The mechanical and physical properties of polymers are determined primarily by the underlying nano-scale structures and characteristics such as entanglements, crystallites, and molecular orientation. These structures evolve in complex manners during the processing of polymers into useful articles. Limitations of available and foreseeable computational capabilities prevent the direct determination of macroscopic properties directly from atomistic computations. As a result, computational tools and methods to bridge the length and time scale gaps between atomistic and continuum models are required. In this research, an internal state variable continuum model has been developed whose internal state variables (ISVs) and evolution equations are related to the nano-scale structures. Specifically, the ISVs represent entanglement number density, crystal number density, percent crystallinity, and crystalline and amorphous orientation distributions. Atomistic models and methods have been developed to investigate these structures, particularly the evolution of entanglements during thermo-mechanical deformations. A new method has been created to generate atomistic initial conformations of the polymer systems to be studied. The use of the hyperdynamics method to accelerate molecular dynamics simulations was found to not be able to investigate processes orders of magnitude slower that are typically measurable with traditional molecular dynamics simulations of polymer systems. Molecular dynamics simulations were performed on these polymer systems to determine the evolution of entanglements during uniaxial deformation at various strain rates, temperatures, and molecular weights. Two methods were evaluated. In the first method, the forces between bonded atoms along the backbone are used to qualitatively determine entanglement density. The second method utilizes rubber elasticity theory to quantitatively determine entanglement evolution. The results of the second method are used to gain a clearer understanding of the mechanisms involved to enhance the physical basis of the evolution equations in the continuum model and to derive the models material parameters. The end result is a continuum model that incorporates the atomistic structure and behavior of the polymer and accurately represents experimental evidence of mechanical behavior and the evolution of crystallinity and orientation.

Determination of the relation between the bulk or rheological properties of a particle suspension and its microscopic structure is an old and important problem in physical science. In general, the rheology of particle suspension is quite complex, and the problem becomes even more complicated if the suspending particle is deformable. Despite these difficulties, a large number of theoretical and experimental investigations have been devoted to the analysis and prediction of the rheological behavior of particle suspensions. However, among these studies there are very few investigations that focus on the role of particle deformability. A novel method for full coupling of the fluid-solid phases with sub-grid accuracy for the solid phase is developed. In this method, the flow is computed on a fixed regular 'lattice' using the lattice Boltzmann method (LBM), where each solid particle, or fiber, is mapped onto a Lagrangian frame moving continuously through the domain. The motion and orientation of the particle are obtained from Newtonian dynamics equations. The deformable particle is modeled by the lattice-spring model (LSM).The fiber deformation is calculated by an efficient flexible fiber model. The no-slip boundary condition at the fluid-solid interface is based on the external boundary force (EBF) method. This method is validated by comparing with known experimental and theoretical results. The fiber simulation results show that the rheological properties of flexible fiber suspension are highly dependent on the microstructural characteristics of the suspension. It is shown that fiber stiffness (bending ratio BR) has strong impact on the suspension rheology in the range BR < 3. The relative viscosity of the fiber suspension under shear increases significantly as BR decreases. Direct numerical simulation of flexible fiber suspension allows computation of the primary normal stress difference as a function of BR. These results show that the primary normal stress difference has a minimum value at BR ∼ 1. The primary normal stress differences for slightly deformable fibers reaches a minimum and increases significantly as BR decreases below 1. The results are explained based on the Batchelor's relation for non-Brownian suspensions. The influence of fiber stiffness on the fiber orientation distribution and orbit constant is the major contributor to the variation in rheological properties. A least-squares curve-fitting relation for the relative viscosity is obtained for flexible fiber suspension. This relation can be used to predict the relative viscosity of flexible fiber suspension based on the result of rigid fiber suspension. The unique capability of the LBM-EBF method for sub-grid resolution and multiscale analysis of particle suspension is applied to the challenging problem of platelet motion in blood flow. By computing the stress distribution over the platelet, the "blood damage index" is computed and compared with experiments in channels with various geometries [43]. In platelet simulation, the effect of 3D channel geometry on the platelet activation and aggregation is modeled by using LBM-EBF method. Comparison of our simulations with Fallon's experiments [43] shows a similar pattern, and shows that Dumont's BDI model [40] is more appropriate for blood damage investigation. It has been shown that channels with sharp transition geometry will have larger recirculation areas with high BDI values. By investigating the effect of hinge area geometry on BDI value, we intend to use this multiscale computational method to optimize the design of Bileaflet mechanical heart valves. Both fiber simulations and platelet simulations have shown that the novel LBM-EBF method is more efficient and stable compare to the conventional numerical methods. The new EBF method is a two-Cway coupling method with sub-grid accuracy which makes the platelet simulations possible. The LBM-EBF is the only method to date, to the best of author's knowledge, that can simulate suspensions with large number of deformable particles under complex flow conditions. It is hoped that future researchers may benefit from this new method and the algorithms developed here.

