Part I (Efficient Endochronic Finite Element Analysis: an Example of a Cyclically Loaded Boron/Aluminum Composite): A convenient and efficient algorithmic tangent matrix approach has been developed for 3-D finite element (FE) analysis using the endochronic theory without a yield surface. The underlying algorithm for integrating the endochronic constitutive equation was derived by piecewise linearization of the plastic strain path. The approach was employed to solve a micromechanics boundary value problem of a cyclically loaded unidirectional boron/6061 aluminum composite. All the FE results consistently demonstrate superior numerical stability and efficiency of the proposed method. Extensions of the method to endochronic plasticity with a yield surface and to the plane stress case are also presented. Part II (Simple and Unified Finite Element Formulation for Doubly Periodic Models: Applications to Boron/Aluminum Composites): A simple and unified weak formulation and its convenient FE implementation have been proposed. The weak formulation is valid for any doubly periodic model under uniform 3-D macro-stress, and serves as a common rational foundation of different FE approaches. The algorithmic tangent matrix approach for the endochronic theory has been incorporated into the FE formulation to model isothermal, rate-independent plastic macro-deformation of unidirectional fibrous composites with idealized two-phase micro-structure and backed-out inelastic matrix properties. Methods for determining inelastic material parameters of the matrix have been established. Numerical results for a B/6061 AI composite subjected to on-axis and off-axis monotonic tensile loadings are in good agreement with experimental data. The micromechanics model also shows the potential for quantitative characterization of complicated cyclic behavior. Finally, some effects of model geometry on overall plastic response of the B/6061 AI composite are discussed from the viewpoint of theoretical-experimental correlation. / Ph. D.

Presented is a model for predicting SMA-induced deformations in an unsymmetric cross ply laminate. A previously developed theory is used to predict the room-temperature shape of the cross-ply laminate by minimizing its total potential energy. Then, using the principle of virtual work, equations relating the shape of the laminate to a force applied on supports fastened to the laminate are derived. Induced strains and displacements are predicted as a function of the applied force. Experiments where the force is generated by known weights are conducted. Good correlations are established between the experimental results and the predictions. The developed theory is able to predict with good accuracy the shape, strains and, displacements of an unsymmetric cross-ply laminate to the force applied on the laminate. This theory is then used to develop a model relating the laminate response to forces produced by a SMA actuator, the actuator being a SMA wire. To describe the mechanics of the SMA actuator, constitutive equations derived by other researchers are used. These constitutive equations relate the temperature of the wire to forces generated in it. Experiments where a SMA wire is used as an actuator are conducted. These experiments consist of resistively heating a SMA wire attached to supports fastened to the laminate. During these experiments, laminate deformations are measured as a function of the applied voltage. Comparisons with the temperature-based constitutive model predictions are not made since the relation between the applied voltage and the SMA temperature is very difficult to establish. However, the experiments show that a SMA used in conjunction with cross-ply unsymmetric laminates can induce very large changes in the laminate shapes. Thus, the concept of using a SMA actuator to control the shape of cross-ply unsymmetric laminates is validated. / Master of Science

The stresses and deformations in cross-ply composite tubes subjected in circumferential temperature gradients are studied. The motivation behind the study is the anticipated use of composite tubes in space structures where the tube is exposed to the heat of the sun on one side and the cryogenic temperatures of space on the other. Experiments were performed to measure the functional form of the temperature gradient and the displacements. It was found that the form of the temperature gradient, T(Ɵ), can accurately be represented by T(Ɵ) = A + BcosƟ¸ and that the displacement of the tube is parabolic in the axial coordinate. Two types of analytical solutions were developed: an exact elasticity U solution and an approximate solution. The approximate solution includes a linear variation of the material properties with temperature and uses the principle of complementary virtual work in conjunction with a Ritz approximation on the stress field. The elasticity solution predicts that high tensile stresses could crack the matrix. The effect of including temperature-dependent material properties is to reduce the circumferential dependency of the stresses. / Master of Science

