abstract: Damage detection in heterogeneous material systems is a complex problem and requires an in-depth understanding of the material characteristics and response under varying load and environmental conditions. A significant amount of research has been conducted in this field to enhance the fidelity of damage assessment methodologies, using a wide range of sensors and detection techniques, for both metallic materials and composites. However, detecting damage at the microscale is not possible with commercially available sensors. A probable way to approach this problem is through accurate and efficient multiscale modeling techniques, which are capable of tracking damage initiation at the microscale and propagation across the length scales. The output from these models will provide an improved understanding of damage initiation; the knowledge can be used in conjunction with information from physical sensors to improve the size of detectable damage. In this research, effort has been dedicated to develop multiscale modeling approaches and associated damage criteria for the estimation of damage evolution across the relevant length scales. Important issues such as length and time scales, anisotropy and variability in material properties at the microscale, and response under mechanical and thermal loading are addressed. Two different material systems have been studied: metallic material and a novel stress-sensitive epoxy polymer. For metallic material (Al 2024-T351), the methodology initiates at the microscale where extensive material characterization is conducted to capture the microstructural variability. A statistical volume element (SVE) model is constructed to represent the material properties. Geometric and crystallographic features including grain orientation, misorientation, size, shape, principal axis direction and aspect ratio are captured. This SVE model provides a computationally efficient alternative to traditional techniques using representative volume element (RVE) models while maintaining statistical accuracy. A physics based multiscale damage criterion is developed to simulate the fatigue crack initiation. The crack growth rate and probable directions are estimated simultaneously. Mechanically sensitive materials that exhibit specific chemical reactions upon external loading are currently being investigated for self-sensing applications. The "smart" polymer modeled in this research consists of epoxy resin, hardener, and a stress-sensitive material called mechanophore The mechanophore activation is based on covalent bond-breaking induced by external stimuli; this feature can be used for material-level damage detections. In this work Tris-(Cinnamoyl oxymethyl)-Ethane (TCE) is used as the cyclobutane-based mechanophore (stress-sensitive) material in the polymer matrix. The TCE embedded polymers have shown promising results in early damage detection through mechanically induced fluorescence. A spring-bead based network model, which bridges nanoscale information to higher length scales, has been developed to model this material system. The material is partitioned into discrete mass beads which are linked using linear springs at the microscale. A series of MD simulations were performed to define the spring stiffness in the statistical network model. By integrating multiple spring-bead models a network model has been developed to represent the material properties at the mesoscale. The model captures the statistical distribution of crosslinking degree of the polymer to represent the heterogeneous material properties at the microscale. The developed multiscale methodology is computationally efficient and provides a possible means to bridge multiple length scales (from 10 nm in MD simulation to 10 mm in FE model) without significant loss of accuracy. Parametric studies have been conducted to investigate the influence of the crosslinking degree on the material behavior. The developed methodology has been used to evaluate damage evolution in the self-sensing polymer. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2014