Existing numerical techniques for modeling saturated deformable porous media are based on homogenization techniques and thus are incapable of performing micro-mechanical investigations, such as the effect of micro-structure on the deformational characteristics of the media. In this research work, a numerical scheme is developed based on the parallelized hybrid lattice-Boltzmann finite-element method, that is capable of performing micro-mechanical investigations through direct numerical simulations. The method has been used to simulate compression of model saturated porous media made of spheres and cylinders in regular arrangements. Through these simulations it is found that in the limit of small Reynolds number, Capillary number and strain, the deformational behaviour of a real porous media can be recovered through model porous media when the parameters porosity, permeability and bulk compressive modulus are matched between the two media. This finding motivated research in using model porous geometries to represent more complex real porous geometries in order to perform investigations of deformation on the latter. An attempt has been made to apply this technique to the complex geometries of ªfeltº, (a fibrous mat used in paper industries). These investigations lead to new understanding on the effect of fiber diameter on the bulk properties of a fibrous media and subsequently on the deformational behaviour of the media. Further the method has been used to investigate the constitutive relationships in deformable porous media. Particularly the relationship between permeability and porosity during the deformation of the media is investigated. Results show the need of geometry specific investigations.

The load-carrying and energy-dissipation capacities of ultra-high-performance concrete (UHPC) under dynamic loading are evaluated in relation to microstructure composition at strain rates on the order of 10⁵ s⁻¹ and pressures of up to 10 GPa. Analysis focuses on deformation and failure mechanisms at the mesostructural level. A cohesive finite element framework that allows explicit account of constituent phases, interfaces, and fracture is used. The model resolves essential deformation and failure mechanisms in addition to providing a phenomenological account of the effects of the phase transformation. Four modes of energy dissipation are tracked, including pressure-sensitive inelastic deformation, damage through the development of distributed cracks, interfacial friction, and energy released through phase transformation of the quartz silica constituent. Simulations are carried out over a range of volume fractions of constituent phases to quantify trends that can be used to design materials for more damage-resistant structures. Calculations show that the volume fractions of the constituents have more influence on the energy-dissipation capacity than on the load-carrying capacity, that inelastic deformation is the source of over 70% of the energy dissipation, and that the presence of porosity changes the role of fibers in the dissipation process. The results also show that the phase transformation has a significant effect on the load-carrying and energy-dissipation capacities of UHPC for the conditions studied. Although transformation accounts for less than 2% of the total energy dissipation, the phase transformation leads to a twofold increase in the crack density and yields nearly an 18% increase to the overall energy dissipation. Microstructure-behavior relations are established to facilitate materials design and tailoring for target-specific applications.