Dielectric elastomers (DEs) are a relatively new electroactive polymer (EAP) transducer technology. They are capable of over 100% strain when actuated, and can be used as sensors to measure large strains. In actuation mode, the DE is subject to an electric field; in sensing mode, the capacitance of the dielectric elastomer is measured. In this work, a dielectric elastomer configured as a circular membrane clamped around its outer edge over a sealed chamber and inflated by a bias pressure is studied in order to characterize its static and dynamic electromechanical behavior. In both cases, the experiments were conducted with prestretched dielectric elastomer actuators fabricated from 0.5 mm or 1 mm thick polyacrylate films and unless stated otherwise carbon grease electrodes were used. The static tests investigate the effect of flexible electrodes and passive layers on the electromechanical response of dielectric elastomer membrane actuators and sensors. To study the effect of the flexible electrodes, four compliant electrodes were tested: carbon grease, silver grease, graphite spray, and graphite powder. The electrode experiments show that carbon grease is the most effective electrode of those tested. To protect the flexible electrodes from environmental hazards, the effect of adding passive elastic layers to the transducers was investigated. A series of tests were conducted whereby the position of the added layers relative to the transducer was varied: (i) top passive layer, (ii) bottom passive layer, and (iii) passive layers on both the bottom and top of the transducer. For the passive layer tests, the results show that adding elastic layers made of the same material as the DE dramatically changes both the mechanical and electrical response of the actuator. The ability to use capacitance measurements to determine the membrane's maximum stretch was also investigated. The experiments demonstrate that the capacitance response can be used to sense large mechanical strains in the membrane ï ³ 25%. In addition, a numerical model was developed which correlates very well with the experimental results especially for strains up to 41%. The dynamic experiments investigate the dynamic response of a dielectric elastomer membrane due to (i) a time-varying pressure input and (ii) a time-varying voltage input. For the time-varying pressure experiments, the prestretched membrane was inflated and deflated mechanically while a constant voltage was applied. The membrane was cycled between various predetermined inflation states, the largest of which was nearly hemispherical, which with an applied constant voltage of 3 kV corresponded to a maximum strain at the pole (center of membrane) of 28%. These experiments show that for higher voltages, the volume displaced by the membrane increases and the pressure inside the chamber decreases. For the time varying voltage experiments, the membrane was passively inflated to various predetermined states, and then actuated. Various experiments were conducted to see how varying certain system parameters changed the membrane's dynamic response. These included changing the chamber volume and voltage signal offset, as well as measuring the displacement of multiple points along the membrane's radius in order to capture its entire motion. The chamber volume experiments reveal that increasing the size of the chamber onto which the membrane is clamped will cause the resonance peaks to shift and change in number. For these experiments, the pole strains incurred during the inflation were as high as 26 %, corresponding to slightly less than a hemispherical state. Upon actuation using a voltage signal with an amplitude of 1.5 kV, the membrane would inflate further, causing a maximum additional strain of 12.1%. The voltage signal offset experiments show that adding offset to the input signal causes the membrane to oscillate at two distinct frequencies rather than one. Lastly, experiments to capture the entire motion of the membrane revealed the different mode shapes the membrane's motion resembles. / Master of Science

