The Eshelby-type problems of an arbitrary-shape polygonal or polyhedral inclusion embedded in an infinite homogeneous isotropic elastic material are analytically solved using a simplified strain gradient elasticity theory (SSGET) that contains a material length scale parameter. The Eshelby tensors for a plane strain inclusion with an arbitrary polygonal cross section and for an arbitrary-shape polyhedral inclusion are analytically derived in general forms in terms of three potential functions. These potential functions, as area integrals over the polygonal cross section and volume integrals over the polyhedral inclusion, are evaluated. For the polygonal inclusion problem, the three area integrals are first transformed to three line integrals using the Green's theorem, which are then evaluated analytically by direct integration. In the polyhedral inclusion case, each of the three volume integrals is first transformed to a surface integral by applying the divergence theorem, which is then transformed to a contour (line) integral based on Stokes' theorem and using an inverse approach. In addition, the Eshelby tensor for an anti-plane strain inclusion with an arbitrary polygonal cross section embedded in an infinite homogeneous isotropic elastic material is analytically solved. Each of the newly derived Eshelby tensors is separated into a classical part and a gradient part. The latter includes the material length scale parameter additionally, thereby enabling the interpretation of the inclusion size effect. For homogenization applications, the area or volume average of each newly derived Eshelby tensor over the polygonal cross section or the polyhedral inclusion domain is also provided in a general form. To illustrate the newly obtained Eshelby tensors and their area or volume averages, different types of polygonal and polyhedral inclusions are quantitatively studied by directly using the general formulas derived. The numerical results show that the components of the each SSGET-based Eshelby tensor for all inclusion shapes considered vary with both the position and the inclusion size. It is also observed that the components of each averaged Eshelby tensor based on the SSGET change with the inclusion size.

This thesis is devoted to the numerical investigation of mechanical behavior of Dual phase (DP) steels. Such grade of advanced high strength steels (AHSS) is favorable to the automotive industry due the unique properties such as high strength and ductility with low finished cost. Many experimental and numerical studies have been done to achieve the optimized behavior of DP steels by controlling their microstructure. Experiments are costly and time consuming so in recent years numerical tools are utilized to help the metallurgist before doing experiments. Most of the numerical studies are based on classical (local) constitutive models where no material length scale parameters are incorporated in the model. Although these models are proved to be very effective in modeling the material behavior in the large scales but they fail to address some critical phenomena which are important for our goals. First, they fail to address the size effect phenomena which materials show at microstructural scale. This means that materials show stronger behavior at small scales compared to large scales. Another issue with classical models is the mesh size dependency in modeling the softening behavior of materials. This means that in the finite element context (FEM) the results will be mesh size dependent and no converged solution exist upon mesh refinement. Thereby by applying the classical (local) models one my loose the accuracy on measuring the strength and ductility of DP steels. Among the non-classical (nonlocal) models, gradient-enhanced plasticity models which consider the effect of neighboring point on the behavior of one specific point are proved to be numerically effective and versatile tools to accomplish the two concerns mentioned above. So in this thesis a gradient-enhanced plasticity model which incorporates both the energetic and dissipative material length scales is derived based on the laws of thermodynamics. This model also has a consistent yield-like function for the interface which is an essential part of the higher-order gradient theories. The main issue with utilizing these theories is the implementation which limits the application of these theories for modeling the real problems. Here a straightforward implementation method based on the classical FEM and Meshless method will be proposed which due to its simplicity it can be applied for many problems. The application of the developed model and implementation will be shown on removing the mesh size dependency and capturing the size effect in microstructure level of dual phase steels.

This thesis analyzes the relationship between stock returns and firm-specific characteristics including market beta, size, book-to-market ratio, leverage, earnings yield, net sales-to-price ratio and prior return performance in Istanbul Stock Exchange during the period 1993-2003. Moreover, the predictability of some macroeconomic variables based on the stock market return behavior is investigated.