Le travail présenté a été réalisé dans le cadre d'un projet de recherche industriel visant à étudier le comportement mécanique des câblés textiles utilisés comme renforts dans les pneumatiques. Les câblés étudiés sont composés de plusieurs dizaines de milliers de filaments, assemblés en brins, qui sont ensuite torsadés ensemble. Le comportement du câble est gouverné par les mécanismes se produisant à l'échelle des fibres élémentaires, et hérite des phénomènes complexes dus aux interactions de contact-frottement entre les filaments. L'objectif de ce travail est de développer une approche permettant de simuler le comportement global de ces câblés au cours des différentes étapes de leur cycle de vie tout en approchant les sollicitations subies à l'échelle des filaments afin d'étudier les mécanismes responsables de l'endommagement de ces structures.La thèse introduit une stratégie multi-échelles originale qui repose sur le développement d'un modèle simplifié de macrofibre. Ce modèle de macrofibre est formulé à une échelle intermédiaire(entre l'échelle microscopique -celle des fibres- et l'échelle macroscopique -celle des câbles-) et dont le comportement soit équivalent à celui d'un paquet de quelques dizaines de fibres. Pour compenser la pauvreté cinématique du modèle de macrofibre, nous proposons de prendre en compte les effets de densification locale des macrofibres (écrasements transverses, réduction des vides) en autorisant des pénétrations importantes entre elles, contrôlées par une loi de contact appropriée. L'objectif de cette modélisation macroscopique est d'estimer le comportement global du câble et de définir des informations à transmettre vers l'échelle microscopique. Le processus d'héritage (choix de quantités macroscopiques pertinentes et manière de les imposer au problème local) constitue l'apport principal de ce travail et se base sur un mode de pilotage mixte à l'échelle microscopique. A terme,les résultats du problème microscopique devront permettre de recaler les paramètres du modèle de contact macroscopique, de manière à obtenir un accord entre les densités déterminées aux deux échelles.La méthode multi-échelles développée est d'abord validée par analyse d'erreur dans un cadre bidimensionnel,puis appliquée sur un câblé textile réel pour mettre en évidence son apport dans un contexte industriel. / Textile ropes made of tows of filaments twisted together can be used as reinforcements for composites.The global nonlinear mechanical behavior of these ropes is largely controlled by contact-frictioninteractions taking place between elementary fibers. A finite element code, called Multifil, has beendeveloped in order to simulate the mechanical behavior of such fibrous material. However, due tocomputational costs, the use of this approach is limited to structures made of few hundred fibers,whereas ropes in the scope of our study are formed of few thousand fibers.The purpose of this work is to develop a multi-scale approach for modeling textile ropes with ahuge number of fibers, in order to compute the global behavior of these structures while approachingthe local stresses at the fibers scale. This strategy is based on the development of a simplified modelof macrofibers to solve the problem at the macroscopic scale, and the formulation of a problem at themicroscopic scale driven by relevant macroscopic quantities. Phenomena originating at microscopicscale, and particularly the densification of fibers, are accounted for at the macroscopic scale throughand adapted contact law. Parameters of this law are adjusted so as to obtain a good agreement betweenthe densities determined at macroscopic and microscopic scales.

Cette thèse porte sur l'étude du comportement mécanique et l'endommagement d'un composite tressé 3D, utilisé pour fabriquer des réservoirs multiformes destinés à l'industrie automobile. L'analyse du matériau se base sur une approche expérimentale et une approche numérique. Sur le plan expérimental, des essais de caractérisation ont permis d'identifier l'ensemble des modules d'élasticité nécessaires pour établir la matrice de rigidité du matériau. De même, des essais expérimentaux ont permis d'étudier le processus d'endommagement du matériau en utilisant deux méthodes de suivie. La première consiste à utiliser une caméra munie d'un zoom pour observer les mécanismes d'endommagement qui se créent au cours du chargement. La deuxième méthode, quant à elle, utilise la technique de l'émission acoustique pour détecter en temps réel les mêmes phénomènes. Le couplage des deux méthodes a permis de dresser la chronologie de l'apparition de ces mécanismes d'endommagement. Sur le plan numérique, une analyse multiéchelle a permis d'évaluer l'influence des fissurations transversales et des décohésions d'interface sur les propriétés mécaniques du matériau. Pour cela, une cellule de base caractéristique de la microstructure a été modélisée. Par une technique d'homogénéisation appliquée à différentes échelles du matériau, les propriétés macroscopiques du composite ont été déterminées à partir de celles de ses constituants de base. Par la suite, des défauts sont introduits de manière discrète sur la même cellule de base. Par le même processus d'homogénéisation à l'échelle mésoscopique, les propriétés du matériau endommagé sont déterminées et comparées à celles du matériau non endommagé. Enfin, un pré-dimensionnement des réservoirs a été effectué en utilisant des critères de rupture classiques pour validation. / This thesis focuses of the mechanical behavior and damage of a 3D braided composite. The material analysis is based on experimental and numerical approaches. First, mechanical tests have identified all the necessary elastic moduli to determine the stiffness matrix of the material. Similarly, experimental tests were performed to study the material damage process using two investigation methods. The first consists on using a camera with a large magnifier in order to observe damage mechanisms created during loading. The second uses the acoustic emission technique to detect in real time the same phenomena. The coupling of the two methods allowed to establish the chronology of the development of these damage mechanisms. In numerical terms, a multiscale analysis approach enables to evaluate the impact of transverse cracks and debonding on the mechanical properties. Thus, a representative cell of the material microstructure is built to predict the macroscopic properties of the material from the properties of its constituents. Defects are introduced during the meshing using a program that allows duplication of nodes at the interfaceto create debonding or to create transverse cracks inside yarns. Through the same homogenization process, the damaged material properties are determined and compared to that of the undamaged material. Finally, a design of tanks are proposed by using strength criteria for their validation.