We use the three-dimensional finite element code DYNA3D to analyze two problems: (a) the normal impact of a cylindrical monolithic or composite rod against a smooth flat rigid target, (commonly known as the Taylor impact test), and (b) the penetration of composite and monolithic steel cylindrical rods into reinforced concrete targets. The composite rod is made of either a steel or copper shell enclosing a ceramic. The ceramic and the steel are assumed to fail at a critical value of the effective plastic strain, whereas no failure is considered in the copper. The thermoviscoplastic response of steel and copper is modeled by the Johnson-Cook relation and the ceramic and concrete are assumed to be elastic-plastic. Values of material parameters in the constitutive relation for the reinforced concrete (RC) are derived by the rule of mixtures. Failure of a material is simulated by the element erosion technique for ceramic and steel, and element erosion along with stiffness reduction for the RC. The effect of the angle of obliquity of impact on the damage induced in the target is ascertained. For the solid cylindrical copper rod impacting a smooth flat rigid target, the time history of the deformed length and the axial variation of the final diameter are found to match well with the experimental findings. For the composite rod, the diameter of the deformed impacted surface, the shape and size of the mushroomed region and the volume fraction of the failed ceramic material strongly depend upon the impact speed, the shell wall thickness and the thickness of the solid copper rod at the front end. Some composite cylindrical rods impacting at normal incidence RC targets were found to buckle during the penetration process in the sense that their outer diameter at a cross-section close to the impacted end increased by at least 20%. For steel penetrators, the damage experienced increased as the nose shape got blunter and the angle of obliquity became larger whereas the damage induced to the target only increased with penetrator bluntness. / Master of Science

在本碩士論文中, 我們闡述了投射有限群表現, 以及其形變理論。 我們亦特別研究這些表示在 GL_1 和 GL_2 之形變, 並且給了可表示化 的判定準則。 最後, 我們解釋相對應的泛形變環之扎里斯基切空間與 群餘調之關連, 並計算了 GL_1 的泛形變表現。 / In this master thesis, we give an exposition of the deformation theory of representations for GL_1 and GL_2, respectively, of certain profinite groups. We give rigidity conditions of the fixed representation and verify several conditions for the representability. Finally, we interpret the Zariski tangent spaces of respective universal deformation rings as certain group cohomology and calculate the universal deformation for GL_1.

