow describing in a statistical way the evolution of the magnetic domain microstructure under the influence of the local load. Also at this scale, the use of the phenomenological Doring model allows for each area, to calculate the resistivity as a function of the relative orientation between local magnetization and electric current. Once this local resistivity is known, a so-called homogenization step based on the Bruggeman model is used to determine the macroscopic resistivity of the RVE. It is thus possible to predict the variation in resistivity between an initial demagnetized state and a state under any magneto-mechanical loading.The results obtained by this approach were successfully compared to experimental results from literature on polycrystalline nickel, pure iron or Permalloy.Then simulations reproducing AMR sensors operating conditions were carried out. These simulations lead to the conclusion that it is possible to improve the sensitivity of AMR sensors by introducing an appropriate biaxial residual stress.

Since its beginnings, the aerospace industry has been interested in lowering the weight of aircraft. Moving from performance and economic drivers to environmental design parameters, the weight has continuously been a major focus for this industry. A possible option to reduce weight is to use lighter materials such as fibre reinforced polymer composites (FRPC). This type of material has the potential to be used into cold or moderate high-temperature sections of aero-engines. One major obstacle that hinders composite insertion into aero-engines is the lack of predictive models. In recent years, there has been increasing interest in multiscale modelling as a possible approach to reliably predict composite behaviour. This modelling refers to the simulation of a material’s behaviour through multiple scales, passing on information from one scale to another. The purpose of the present work is to use a commercially available software tool (Altair Multiscale Designer™) to virtually characterize an FRPC made from a non-crimp fabric reinforcement based on its individual constituent properties. The studied composite was a carbon fibre and epoxy system developed by GKN Aerospace. In order to achieve this, a well-characterized unidirectional (UD) carbon fibre prepreg composite was used to calibrate the software. After calibration and verification, different repetitive unit cells were created to capture the non-crimp fabric (NCF) architecture where the effect of fibre waviness was studied. The calibration step allowed for fairly accurate and acceptable results when testing unidirectional or ±45 laminates with different tested UD prepreg material systems. The higher deviation from experimental values was up to 20% with these laminates’ configurations. When simulating more complex layups, such as quasi-isotropic ones, the simulations resulted in over-predicting up to 40% of the composite strength in comparison to experimental data. The study of NCF composites appeared to be more complicated than anticipated. Their complex architecture exhibits complicated failure modes, which could not be captured by the software tool. Large inaccuracy up to 100% were observed between simulation and experimental values of the laminate strengths. In spite of its limitations, the study of NCF composites allowed for a deeper understanding of the software functionalities and findings on the fibre waviness impact onto the predicted stiffness, while the strength of the laminate did not show dependency with the fibre waviness.

In this thesis we study a parameter identification problem for a stationary diffusion equation posed in heterogeneous media. This problem is closely related to the Calderón problem with anisotropic conductivities. The anisotropic case is particularly difficult and is ill-posed both in regards to uniqueness of solution and stability on the data. Since the present problem is posed in heterogeneous media, we can take advantage of multiscale modelling and the tools of homogenization theory in the study of the inverse problem, unlike the original Calderón problem. We investigate the possibilities of combining the theory of the Calderón problem with homogenization theory in order to obtain a well-posed parameter identification. We find that homogenization theory indeed can be used to make progress towards a well-posed identification of the diffusion coefficient. The success of the method is, however, dependent both on the precise structure of the heterogeneous media and on the modelling of the measurements in the invese problem framework. We have in mind a particular problem formulation which is motivated by an experiment to determine effective coefficients of materials used in food packaging. This experiment comes with a set of requirements on both the heterogeneous media and on the method for making measurements that, unfortunately, are in conflict with the currently available results for well-posedness. We study also an optimization approach to solving the inverse problem under these application specific requirements. Some progress towards well-posedness of the optimization problem is made by proving existence of minimizer, again with homogenization theory playing a key role in obtaining the result. In a proof-of-concept computational study this optimization approach is implemented and compared to two other optimization problems. For the two tested heterogeneous media, the only optimization method that manages to identify reasonably well the diffusion coefficient is the one which makes use of homogenization theory.

The present paper is devoted to the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme. On the given mesh we construct a wavelet basis providing vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates can be compressed to $\mathcal{O}(N\log N)$ relevant matrix coefficients, where $N$ denotes the number of unknowns. The compressed system matrix can be computed within suboptimal complexity by using techniques from the fast multipole method or panel clustering. Numerical results prove that we succeeded in developing a fast wavelet Galerkin scheme for solving the considered class of problems.