We propose a new approach for defining mechanical properties of the brain tissue in-vivo by taking MRI or CT images of a brain response to ventriculostomy operation, i.e., the relief of the elevated pressure in the ventricular cavities. Then, based on 3-D image analysis, the displacement fields are recovered from these images. Constitutive parameters of the brain tissue are determined using inverse analysis and a numerical method allowing for computations of large strain deformations. We tested this approach in controlled laboratory experiments with silicone brain models mimicking brain geometry, mechanical properties, and boundary conditions. The ventriculostomy was simulated by inflating and deflating internal cavities that model cerebral ventricles. Subsequently, the silicone brain model was described by a hyperelastic (neo-Hookean) material. The obtained mechanical properties have been verified with direct laboratory tests. Properties of real brain tissue are more complicated, but the proposed approach requires only conventional medical images collected before and after ventriculostomy. Breast cancer is the second most prevalent cancer in women, and an operative mastectomy is frequently a part of the treatment. Women often choose to follow a mastectomy with a reconstruction surgery using a breast implant. Furthermore, there is a growing demand for breast augmentation for the sake of aesthetic improvement. In this dissertation, we also developed a quantitative large-strain 3-D mechanical model of female breast deformation. The results show that the stiffness of skin and the constitutive parameters of the breast tissue are important factors affecting breast shape. Our results also suggest that the published Mooney-Rivlin parameters of breast tissue are underestimated by at least one or two orders of magnitude. Scale analysis, representing female breast as a cantilever beam, confirms these conclusions. Subdural hematoma (tearing and bleeding between scull and brain) is one of the major complications of the ventriculostomy operations. Understanding the mechanism of subdural hematoma is critically important for development of more effective medical treatments. In this work, we developed a simple, spherically-symmetrical poroelastic model of the ventriculostomy operation and studied brain response to the pressure change in the ventricles. The observed effect of the material properties on the occurrence of subdural hematoma may be useful for making clinical decisions.

An investigation of the high-strain-rate mechanical properties, deformation mechanisms, and fracture characteristics of a Zr-based bulk metallic glass (BMG) and its composite with tungsten was conducted through the use of controlled impact experiments and constitutive modeling. The overall objective of this research was to determine the high-strain-rate deformation and failure mechanisms of a BMG and its composite as a function of stress state and strain rate, and describe the mechanical behavior over a range of loading conditions. The research involved performing controlled impact experiments on BMG composites consisting of an amorphous Zr57Nb5Cu15.4Ni12.6Al10 (LM106) with crystalline tungsten reinforcement particles. Monolithic LM106 was also examined to aid in the understanding of the composite. The mechanical behavior of the composite was investigated over a range of strain rates (10^3 s^-1 to 10^6 s^-1), stress states (compression, compression-shear, tension), and temperatures (RT to 600 C) to determine the dependence of mechanical properties and deformation and failure modes (i.e., homogeneous deformation vs. inhomogeneous shear banding) on these parameters. Mechanical testing in the quasi-static to intermediate strain rate regimes was performed using an Instron, Drop Weight Tower, and Split Hopkinson Pressure Bar, respectively. High-strain-rate mechanical properties of the BMG-matrix composite and monolithic BMG were investigated using dynamic compression (reverse Taylor) and dynamic tension (spall) impact experiments performed using a gas gun instrumented with velocity interferometry and high-speed digital photography. These experiments provided information about dynamic strength and deformation modes, and allowed for validation of constitutive models via comparison of experimental and simulated transient deformation profiles and free surface velocity traces. Hugoniot equation of state measurements were performed on the monolithic BMG to investigate the high pressure phase stability of the glass and the possible implications of a high pressure phase transformation on mechanical properties. Specimens were recovered for post-impact microstructural and thermal analysis to gain information about the mechanisms of dynamic deformation and fracture, and to examine for possible shock-induced phase transformations of the amorphous phase.