The paper proposes a method for characterizing the in-situ interaction between filaments in a multifilament yarn. The stress transfer between neighboring filaments causes the reactivation of a broken filament at some distance from the break. The utilized statistical bundle models predict a change in the slope of the mean size effect curve once the specimen length becomes longer than the stress transfer length. This fact can be exploited in order to determine the stress transfer length indirectly using the yarn tensile test with appropriately chosen test lengths. The identification procedure is demonstrated using two test series of tensile tests with AR-glass and carbon yarns.

This thesis contributes towards understanding of mechanical response of 3D composites and ceramics. Composite materials have widespread applications ranging from aerospace, civil sectors to sports and drones. One important application is in composite armours where composites and ceramic layers are used together. Therefore, it is important to study the mechanical response of these components to develop better armour systems. The first part of this thesis concerns with dynamic penetration response of confined ceramic targets. In the second part, mechanics of a novel 3D composite consisting of orthogonal carbon fibre tows is studied. The dynamic penetration of ceramic target by a long-rod projectile is studied using a mechanism based ceramic constitutive model. This is to capture and explain the essential physics observed during penetration of a ceramic target such as dwell and structural size effect. Dwell is captured using the constitutive model and the related physics is studied along with identification of causes of dwell. Origins of structural size effect in ceramics are identified and their influences are studied. In the second part of the thesis a novel 3D composite consisting of three mutually perpendicular orthogonal tows is studied under compression, indentation and three-point bending. Under compression along low fibre volume fraction direction (Z), the 3D composite forms stable and multiple kinks in the Z tows resulting in 10% ductility. This contrasts with traditional UD or 2D composites which fail catastrophically at 2% strain. The stability in the case of the 3D composite is due to the constraint imposed by the surrounding material. Under indentation, the 3D composite has a near isotropic and ductile response. In contrast, traditional cross-ply composites show highly anisotropic response where indentation results in brittle failure along in-plane direction. Under three-point bending, the response was ductile in Z-direction and brittle in other two directions. Overall, the 3D composite studied in this thesis shows improvement over traditional CFRPs in ductility and energy absorption capability. The 3D composite has been demonstrated to have smooth load-displacement curves reminiscent to indentation of metal in all three directions achieved at densities significantly lower than structural metals that display equivalent ductility. Thus, these 3D composites are strong candidates for applications where loading direction is unknown a-priori, and where high energy absorption is required along with reusability of the material.

No trabalho estuda-se o crescimento de trincas em carga monotônica e cíclica nos casos de materiais quase-frágeis, introduzindo uma lei de dano cíclico. Revisam-se conceitos sobre modelos coesivos, leis de carga-descarga, leis de evolução de dano e efeito de escala. É seguido o modelo coesivo irreversível proposto por Wang e Siegmund (2006). Em particular se dá ênfase aos efeitos de escala não estatísticos. O modelo de zona coesiva irreversível apresenta uma formulação de dano e considera carregamento em fadiga. Quando o tamanho estrutural é reduzido (ou as trinca se extendem), a fratura por fadiga não mais ocorre por propagação de trinca, mas sim por uma decoesão uniforme. O objetivo desde trabalho é implementar este modelo e verificar sua potencialidade na captura de efeitos de escala, comparando com experimentos e dados disponíveis na literatura. / At present work is intended to study crack growth in cyclic and monotonic loading in the case of quasi-brittle materials, introducing a damage mechanism, is reviewed concepts of cohesive models, loading-unloading laws, damage evolution laws and effect of scale. The irreversible cohesive zone model proposed by Wang e Siegmund (2006) is followed. In particular emphasizes in the not statistical size effects. The irreversible cohesive zone model, presents a damage formulation and considers fatigue loading. It is demonstrated in this study that, when the structure size is reduced (or extend cracks), the fatigue fracture no longer occurs by crack propagation, then occurs by uniform decohesion . The objetive of this work is implementing this model and verify its capability to capture the scale effect compared with experiments and data available in literature.