Le séchage et l’imbibition sont des phénomènes physiques indispensables, de nos jours, à la formulation de nombreux matériaux en milieu industriel. Ces phénomènes, comme on peut l’observer avec l’apparition de fissures lors du séchage d’une peinture fraichement appliquée, peuvent affecter de manière irréversible l’aspect, l’intégrité ou la durabilité du matériau concerné. De plus, dans l’industrie, la connaissance des mécanismes physiques mis en jeu lors de ces étapes de séchage ou d’imbibition reste fréquemment empirique, conduisant à de fortes consommations d’énergie. La compréhension fondamentale de ces phénomènes représente donc un enjeu industriel majeur.En utilisant des techniques de mesure telles que l’Imagerie à Résonnance Magnétique (IRM) ou la microscopie électronique, nous nous sommes intéressés à la physique des écoulements fluides dans des milieux poreux modèles, déformables ou non-déformables, dont la taille caractéristique des pores varie de l’échelle du millimètre à celle de quelques nanomètres.Le résultat essentiel de ces travaux de thèse est la démonstration que l’évolution de la distribution de liquide dans ces milieux modèles, lors du séchage, provient de la compétition entre deux phénomènes physiques, quelle que soit la taille des pores, et que le matériau fissure ou subisse du retrait. Ces phénomènes physiques sont : le ré-équilibrage capillaire, ayant lieu lors de la substitution de l’eau par l’air dans le milieu poreux, provoquant un écoulement fluide selon la direction du gradient des pressions de Laplace imposé au liquide par l’évaporation, et le développement d’une région sèche apparente depuis la surface libre de l’échantillon.Plus précisément, nous montrons que le phénomène de ré-équilibrage capillaire est permanent lors du séchage et permet de maintenir une saturation homogène dans les régions humides de l’échantillon quel que soit le régime de séchage rencontré ou la taille des pores de cet échantillon. Pour des pores de dimension supérieure à quelques nanomètres, nous montrons que le séchage s’opère en deux étapes : une première période à fort taux de séchage dont la durée décroit avec la réduction de la taille des pores, cette étape est suivie d’une seconde période présentant le développement d’une région sèche depuis la surface de l’échantillon provoquant une chute du taux de séchage. Nous démontrons aussi que les phénomènes de fracturation et de retrait peuvent influer de façon significative sur la durée de cette première période.Quand la taille des pores devient inferieure à quelques nanomètres, nous montrons que l’infime rayon de courbure de l’interface eau-air développant dans les pores du milieu poreux tend à limiter le taux d’évaporation de l’échantillon et entraine sa décroissance progressive au cours du séchage. De manière surprenante, dans ce cas particulier, la distribution d’eau à travers l’échantillon reste homogène tout au long du séchage. Cette dernière observation nous renseigne sur le fonctionnement du mécanisme de ré-équilibrage capillaire dans les nano-pores et montre que les propriétés d’écoulement liquides en milieux confinés diffèrent grandement de celles rencontrées dans des milieux plus grossiers / Drying and imbibition are widely used in industry to formulate and process materials. Familiar to anyone who ever filled a sponge with water and left it to dry, or spread a coat of paint, fluid to solid transitions may affect the aspect, the integrity and the durability of the material processing. Moreover, in industry this transitional steps frequently relies on empirical techniques for the control of both of these phenomena, resulting in an overconsumption of energy. The understanding of the mechanisms behind drying and imbibition are therefore of crucial industrial stakes.Using measurement techniques such as MRI imaging or electron microscopy, we studied the physics of fluid flow within model deformable and non-deformable porous media with pore sizes ranging from a couple of millimiters to a few nanometers, during imbibition or drying.A fundamental discovery our work features is the demonstration that during convective drying, in any case, namely even down to a nanometric pore size, and even if the material shrinks or fracture during the process, the liquid distribution within a sample evolves from the competition between two phenomena. Particularly, capillary re-equilibration caused by capillary effects inducing liquid flow to equilibrate Laplace pressure throughout the partially saturated regions of the samples, and, the inward development of an apparent dry region from the surface of the sample exposed to the airflow.In details, this manuscript shows that at all time capillary-equilibration enables to maintain a homogeneous saturation within the wet region of the porous sample and two regimes may be distinguished from considerations on the drying rate and the pore size of the material. Namely, for pore sizes superior to a couple of nano meters, a first regime exhibits a high drying rate down to lower saturation with increasing pore size, followed by a second regime where a dry region develops from the sample free surface, resulting in a falling rate period. Note that deformation such as shrinkage and crack may convey the extension of the period of high rate. However, in smaller pores the small curvature of the air-water interface limits the evaporation rate from the very beginning of the process and gives rise to a progressively decreasing drying rate while a homogeneous distribution of water is maintained throughout the sample. This last piece of information emphasizes that in nano-pores capillary equilibration still occurs in a series of instantaneous scattered rearrangements of liquid throughout the sample and finally that the flowing properties of the liquid strongly differ from standard unidirectional liquid flow

This study intends to develop a useful tool for the investigation of the behavior of three-dimensional elastic frame structures undergoing large deformations and large rotations, using a mini-computer with an attached array processor. An updated Lagrangian finite element formulation is established by employing conventional two node-twelve degree of freedom beam elements. In order to trace the pre- and post-buckling equilibrium path, an improved nonlinear solution procedure is proposed. The software is designed to make it possible to solve large-scale problems on a mini-computer by adopting a hypermatrix scheme and the segmentation into a number of processors which are independent programs. The software is simulated to estimate the performance of the software on a combined mini-computer/array processor system. By using the simulator time measurements are performed for three different cases of large-scale three-dimensional frame structure models, which verify the usefulness of the array processor in the solution of non-linear finite element structural problems. With the use of the hypermatrix scheme, an alternative solution algorithm for system of linear equations is proposed. The accuracy of the finite element formulation and the effectiveness of the solution algorithms implemented are demonstrated by carefully selected two- and three-dimensional frame examples. Finally, directions for further research are discussed.

