When foundations are designed on weak clay layers, it is a common practice to modify the subgrade by installing stone columns. Currently used methods for determining the level of ground modification, represented by the percentage of soil replaced (replacement ratio), assume a rigid foundation. These analytical methods provide the designer with the potential settlement reduction based on the compressibility parameters of the subgrade and the replacement ratio. The deficiencies of these methods are the assumption of rigidity of the foundation and the consideration of the settlement reduction as the only design criterion. Furthermore, they do not consider the effects that ground modification has on differential settlement, moments, and shear forces within the slab. In order to determine the effects of ground modification on the overall performance of a flexible foundation, a computer program was formulated which compares a multitude of design parameters of the modified subgrade to those of the unmodified subgrade to determine the impact of ground modification. By performing this investigation, correlations were found between the replacement ratio and the settlement reduction factors. Similarly, correlations were also found between the ratio of the length of the foundation to the radius of relative stiffness, and the moments and shear forces generated within the slab. The use of the findings of this thesis would allow the design to make more informed decisions when designing foundations on modified subgrade resulting in safer and more economical designs.

3D reinforced composites are favored for aerospace, automotive and wind turbine applicationbecause of their high specific stiffness and strength in the in-plane and out-ofplanedirections. In these composites, pins, stitching yarns and binder yarns are insertedthrough-the-thickness of the in-plane fiber-reinforced regions. Binder parameters as diameter,content, pattern and tensioning can further be varied to regulate the out-of-planeproperties. However, the insertion of these binders distorts the reinforcement which furthercan affect the global and local mechanical behaviour. Unit-cell models offered avaluable approach to assess the effect of the distortions on these mechanical features.An approach is presented to include the main geometrical features of pinned, stitchedand 3D woven composites into mesoscopic unit-cell models. Discretised lines, whichrepresent the main geometrical features, are hereby gradually shaped by geometrical operationswhile a geometrical contact treatment account for line interactions. The localfiber volume fraction and fiber direction distributions are afterwards modelled on crosssectionsin a post-processing step. Tools are further proposed to automatically transformthe geometrical models into finite element models. The effect of distortions, local fibervolume fraction and fiber direction, and typical geometrical features for each 3D reinforcedcomposite, on the stiffness and damage initiation stress levels is investigated bymeans of elastic finite element (FE)-computations.The shape of geometrical features corresponding to the different binder parameters couldautomatically be generated and the dimensions of features could be controlled by the parametersof the geometrical operations. The stiffness of a 3D reinforced composite havebeen observed to be either decreased or increased (dependent on the stacking sequence,the binder type and the loading direction). Early damage initiation in the FE-modelswas observed to take place near the binder locations, which was mainly caused by transverseand shear cracking in the fiber-reinforced regions. Local fiber volume fraction andfiber direction have shown to affect damage initation mechanisms and stress levels, andshould therefore be properly included in the models. In future work, the possibility ofthe framework to generate unit-cells including voids and micro-vascular networks canbe investigated and the finite element models can be extended with damage and crackpropagation mechanisms for damage and failure computations. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

<p> The symmetries and unit cell dimensions of crystals of Na4P2O7, δ-Ba2P2O7 and H4P2O7 have been determined by X-ray diffraction methods. Changes in symmetry and unit cell dimensions of Na4P2O7 as a function of temperature have been described and a model has been proposed describing the statistics of these changes. The existence of disorder in the crystal structure of δ-Ba2P2O7 has been established and the unit cell dimensions of a previously unreported low temperature form are reported.</p> / Thesis / Master of Science (MSc)