<div><div><div><p>The exceptional long-term performance of concrete is a primary reason that this material represents a significant portion of the construction industry. However, a portion of this construction material is prone to premature deterioration for multi-physical durability issues such as internal frost damage, restrained shrinkage damage, and aggregate susceptibility to fracture. Since each durability issue is associated with a unique damage mechanism, this study aims at investigating the underlying physical mechanisms individually by characterizing the mechanical and thermal properties development and indicating how each unique damage mechanism may compromise the properties development over the design life of the material.</p><p>The first contribution of this work is on the characterization of thermal behavior of porous media (e.g., cement-based material) with a complex solid-fluid coupling subject to thermal cycling. By combining Young-Kelvin-Laplace equation with a computational heat transfer approach, we can calculate the contributions of (i) pore pressure development associated with solidification and melting of pore fluid, (ii) pore size distribution, and (iii) equilibrium phase diagram of multiple phase change materials, to the thermal response of porous mortar and concrete during freezing/thawing cycles. Our first finding indicates that the impact of pore size (and curvature) on freezing is relatively insignificant, while the effect of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to -35 °C). Our second finding shows that porous cementitious composites containing lightweight aggregates (LWAs) impregnated with an organic phase change material (PCM) as thermal energy storage (TES) agents have the significant capability of improving the freeze-thaw performance. We also find that the phase transitions associated with the freezing/melting of PCM occur gradually over a narrow temperature range (rather than an instantaneous event). The pore size effect of LWA on freezing and melting behavior of PCM is found to be relatively small. Through validation of simulation results with lab-scale experimental data, we then employ the model to investigate the effectiveness of PCMs with various transition temperatures on reducing the impact of freeze-thaw cycling within concrete pavements located in different regions of United States.</p><div><div><div><p>The second contribution of this work is on quantification of mechanical properties development of cementitious composites across multiple length scales, and two damage mechanisms associated with aggregate fracture and restrained shrinkage cracking that lead to compromising the long-term durability of the material. The former issue is addressed by combining finite element method-based numerical tools, computational homogenization techniques, and analytical methods, where we observe a competing fracture mechanism for early- age cracking at two length scales of mortar (meso-level) and concrete (macro-level). When the tensile strength of the cement paste is lower than the tensile strength of the aggregate phase, the crack propagates across the paste. When the tensile strength of the cement paste exceeds that of the aggregate, the cracks begin to deflect and propagate through the aggregates. As such, a critical degree of hydration (associated with a particular time) exists below which the cement paste phase is weaker than the aggregate phase at the onset of hydration. This has implications on the inference of kinetic based parameters from mechanical testing (e.g., activation energy). Next, we focus on digital fabrication of a cement paste structure with controlled architecture to allow for mitigating the intrinsic damage induced by inherent shrinkage behavior followed by extrinsic damage exerted by external loading. Our findings show that the interfaces between the printed filaments tend to behave as the first layer of protection by enabling the structure to accommodate the damage by deflecting the microcrack propagation into the stable configuration of interfaces fabricated between the filaments of first and second layers. This fracture behavior promotes the damage localization within the first layer (i.e., sacrificial layer), without sacrificing the overall strength of specimen by inhibiting the microcrack advancement into the neighboring layers, promoting a novel damage localization mechanism. This study is undertaken to characterize the shrinkage-induced internal damage in 7-day 3D-printed and cast specimens qualitatively using X-ray microtomography (μCT) technique in conjunction with multiple mechanical testing, and finite element numerical modeling. As the final step, the second layer of protection is introduced by offering an enhanced damage resistance property through employing bioinspired Bouligand architectures, promoting a damage delocalization mechanism throughout the specimen. This novel integration of damage localization-delocalization mechanisms allows the material to enhance its flaw tolerant properties and long-term durability characteristics, where the reduction in the modulus of rupture (MOR) of hardened cement paste (hcp) elements with restrained shrinkage racking has been significantly improved by ~ 25% when compared to their conventionally cast hcp counterparts.</p></div></div></div></div></div></div>

In organizations with decision makers across multiple hierarchical levels, conflicting objectives are commonly observed. The decision maker, or agent, at the highest level usually makes decisions in the interest of the organization, while a subordinate agent may have a conflict of interest between taking a course of action that is best for the organization and the course of action that is best for itself. The Multiscale Decision-Making (MSDM) model was established by Wernz (2008). The model has been developed to capture interactions in multi-agent systems, by integrating both the hierarchical and temporal scale of decisions made in organizations. This thesis contributes towards expanding the results in the hierarchical interaction domain of MSDM by extending the model to incorporate N decision alternatives and outcomes instead of two, and studying its effect on the interaction between agents. We consider decisions with uncertain outcomes, where the outcomes of the decisions made by agents lower in hierarchy affect the transition probabilities of the decisions made by agents above them in hierarchy. This leads to a game theoretic situation, where the lower-level agents need to be sufficiently incentivized in order to shift their best response strategy to one in the interest of their superior and the organization. Mathematical expressions for the optimal incentives at each hierarchical level are developed. We analyze systems with agents interacting across two and three organizational levels. We then study the effect of introducing the cost of taking an action on the optimal incentives. We discuss a health care application of MSDM. / Master of Science