Description of the interaction of a shallow-water wave with variable topography is a classical and fundamental problem of fluid mechanics. The behaviour of linear waves and isolated solitary waves propagating over an uneven bottom is well understood. Much less is known about the propagation of nonlinear wavetrains over obstacles. For shallow-water waves, the nonlinear wavetrains are often generated in the form of undular bores, connecting two different basic flow states and having the structure of a slowly modulated periodic wave with a solitary wave at the leading edge. In this thesis, we examine the propagation of shallow-water undular bores over a nonuniform environment, and also subject to the effect of weak dissipation (turbulent bottom friction or volume viscosity). The study is performed in the framework of the variable-coefficient Korteweg-de Vries (vKdV) and variable-coefficient perturbed Korteweg-de Vries (vpKdV) equations. The behaviour of undular bores is compared with that of isolated solitary waves subject to the same external effects. We show that the interaction of the undular bore with variable topography can result in a number of adiabatic and non-adiabatic effects observed in different combinations depending on the specific bottom profile. The effects include: (i) the generation of a sequence of isolated solitons -- an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore; (ii) the generation of an extended weakly nonlinear wavetrain behind the bore; (iii) the formation of a transient multi-phase region inside the bore; (iv) a nonlocal variation of the leading solitary wave amplitude; (v) the change of the characteristics wavelength in the bore; and (vi) occurrence of a ``modulation phase shift" due to the interaction. The non-adiabatic effects (i) -- (iii) are new and to the best of our knowledge, have not been reported in previous studies. We use a combination of nonlinear modulation theory and numerical simulations to analyse these effects. In our work, we consider four prototypical variable topography profiles in our study: a slowly decreasing depth, a slowly increasing depth , a smooth bump and a smooth hole, which leads to qualitatively different undular bore deformation depending on the geometry of the slope. Also, we consider (numerically) a rapidly varying depth topography, a counterpart of the ``soliton fission" configuration. We show that all the effects mentioned above can also be observed when the undular bore propagates over a rapidly changing bottom . We then consider the modification of the variable topography effects on the undular bore by considering weak dissipation due to turbulent bottom friction or volume viscosity. The dissipation is modelled by appropriate right-hand side terms in the vKdV equation. The developed methods and results of our work can be extended to other problems involving the propagation of undular bores (dispersive shock waves in general) in variable media.

Mg alloys have spurred a renewed academic and industrial interest because of their ultra-light-weight and high specific strength properties. Hexagonal close packed Mg has low deformability and a high plastic anisotropy between basal and non-basal slip systems at room temperature. Alloying with Li and other elements is believed to counter this deficiency by activating non-basal slip by reducing their nucleation stress. In this work I study how Li addition affects deformation mechanisms in Mg using atomistic simulations. In the first part, I create a reliable and transferable concentration dependent embedded atom method (CD-EAM) potential for my molecular dynamics study of deformation. This potential describes the Mg-Li phase diagram, which accurately describes the phase stability as a function of Li concentration and temperature. Also, it reproduces the heat of mixing, lattice parameters, and bulk moduli of the alloy as a function of Li concentration. Most importantly, our CD-EAM potential reproduces the variation of stacking fault energy for basal, prismatic, and pyramidal slip systems that influences the deformation mechanisms as a function of Li concentration. This success of CD-EAM Mg-Li potential in reproducing different properties, as compared to literature data, shows its reliability and transferability. Next, I use this newly created potential to study the effect of Li addition on deformation mechanisms in Mg-Li nanocrystalline (NC) alloys. Mg-Li NC alloys show basal slip, pyramidal type-I slip, tension twinning, and two-compression twinning deformation modes. Li addition reduces the plastic anisotropy between basal and non-basal slip systems by modifying the energetics of Mg-Li alloys. This causes the solid solution softening. The inverse relationship between strength and ductility therefore suggests a concomitant increase in alloy ductility. A comparison of the NC results with single crystal deformation results helps to understand the qualitative and quantitative effect of Li addition in Mg on nucleation stress and fault energies of each deformation mode. The nucleation stress and fault energies of basal dislocations and compression twins in single crystal Mg-Li alloy increase while those for pyramidal dislocations and tension twinning decrease. This variation in respective values explains the reduction in plastic anisotropy and increase in ductility for Mg-Li alloys.