This study is devoted to the development of an integrated numerical modeling enabling one to investigate the static and the dynamic behaviors and failures of 2-D textile composite as well as 3-D orthogonal woven composite structures weakened by cracks and subjected to static-, impact- and ballistic-type loads. As more complicated modeling about textile composite structures is introduced, some of homogenization schemes, geometrical modeling and crack propagations become more difficult problems to solve. To overcome these problems, this study presents effective mesh-generation schemes, homogenization modeling based on a repeating unit cell and sinusoidal functions, and also a cohesive element to study micro-crack shapes. This proposed research has two: 1) studying behavior of textile composites under static loads, 2) studying dynamic responses of these textile composite structures subjected to the transient/ballistic loading. In the first part, efficient homogenization schemes are suggested to show the influence of textile architectures on mechanical characteristics considering the micro modeling of repeating unit cell. Furthermore, the structures of multi-layered or multi-phase composites combined with different laminar such as a sub-laminate, are considered to find the mechanical characteristics. A simple progressive failure mechanism for the textile composites is also presented. In the second part, this study focuses on three main phenomena to solve the dynamic problems: micro-crack shapes, textile architectures and textile effective moduli. To obtain a good solutions of the dynamic problems, this research attempts to use four approaches: I) determination of governing equations via a three-level hierarchy: micro-mechanical unit cell analysis, layer-wise analysis accounting for transverse strains and stresses, and structural analysis based on anisotropic plate layers, II) development of an efficient computational approach enabling one to perform transient response analyses of 2-D plain woven, 2-D braided and 3-D orthogonal woven composite structures featuring matrix cracking and exposed to time-dependent ballistic loads, III) determination of the structural characteristics of the textile-layered composites and their degraded features under smeared and discrete cracks, and assessment of the implications of stiffness degradation on dynamic response to impact loads, and finally, IV) the study of the micro-crack propagation in the textile/ceramic layered plates. A number of numerical models have been carried out to investigate the mechanical behavior of 2-D plain woven, 2-D braided and 3-D orthogonal woven textile composites with several geometrical representations, and also study the dynamic responses of multi-layered or textile layered composite structures subjected to ballistic impact penetrations with a developed in-house code. / Ph. D.

Natural fibers have drawn attention of researchers as an environmentally-friendly alternative to synthetic fibers. Developing natural fiber reinforced bio-composites are a viable alternative to the problems of non-degrading and energy consuming synthetic composites. This study focuses on (i) the application of kenaf fiber as a potential reinforcement and, (ii) determining the tensile properties of the randomly oriented short kenaf fiber composite both experimentally and numerically. Kenaf fiber micro-structure and its Young's modulus with varying gage length (10, 15, 20, and 25.4 mm) were investigated. The variation in tensile strength of kenaf fibers was analyzed using the Weibull probability distribution function. It was observed that the Young's modulus of kenaf fiber increased with increase in gage length. Fabrication of randomly oriented short kenaf fiber using vacuum bagging techniques and hand-lay-up techniques were discussed and the tensile properties of the specimens were obtained experimentally. The tensile modulus of the composite sample at 22% fiber volume fraction was found to be 6.48 GPa and tensile strength varied from 20 to 38 MPa. Numerical models based on the micro mechanics concepts in conjunction with finite element methods were developed for predicting the composite properties. A two-step homogenization procedure was developed to evaluate the elastic constants at the cell wall level and the meso-scale level respectively. Von-Mises Fisher probability distribution function was applied to model the random orientation distribution of fibers and obtain equivalent modulus of composite. The predicted equivalent modulus through numerical homogenization was in good agreement with the experimental results.