Multi-scale modelling and analysis is becoming increasingly important and relevant. Analysis of the emergent properties from the interactions between scales of multi-scale systems is important to aid in solutions. There is no universally adopted theoretical/computational framework or language for the construction of multi-scale models. Most modelling approaches are specific to the problem that they are addressing and use a hybrid combination of modelling languages to model specific scales. This thesis addresses if process algebra can offer a unique opportunity in the definition and analysis of multi-scale models. In this thesis the generic Process Algebra with Layers (PAL) is defined: a language for multi-scale integration modelling. This work highlights the potential of process algebra to model multi-scale systems. PAL was designed based on features and challenges found from modelling a multi-scale system in an existing process algebra. The unique features of PAL are the layers: Population and Organism. The novel language modularises the spatial scales of the system into layers, therefore, modularising the detail of each scale. An Organism can represent a molecule, organelle, cell, tissue, organ or any organism. An Organism is described by internal species. An internal species, dependent on the scale of the Organism, can also represent a molecule, organelle, cell, tissue, organ or any organism. Populations hold specific types of Organism, for example, life stages, cell phases, infectious states and many more. The Population and Organism layers are integrated through mirrored actions. This novel language allows the clear definition of scales and interactions within and between these scales in one model. PAL can be applied to define a variety of multi-scale systems. PAL has been applied to two unrelated multi-scale system case studies to highlight the advantages of the generic novel language. Firstly the effects of ocean acidification on the life stages of the Pacific oyster. Secondly the effects of DNA damage from cancer treatment on the length of a cell cycle and cell population growth.

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

<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>

<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>

This study focuses on molecular dynamics (MD) simulations, coupled with a discrete mathematical framework, and crystal plasticity (CP) simulations to investigate micro void nucleation and the plastic spin. The origin and historical use of the plastic spin are discussed with particular attention to quantifying the plastic spin at the atomistic scale. Two types of MD simulations are employed: (a) aluminum single crystals undergoing simple shear and (b) aluminum triple junctions (TJ) with varying grain orientations and textures undergoing uniaxial tension. The high-angle grain boundary simulations nucleate micro voids at or around the TJ and the determinant of the deformation gradient shows the ability to predict such events. Crystal plasticity simulations are used to explore the stress-state of the aluminum TJ from uniaxial tension at a higher length scale with results indicating a direct correlation between CP stress-states and the location of micro void nucleation in the MD simulations.

When an anode electrode potential is larger than the lowest unoccupied molecular orbital (LUMO) of the electrolyte, Li-ions and electrolyte molecules will participate in reduction reactions on the anode surface and form a solid electrolyte interface (SEI) layer. Active Li-ion consumption in the formation reactions is the main source of capacity loss (>50) and ageing in Li-ion batteries (LIBs). Due to the fast-occurring and complex nature of the electrochemical processes, conventional experimental techniques are not a feasible approach for capturing and characterizing the SEI formation phenomenon. The lack of experimental data and consequently the absence of potential parameters for crystal structures in this layer makes molecular dynamics~(MD) simulations inapplicable to it. Also, due to the multi-component multi-layer structure of the SEI, the smallest system representing an SEI layer is too large for employing the principles of quantum mechanics~(QM), that traditionally work with much smaller system sizes. Addressing this, this thesis presents a novel computational framework for coupling QM and MD calculations to simulate a system with the size limits of MD simulations independent of the experimental data. The QM evaluates sub-atomic properties such as energy barriers against diffusion and employs seven new algorithms to estimate potential parameters as the input of the MD simulations. Then MD simulations forecast SEI's properties including density, Young's Modules, Poisson's Ratio, thermal conductivity, and diffusion coefficient mechanisms. The output of the QM and MD calculations are employed to develop two macro-scale mathematical models for predicting battery ageing and battery performance, incorporating the impact of the SEI layer in addition to the cathode, anode, and separator parts. Finally, the results obtained have been validated with respect to the experimental data in different operational conditions. / Thesis / Doctor of Philosophy (PhD) / The limited lifespan of expensive batteries is the main obstacle to electrification of the transport sector, despite its necessity for addressing the current environmental issues. Li+/electrolyte reduction on the electrode surface is responsible for more than 50% of capacity loss and the consequent ageing is a complex and fast-occurring phenomenon (few ns) that cannot be easily resolved using conventional experimental and computational techniques. This thesis presents the development of some computational frameworks and demonstrates their employment to investigate this phenomenon from a multi-scale perspective, i.e., from a few electrons to an entire battery length scale, with the operating cycles ranging from a few ps to several months, employing Quantum Mechanics, Molecular Dynamics, and Macro-Scale Modeling. The frameworks have been successfully validated with respect to experimental data from the literature and have been applied successfully to highlight the parameters that impact ageing in batteries. The findings presented in this thesis can be used as the base for further research on next-gen durable batteries with liquid and solid-state electrolytes.