Ce travail se concentre sur le développement d'une procédure expérimentale d’essai mécanique à haute vitesse de déformation de matériaux. La nouveauté de ce travail est l'utilisation de champs d’accélération mesurés comme cellule de force, évitant la nécessité des mesures des forces externes. Pour identifier les paramètres constitutifs des matériaux testés à partir des mesures de champs, la méthode champs virtuels (MCV) basé sur le principe des puissances virtuelles (PPV) est utilisée. En dynamique, avec la MCV, il est possible de définir des champs virtuels qui mettent à zéro les puissances virtuelles des forces externes. Au lieu de cela, l'accélération obtenue grâce à une double dérivation temporelle des déplacements peut être utilisée comme une cellule de force. Enfin, les paramètres élastiques peuvent être identifiés directement à partir d’un système linéaire qui se construit en réécrivant le PPV avec autant de champs virtuels indépendants que d’inconnues à identifier. Cette procédure est d'abord validée numériquement par des simulations éléments finis puis mise en œuvre expérimentalement en utilisant deux configurations d’impact différentes. Les résultats confirment que effets inertiels peuvent être utilisés pour identifier les paramètres des matériaux sans la nécessité de mesurer la force d’impact, et sans exigence de déformations uniformes comme dans les procédures actuelles basées sur le montage de barres d’Hopkinson. Ces nouveaux développement ont le potentiel de mener à de nouveaux essais standards en dynamique rapide / This work focuses on the development of a novel experimental procedure for high strain rate testing of materials. The underpinning novelty of this work is the use of the full-field acceleration maps as a volume distributed load cell, avoiding the need for impact force measurement. To identify the constitutive parameters of materials from the full-field data, the Virtual Fields Method (VFM) based on the principle of virtual work is used here. In dynamics, using the VFM, it is possible to define particular virtual fields which can zero out the virtual work of the external forces. Instead, the acceleration obtained through second order temporal differentiation from displacement can be used as a load cell. Finally, the elastic parameters can be identified directly from a linear system which is built up through rewriting the principle of virtual work with as many independent virtual fields as unknowns. Thus, external force measurement is avoided, which is highly beneficial as it is difficult to measure in dynamics. This procedure is first numerically validated through finite element simulations and then experimentally implemented using different impact setups. Both results confirm that inertial effects can be used to identify the material parameters without the need for impact force measurements, also relieving the usual requirements for uniform/uniaxial stress in SHPB like test configurations. This exciting development has the potential to lead to new standard testing techniques at high strain rates

Cette thèse est située dans le cadre du projet FUI OASIS ayant comme objectif la modélisation d'un processus d'emboutissage optimisé. Le travail consiste essentiellement au développement des algorithmes de contact plus appropriés à ce type de mise en forme. Dans la littérature et pour plusieurs codes de calcul industriels, l'approche NTS (nœud à segment) demeure la plus utilisée pour la résolution d'un problème de contact. Dans certaine configuration, cette méthode présente des insuffisances et un manque de précision. On la remplaçant par l'approche mortier, on arrive à résoudre une gamme assez large de problèmes de contact. La méthode mortier, utilisée au initialement pour un calcul avec décomposition de domaine, a été le centre d'intérêt de plusieurs travaux de recherche pour la modélisation du contact. Dans ce travail, on va regrouper plusieurs méthodes de gestion du contact en les combinant avec l'approche mortier. L'algorithme de résolution, les éléments d'implémentation ainsi quelques exemples de validation présentant une critique des avantages et les limites de chaque techniques sont détaillés dans ce travail afin d'obtenir un support technique pour tous travail ultérieurs avec la méthode mortier. Le principal avantage de la méthode mortier se manifeste dans l'application des conditions de contact sous forme d'intégrale dans l'interface. Bien que cette méthode permette de réduire la différence des contraintes dans l'interface de contact d'un élément à un autre pour obtenir une meilleure continuité de la pression de contact, elle demeure insuffisante dans certaines applications en particulier pour les problèmes en grande déformation. Le lissage des surfaces de contact, qu'on peut appliquer par différentes techniques, présente une solution classique à ce genre de problème en mécanique de contact. L'originalité de ce travail, c'est la combinaison de l'utilisation des courbes B-Spline cubiques pour la description presque exacte de la surface de contact d'un côté avec une formulation avec l'approche mortier pour l'application des conditions de contact d'un autre côté. Cette combinaison forme un duo gagnant permettant de résoudre un problème de contact en grandes déformation. Les termes permettant l'implémentation des différentes techniques de lissage pour la résolution d'un problème de contact sont détaillés. Une attention particulière est accordée au lissage avec les B-Spline Cubiques.Tous les algorithmes détaillés dans ce travail sont implémentés dans un code maison FiEStA. C'est un code de calcul par éléments finis libre en langage C++. Certains développements concernant la loi de comportement hyper-élastique et l'intégralité du module du contact sont développés dans ce travail de thèse. / This thesis is situated in the FUI OASIS project which the objective is the modeling of an optimized stamping process. The work mainly involves the development of the most appropriate contact algorithms such formatting. In the literature and several industrial computing codes, the NTS approach (node to segment) remains the most used for the resolution of a contact problem. In certain configuration, this method has shortcomings and a lack of precision. We replacing it with mortar approach, we manage to solve a broad range of contact problems. The mortar method, used for the initial for calculation using domain decomposition, was the focus of several research projects for the modeling of the contact. In this work, we will consolidate multiple contact formulation methods in combination with mortar approach. The resolution algorithm, the elements of implementation and some examples of validation with a review of the advantages and limitations of each technique are detailed in this work in order to get technical support for subsequent work with the mortar method. The main advantage of the mortar method is in the application of the contact conditions in integral form in the interface. Although this method reduces the difference of the stresses in the contact interface of a component to another to obtain a better continuity of the contact pressure, it is still insufficient in some applications, particularly for large deformation problems. The smoothing of contact surfaces, which can be applied by various techniques, presents a classic solution to this problem in mechanical contact. The originality of this work is the combination of using cubic B-Spline curves for the almost exact description of the contact surface on one side with the use of the mortar approach to the application of the contact conditions on the other hand. This combination forms a winning combination for solving a contact problem in large deformation. The terms allowing the implementation of the different smoothing techniques for solving a problem of contact are detailed. Particular attention is paid to smoothing with Cu bic B-Spline. All algorithms detailed in this work are implemented in a house code 'Fiesta'. This is a free finite elements computer code in C ++. Some developments in the law of hyper-elastic behavior and completeness of the contact module are developed in this thesis.