A multi-domain homogenization method is proposed and developed in this thesis based on a two-scale technique. The method is capable of analyzing composite structures with several periodic distributions by partitioning the entire domain of the composite into substructures making use of the classical homogenization theory following a first-order standard continuum mechanics formulation. The need to develop the multi-domain homogenization method arose because current homogenization methods are based on the assumption that the entire domain of the composite is represented by one periodic or quasi-periodic distribution. However, in some cases the structure or composite may be formed by more than one type of periodic domain distribution, making the existing homogenization techniques not suitable to analyze this type of cases in which more than one recurrent configuration appears. The theoretical principles used in the multi-domain homogenization method were applied to assemble a computational tool based on two nested boundary value problems represented by a finite element code in two scales: a) one global scale, which treats the composite as an homogeneous material and deals with the boundary conditions, the loads applied and the different periodic (or quasi-periodic) subdomains that may exist in the composite; and b) one local scale, which obtains the homogenized response of the representative volume element or unit cell, that deals with the geometry distribution and with the material properties of the constituents. The method is based on the local periodicity hypothesis arising from the periodicity of the internal structure of the composite. The numerical implementation of the restrictions on the displacements and forces corresponding to the degrees of freedom of the domain's boundary derived from the periodicity was performed by means of the Lagrange multipliers method. The formulation included a method to compute the homogenized non-linear tangent constitutive tensor once the threshold of nonlinearity of any of the unit cells has been surpassed. The procedure is based in performing a numerical derivation applying a perturbation technique. The tangent constitutive tensor is computed for each load increment and for each iteration of the analysis once the structure has entered in the non-linear range. The perturbation method was applied at the global and local scales in order to analyze the performance of the method at both scales. A simple average method of the constitutive tensors of the elements of the cell was also explored for comparison purposes. A parallelization process was implemented on the multi-domain homogenization method in order to speed-up the computational process due to the huge computational cost that the nested incremental-iterative solution embraces. The effect of softening in two-scale homogenization was investigated following a smeared cracked approach. Mesh objectivity was discussed first within the classical one-scale FE formulation and then the concepts exposed were extrapolated into the two-scale homogenization framework. The importance of the element characteristic length in a multi-scale analysis was highlighted in the computation of the specific dissipated energy when strain-softening occurs. Various examples were presented to evaluate and explore the capabilities of the computational approach developed in this research. Several aspects were studied, such as analyzing different composite arrangements that include different types of materials, composites that present softening after the yield point is reached (e.g. damage and plasticity) and composites with zones that present high strain gradients. The examples were carried out in composites with one and with several periodic domains using different unit cell configurations. The examples are compared to benchmark solutions obtained with the classical one-scale FE method. / En esta tesis se propone y desarrolla un método de homogeneización multi-dominio basado en una técnica en dos escalas. El método es capaz de analizar estructuras de materiales compuestos con varias distribuciones periódicas dentro de un mismo continuo mediante la partición de todo el dominio del material compuesto en subestructuras utilizando la teoría clásica de homogeneización a través de una formulación estándar de mecánica de medios continuos de primer orden. La necesidad de desarrollar este método multi-dominio surgió porque los métodos actuales de homogeneización se basan en el supuesto de que todo el dominio del material está representado por solo una distribución periódica o cuasi-periódica. Sin embargo, en algunos casos, la estructura puede estar formada por más de un tipo de distribución de dominio periódico. Los principios teóricos desarrollados en el método de homogeneización multi-dominio se aplicaron para ensamblar una herramienta computacional basada en dos problemas de valores de contorno anidados, los cuales son representados por un código de elementos finitos (FE) en dos escalas: a) una escala global, que trata el material compuesto como un material homogéneo. Esta escala se ocupa de las condiciones de contorno, las cargas aplicadas y los diferentes subdominios periódicos (o cuasi-periódicos) que puedan existir en el material compuesto; y b) una escala local, que obtiene la respuesta homogenizada de un volumen representativo o celda unitaria. Esta escala se ocupa de la geometría, y de la distribución espacial de los constituyentes del compuesto así como de sus propiedades constitutivas. El método se basa en la hipótesis de periodicidad local derivada de la periodicidad de la estructura interna del material. La implementación numérica de las restricciones de los desplazamientos y las fuerzas derivadas de la periodicidad se realizaron por medio del método de multiplicadores de Lagrange. La formulación incluye un método para calcular el tensor constitutivo tangente no-lineal homogeneizado una vez que el umbral de la no-linealidad de cualquiera de las celdas unitarias ha sido superado. El procedimiento se basa en llevar a cabo una derivación numérica aplicando una técnica de perturbación. El tensor constitutivo tangente se calcula para cada incremento de carga y para cada iteración del análisis una vez que la estructura ha entrado en el rango no-lineal. El método de perturbación se aplicó tanto en la escala global como en la local con el fin de analizar la efectividad del método en ambas escalas. Se lleva a cabo un proceso de paralelización en el método con el fin de acelerar el proceso de cómputo debido al enorme coste computacional que requiere la solución iterativa incremental anidada. Se investiga el efecto de ablandamiento por deformación en el material usando el método de homogeneización en dos escalas a través de un enfoque de fractura discreta. Se estudió la objetividad en el mallado dentro de la formulación clásica de FE en una escala y luego los conceptos expuestos se extrapolaron en el marco de la homogeneización de dos escalas. Se enfatiza la importancia de la longitud característica del elemento en un análisis multi-escala en el cálculo de la energía específica disipada cuando se produce el efecto de ablandamiento. Se presentan varios ejemplos para evaluar la propuesta computacional desarrollada en esta investigación. Se estudiaron diferentes configuraciones de compuestos que incluyen diferentes tipos de materiales, así como compuestos que presentan ablandamiento después de que el punto de fluencia del material se alcanza (usando daño y plasticidad) y compuestos con zonas que presentan altos gradientes de deformación. Los ejemplos se llevaron a cabo en materiales compuestos con uno y con varios dominios periódicos utilizando diferentes configuraciones de células unitarias. Los ejemplos se comparan con soluciones de referencia obtenidas con el método clásico de elementos finitos en una escala.