<div>Polymer matrices present in composite materials are prone to have time-dependent behavior very sensitive to changes in temperature. The modeling of thermoviscoelasticity is fundamental for capturing the performance of anisotropic viscoelastic materials subjected to both mechanical and thermal loads, or for manufacturing simulation of composites. In addition, improved plate/shell and beam models are required to efficiently design and simulate large anisotropic composite structures. Numerical models have been extensively used to capture the linear viscoelasticity in composites, which can be generalized in integral or differential forms. The hereditary integral constitutive form has been adopted by many researchers to be implemented into finite element codes, but its formulation is complex and time consuming as it is function of the time history. The differential formulation provides faster computation times, but its applicability has been limited to capture the behavior of three-dimensional thermoviscoelastic orthotropic materials.</div><div><br></div><div>This work extends mechanics of structure genome (MSG) to construct linear thermoviscoelastic solid, plate/shell and beam models for multiscale constitutive modeling of three-dimensional heterogeneous materials made of time and temperature dependent constituents. The formulation derives the transient strain energy based on integral formulation for thermorheologically simple materials subject to finite temperature changes. The reduced time parameter is introduced to relate the time-temperature dependency of the anisotropic material by means of master curves at reference conditions. The thermal expansion creep is treated as inherent material behavior. Exact three-dimensional thermoviscoelastic homogenization solutions are also formulated for laminates modeled as an equivalent, homogeneous, anisotropic solid. The new model is implemented in SwiftComp, a general-purpose multiscale constitutive modeling code based on MSG, to handle real heterogeneous materials with arbitrary microstructures, mesostructures or cross-sectional shapes.</div><div><br></div><div>Three-dimensional representative volume element (RVE) analyses and direct numerical simulations using a commercial finite element software are conducted to verify the accuracy of the MSG-based constitutive modeling. Additionally, MSG-based plate/shell results are validated against thin-ply high-strain composites experimental data showing good agreement. Numerical cases with uniform and nonuniform cross-sectional temperature distributions are studied. The results showed that unlike MSG, the RVE method exhibits limitations to properly capture the long-term behavior of effective coefficients of thermal expansion (CTEs) when time-dependent constituent CTEs are considered. The analyses of the homogenized properties also revealed that despite the heterogeneous nature of the composite material, from a multiscale analysis perspective, the temperature dependencies of the effective stiffness and thermal stress properties are governed by the same shift factor as the polymer matrix. This conclusion remains the same for MSG-based solid, plate/shell and beam models with uniform temperature distributions.</div>

Cancer is a complex illness that affects millions of people every year. Amongst the most frequently encountered variants of this illness are solid tumours. The growth of solid tumours depends on a large number of factors such as oxygen concentration, cell reproduction, cell movement, cell death, and vascular environment. The aim of this thesis is to provide further insight in the interconnections between these factors by means of numerical simulations. We present a multiscale model for tumor growth by coupling a microscopic, agent-based model for normal and tumor cells with macroscopic mean-field models for oxygen and extracellular concentrations. We assume the cell movement to be dominated by Brownian motion. The temporal and spatial evolution of the oxygen concentration is governed by a reaction-diffusion equation that mimics a balance law.To complement this macroscopic oxygen evolution with microscopic information, we propose a lattice-free approach that extends the vascular distribution of oxygen. We employ a Markov chain to estimate the sprout probability of new vessels. The extension of the new vessels is modeled by enhancing the agent-based cell model with chemotactic sensitivity. Our results include finite-volume discretizations of the resulting partial differential equations and suitable approaches to approximate the stochastic differential equations governing the agent-based motion. We provide a simulation framework that evaluates the effect of the various parameters on, for instance, the spread of oxygen. We also show results of numerical experiments where we allow new vessels to sprout, i.e. we explore angiogenesis. In the case of a static vasculature, we simulate the full multiscale model using a coupled stochastic/deterministic discretization approach which is able to reduce variance at least for a chosen computable indicator, leading to improved efficiency and a potential increased reliability on models of this type.