<p>The mechanical behavior of tissues at the macroscale is tightly coupled to cellular activity at the microscale and tuned by microstructure at the mesoscale. Dermal wound healing is a prominent example of a complex system in which multiscale mechanics regulate restoration of tissue form and function. In cutaneous wound healing, a fibrin matrix is populated by fibroblasts migrating in from a surrounding tissue made mostly out of collagen. Fibroblasts both respond to mechanical cues such as fiber alignment and stiffness as well as exert active stresses needed for wound closure. </p> <p>To model wound healing mechanobiology, we first develop a multiscale model with a two-way coupling between a microscale cell adhesion model and a macroscale tissue mechanics model. Starting from the well-known model of adhesion kinetics proposed by Bell, we extend the formulation to account for nonlinear mechanics of fibrin and collagen and show how this nonlinear response naturally captures stretch-driven mechanosensing. We then embed the new nonlinear adhesion model into a custom finite element implementation of tissue mechanical equilibrium. Strains and stresses at the tissue level are coupled with the solution of the microscale adhesion model at each integration point of the finite element mesh. In addition, solution of the adhesion model is coupled with the active contractile stress of the cell population. The multiscale model successfully captures the mechanical response of biopolymer fibers and gels, contractile stresses generated by fibroblasts, and stress-strain contours observed during wound healing. We anticipate this framework will not only increase our understanding of how mechanical cues guide cellular behavior in cutaneous wound healing, but will also be helpful in the study of mechanobiology, growth, and remodeling in other tissues. </p> <p>Next, we develop another multiscale model with a bidirectional coupling between a microscale cell adhesion model and a mesoscale microstructure mechanics model. By mimicking the generation of fibrous network in experiment, we established a discrete fiber network model to simulate the microstructure of biopolymer gels. We then coupled the cell adhesion model to the discrete model to obtain the solution of microstructure equilibrium. This multiscale model was able to recover the volume loss of fibrous gels and the contraction from cells in the networks observed in experiment. We examined the influence of RVE size, stiffness of single fibers and stretch of the gels. We expect this work will help bridge the activity of cell to the microstructure and then to the tissue mechanics especially in wound healing. We hope this work will provide more rigorous understanding in the study of mechanobiology.</p> <p>At last, we established a computational model to accurately capture the mechanical response of fibrin gels which is a naturally occurring protein network that forms a temporary structure to enable remodeling during wound healing and a common tissue engineering scaffold due to the controllable structural properties. We formulated a strategy to quantify both the macroscale (1–10 mm) stress-strain response and the deformation of the mesoscale (10–1000 microns) network structure during unidirectional tensile tests. Based on the experimental data, we successfully predict the strain fields that were observed experimentally within heterogenous fibrin gels with spatial variations in material properties by developing a hyper-viscoelastic model with non-affined evolution under stretching. This model is also potential to predict the macroscale mechanics and mesoscale network organization of other heterogeneous biological tissues and matrices.</p>