The advent of rapid manufacturing has enabled the realization of countless products that have heretofore been infeasible. From customized clear braces to jet fighter ducts and one-off dental implants, rapid manufacturing allows for increased design complexity and decreased manufacturing costs. The manufacturing capabilities of this process have evolved to the point that they have surpassed current design capabilities. Meso-scale lattice structures can now be built that contain more lattice struts than it is reasonable to efficiently define. This work has attempted to create a method for designing such lattice structures that is efficient enough to allow for the design of large or complex problems. The main hindrance to the design of complex meso-scale lattice problems is essentially the need to define the strut diameters. While it is obvious that a large design would contain more struts than can be specified by hand, designs also quickly surpass the current capabilities of computational optimization routines. To overcome this problem, a design method has been developed that uses a unit-cell library correlated to finite element analysis of the bounding geometry to tailor the structure to the anticipated loading conditions. The unit-cell library is a collection of base lattice primitives, or unit-cells, that have been specialized for certain applications. In this case, primitives have been created that perform best under the types of stress analyzed by finite element analysis. The effectiveness of this process has been demonstrated through several example problems. In all cases, the unit-cell library approach was able to create structures in less time than current methods. The resulting structures had structural performance slightly lower than similar models created through optimization methods, although the extent of this degradation was slight. The method developed in this work performs extremely well, and is able to create designs for even the most complex lattice structures. There is room for future development, however, in the streamlining of the design process and consideration of higher-order affects within unit-cells.

This study investigates the through-thickness behaviour of carbon/epoxy laminates. A through-thickness compression test regime was conducted utilising three specimen designs, which are waisted, hollow cylindrical and cubic specimens. An assessment and comparison of each specimen is given regarding their advantages and disadvantages in characterising the through-thickness response of [+45/-45/90/0]s quasi-isotropic AS4/8552 carbon/epoxy laminates. A finite element (FE) study of the three specimens is presented which results in specimen geometries that provided a macroscopically uniform stress response throughout the gauge length whilst also minimising other features such as stress concentrations. Further to the final geometries being presented, the method of manufacture for the laminate and machining processes for each of the specimens is given. A mesoscopic FE study is presented relating to the free-edge effects induced by through-thickness loading in quasi-isotropic laminates. The results presented show that free-edge effects will be present in the test specimens and will have a larger overall impact on the hollow cylindrical specimen. The free-edge effects also increase the stress concentrations present in the corners of the waisted and cubic specimens. Characteristic stress strain curves are presented for each specimen with strain data taken from post yield strain gauges attached to the specimens. The extracted initial Young's modulus Ez and Poisson's ratios vzx and vzy show a small variation between specimens. The strength values for the three specimens vary greatly with the waisted specimen being the strongest and cylindrical specimen the weakest, indicating that the chosen specimen geometry dominates failure. The experimental data will be used for test case 12 in the Second World Wide Failure Exercise (WWFE-II). A study is presented to predict the effective elastic properties of Z-pinned laminates. The materials under consideration are UD and [0/90]s cross-ply AS4/3501-6 carbon/epoxy laminates. Estimates on the effective properties are provided by two FE approaches and two analytical bounding approaches; namely Voigt and Reuss bounds and Walpole's bounding theory. The two FE approaches are based on extreme assumptions about the in-plane fibre volume fraction in the presence of Z-pins and provide a tight range of values in which the real result should lie. Furthermore, whilst the bounding methods are simple and in the case of Young's moduli produce very wide bounds the selection of the suitable bound result can lead to a good estimate in comparison with the FE data. Typically the best bounding method result for each elastic property is within 10% of the FE predictions.

