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

Collagen is the most abundant protein in mammals and has special mechanical behavior that enables it to play an important role in the structural integrity of many tissues, e.g., skin, tendon, bone, cartilage and blood vessels. The mechanical properties of collagen are governed by hierarchical mechanisms in different length-scales from molecule to tissue level. Currently, there is no multi-scale model that can predict the mechanical properties of collagen at macroscopic length scales from the behavior of microstructural elements at smaller length scales. This dissertation aimed at developing a multi-scale model using a bottom-up approach to predict the elastic and viscoelastic behaviors of collagen at length scales spanning from nano to microscale. Creep simulations were performed using steered molecular dynamics (SMD) method on collagen molecules, cross-link, and micro-fibrils with various lengths. A micro-fibril is considered as a combination of two collagen molecules connected by a cross-link. The strain time histories for force levels in the range of 10 to 4000 pN were characterized using quasilinear viscoelastic models. These models were utilized to make a reduced model of a micro-fibril and the reduced models, in turn, were combined to make a model of a fibril up to 300 micrometers in length. The micro-fibril and fibril models were validated with available experimental measurements. Hydrogen bonds rupture and formation of collagen molecule played a central role in its viscoelastic behavior and were used to estimate the creep growth rate. The propagation of force wave in the molecule was shown to be an important factor in providing the time-dependent properties of the fibrils. This propagation was modeled with delay elements and this allowed reducing the micro-fibril model to only three degrees of freedom. In conclusion, the results confirmed that the combination of molecular dynamics simulations and viscoelastic theory could be successfully utilized to investigate the viscoelastic behavior of collagen at small scales. The model reported in this dissertation, lays the groundwork for future studies on collagen, particularly in elucidating how each particular level of hierarchy affects the overall tissue behavior. / Mechanical Engineering

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Schlüsselfaktoren der bemerkenswerten mechanischen Eigenschaften von Knochen sind seine komplexe hierarchische Struktur und chemische Zusammensetzung. Ziel dieser Dissertation war die simultane Untersuchung von Materialkomposition und 3D Struktur in Relation zu lokalen elastischen Eigenschaften von Knochengewebe unter Verwendung von neuen hochauflösenden experimentellen Konzepten. Im ersten Teil wurde polarisierte Raman Spektroskopie (PRS) eingesetzt um gesunden humanen kortikalen Knochen zu analysieren. Es konnte gezeigt werden, dass sich PRS eignet, um sowohl die chemische Zusammensetzung als auch die 3D Organisation der Kollagenfasern in einer Messung aufzuklären. Dominante Faserorientierungen ganzer Gewebedomänen konnten identifiziert und mit der Koexistenz zweier Faserorganisationsmuster verknüpft werden. Durch Kombination derPRS Experimente mit ko-lokalisierten Synchrotron-Phasenkontrast-Nano-Tomografie- undUltraschallmikroskopie-Messungen wurde eine komplementäre Untersuchung von Faserarchitektur, chemischer Komposition und elastischen Eigenschaften einzelner Knochenlamellen ermöglicht. Die multimodale Analyse ergab, dass die charakteristischen lamellären Ondulationen der Elastizität in erster Linie durch sich lokal ändernde Faserorientierungen bedingt werden und nicht durch Variationen der Materialzusammensetzung, Abweichungen der Mineralkristallpartikeleigenschaften oder durch Fluktuationen der Massendichte. Im letzten Teil wurde mittels akustischer Mikroskopie der Einfluss der Mutation des Neurofibromin 1 Genes auf die pathologische Entwicklung von mechanischen Knocheneigenschaften untersucht. Anhand zweier Knockout-Mausmodelle wurde festgestellt, dass nur eine Mutation in frühen mesenchymalen Vorläuferzellen die Steifigkeit der langen Röhrenknochen signifikant beeinträchtigt. Perspektivisch eignet sich der vorgestellte multimodale Ansatz für nicht-destruktive Charakterisierung eines breiten Spektrums biologischer und synthetischer Faserverbundwerkstoffe. / Key factors determining the remarkable mechanical performance of bone are its material composition and complex hierarchically structure. The aim of this thesis was the concurrent investigation of the chemical composition and 3D structure of bone tissue in relation to the local elastic properties by introducing novel high resolution experimental approaches. In the first part, polarized Raman spectroscopy (PRS) was applied to analyze healthy human cortical bone. In particular, it was demonstrated that PRS can be employed to simultaneously investigate the chemical composition and the 3D organization of collagen fibrils in a single experiment. Predominant fibril orientations in entire tissue domains were identified and linked to the coexistence of two fibril organization patterns. To further extend the analysis, PRS experiments were combined with synchrotron X-ray phase contrast nano tomography and scanning acoustic microscopy measurements in a site-matched study design. This multimodal approach enabled complementary imaging of the fibrillar architecture, tissue composition and resulting elastic properties of single bone lamellae. In line with earlier studies, crosscorrelation analysis strongly suggested that the characteristic elastic undulations of bone lamellae are the result of the twisting fibrillar orientation, rather than compositional variations, modulations of the mineral particle maturity, or mass density fluctuations. Finally, acoustic microscopy was applied to analyze the impact of the neurofibromin 1 gene mutation on the pathologic development of the mechanical properties of bone. Analysis of two knock-out mouse models revealed that only Nf1 ablation in early mesenchymal progenitor cells significantly impairs the elastic stiffness of long bones. In future studies, the presented multimodal methodology can be translated for non-destructive and high resolution characterization of a broad range of biological and synthetic fiber composite materials.