Shape memory alloys (SMAs) exhibit the ability to absorb large dynamic loads and, therefore, are excellent candidates for structural components where impact loading is expected. Compared to the large amount of research on the shape memory effect and/or pseudoelasticity of polycrystalline SMAs under quasi-static loading conditions, studies on dynamic loading are limited. Experimental research shows an apparent difference between the quasi-static and high strain rate deformation of SMAs. Research reveals that the martensitic phase transformation is strain rate sensitive. The mechanism for the martensitic phase transformation in SMAs during high strain rate deformation is still unclear. Many of the existing high strain rate models assume that the latent heat generated during deformation contributes to the change in the stress-strain behavior during dynamic loading, which is insufficient to explain the large stress observed during phase transformation under high strain rate deformation. Meanwhile, the relationship between the phase front velocity and strain rate has been studied. In this dissertation, a new resistance to phase transformation during high strain rate deformation is discussed and the relationship between the driving force for phase transformation and phase front velocity is established. With consideration of the newly defined resistance to phase transformation, a new model for phase transformation of SMAs during high strain rate deformation is presented and validated based on experimental results from an austenitic NiTi SMA. Stress, strain, and martensitic volume fraction distribution during high strain rate deformation are simulated using finite element analysis software ABAQUS/standard. For the first time, this dissertation presents a theoretical study of the microscopic band structure during high strain rate compressive deformation. The microscopic transformation band is generated by the phase front and leads to minor fluctuations in sample deformation. The strain rate effect on phase transformation is studied using the model. Both the starting stress for transformation and the slope of the stress-strain curve during phase transformation increase with increasing strain rate.

This thesis aims to develop a new type of highly stretchable strain sensor to measure large deformation of a specimen subjected to dynamic loading. The sensor was based on the piezo-resistive response of carbon nanotube(CNT)/polydimethysiloxane (PDMS) composites thin films, some nickel particles were added into the sensor composite to improve the sensor performance. The piezo-resistive response of CNT composite gives high frequency response in strain measurement, while the ultra-soft PDMS matrix provides high flexibility and ductility for large strain measuring large strain (up to 26%) with an excellent linearity and a fast frequency response under quasi-static test, the delay time for high strain rate test is just 30 μs. This stretchable strain sensor is also able to exhibit much higher sensitivities, with a gauge factor of as high as 80, than conventional foil strain gauges.