The issue of accurately determining the effective properties of composite materials has received the attention of numerous researchers in the last few decades and continues to be in the forefront of material research. Micromechanics models have been proven to be very useful tools for design and analysis of composite materials. In the present work, a versatile micromechanics modeling framework, namely, the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH), has been invented and various micromechancis models have been constructed in light of this novel framework. Considering the periodicity as a small parameter, we can formulate the variational statements of the unit cell through an asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. Finally, we employed the finite element method to solve the numerical solution of the constrained minimization problem. If the local fields within the unit cell are of interest, the proposed models can also accurately recover those fields based on the global behavior. In comparison to other existing models, the advantages of VAMUCH are: (1) it invokes only two essential assumptions within the concept of micromechanics for heterogeneous material with identifiable unit cells; (2) it has an inherent variational nature and its numerical implementation is shown to be straightforward; (3) it calculates the different material properties in different directions simultaneously, which is more efficient than those approaches requiring multiple runs under different loading conditions; and (4) it calculates the effective properties and the local fields directly with the same accuracy as the fluctuation functions. No postprocessing calculations such as stress averaging and strain averaging are needed. The present theory is implemented in the computer program VAMUCH, a versatile engineering code for the homogenization of heterogeneous materials. This new micromechanics modeling approach has been successfully applied to predict the effective properties of composite materials including elastic properties, coefficients of thermal expansion, and specific heat and the effective properties of piezoelectric and electro-magneto-elastic composites. This approach has also been extended to the prediction of the nonlinear response of multiphase composites. Numerous examples have been utilized to clearly demonstrate its application and accuracy as a general-purpose micromechanical analysis tool.

To seek better material behaviors, the research of material properties has been mas- sively carried out in both industrial and academic fields throughout the twentieth century. Composite materials are known for their abilities of combining constituent materials in or- der to fulfill the desirable overall material performance. One of the advantages of composite materials is the adjustment between stiffness and lightness of materials in order to meet the needs of various engineering designs. Even though the finite element analysis is mature, composites are heterogeneous in nature and can present difficulties at the structural level with the acceptable computational time. A way of simplifying such problems is to find a way to connect structural analysis with corresponding analysis of representative microstructure of the material, which is normally called micromechanics modeling or homogenization.Generally speaking, the goal of homogenization is to predict a precise material behavior by taking into account the information stored in both microscopic and macroscopic levels of the composites. Of special concern to researchers and engineers is the thermomechanical behavior of composite materials since thermal effect is almost everywhere in real practical cases of engineering. In aerospace engineering, the thermomechanical behaviors of compos- ites are even more important since flight under high speed usually produces a large amount of heat which will cause very high thermal-related deformation and stress.In this dissertation, the thermomechanical behavior of composites will be studied based on the variational asymptotic method for unit cell homogenization (VAMUCH) which was recently developed as an efficient and accurate micromechanics modeling tool. The theories and equations within the code are based on the variational asymptotic method invented by Prof. Berdichevsky. For problems involving small parameters, the traditional asymptotic method is often applied by solving a system of differential equations while the variational asymptotic method is using a variational statement that only solves one functional of such problems where the traditional asymptotic method may apply.First, we relax the assumption made by traditional linear thermoelasticity that not only a small overall strain is assumed to be small but also the temperature variation. Of course, in this case we need to add temperature dependent material properties to VAMUCH so that the secant material properties can be calculated. Then, we consider the temperature field to be point-wise different within the microstructure; a micromechanics model with nonuniformly distributed temperature field will be addressed. Finally, the internal and external loads induced energies are considered in order to handle real engineering structures under their working conditions.