L'absence de structure cristalline dans les verres métalliques tendrait à suggérer qu'aucun effet d'échelle sur leur comportement mécanique ne pourrait exister. Cependant, la diminution de la taille des éprouvettes de verre métallique, principalement solliciter en micro-compression sur des micro-pilliers usiné au FIB à partir de BMG révèlent une transition entre des mécanismes de déformation localisés dans des bandes de cisaillement pour des échelles supérieures à 400 nm et des mécanismes qui présentent des déformations homogènes en dessous de 400 nm. Des interrogations demeurent cependant sur l'impact des procédés d'élaboration des échantillons. Dans cette thèse, on s'intéresse à une autre voie de caractérisation des effets d'échelle sur le comportement mécanique des verres métalliques par l'élaboration et la caractérisation d'éprouvettes obtenues par des procédés de microélectronique dans des films minces de verre métallique de différentes épaisseurs, sans recours à de l'usinage FIB. La structure amorphe et la composition des dépôts réalisés par MS-PVD ont été confirmées par des analyses DRX et MET. L'homogénéité des dépôts entre les différentes épaisseurs a été confirmée par l'invariance du module de Young et du module de cisaillement déterminé par diffusion Brillouin sur chaque épaisseur. Des mesures de nano indentation ont cependant révélé une diminution de la dureté, une augmentation du module de compressibilité et du coefficient de Poisson avec l'augmentation de l'épaisseur des films. L'observation des déformations d'éprouvettes de flexion et des empreintes en nano indentation confirme l'existence d'une taille critique d'éprouvette. Les relations entre les différentes propriétés mécaniques et les observations sur les effets d'échelle sont discutées à partir du modèle des STZ et d'une loi de comportement élasto-plastique parfaite pour toutes les épaisseurs. / The lack of cristalline structure in metallic glasses suggests that no mechanical size effect could be expected. However, if the sample size decreases, a transition around 400 nm in size between deformations localized in shear band and homogeneous deformations was observed mainly on micropillars machined by FIB. But there are still a few questions which remained unanswered on elaboration process and their influence on amorphous structure with the size decreasing. This thesis deals with on a new way to characterize the size effect on the mechanical behaviour of metallic glasses. Metallic glasses thin films were elaborated by MS-PVD and mechanical samples were designed thanks to microelectronic process. Homogeneity of the amorphous structure and of the composition were determined by XRD and TEM. Elastic constant such as Young modulus and shear modulus obtained by Brillouin scattering analysis are also steady whatever the thicknesses. Nevertheless, nano indentation measures showed that Poisson ratio and Bulk modulus increase when the thin films thicknesses increase. Deformations observed on nano bending sample and imprints in nano indentation show also a transition between homogeneous deformation and deformations with shear bands. The origins of these transitions between the mechanical properties are discussed from a elastic perfectly plastic model and the Shear Transition Zone model.

This paper shows the existence of the size effect in the cryptocurrency market. The size effect is a market phenomenon observed in the stock market in which smaller assets outperform larger assets. Recent literature has revealed the size effect in other financial markets as well. In order to explain the size effect, this paper proposes a general quantitative theory that supports its existence in any financial markets under specific conditions. Furthermore, the paper tests for the size effect in the cryptocurrency market using daily price data from April 2013 to April 2018. The paper finds a statistically significant size effect across the cryptocurrency market during the sample period. In the process, we test a profitable pair-trading strategy that involves opening a short position on the higher rank (larger assets) and opening a long position on the lower rank (smaller assets) of the cryptocurrency market. Based on our findings, we discuss the implications on modern finance, specifically on the subjects of Efficient Market Hypothesis and asset pricing models.

No trabalho estuda-se o crescimento de trincas em carga monotônica e cíclica nos casos de materiais quase-frágeis, introduzindo uma lei de dano cíclico. Revisam-se conceitos sobre modelos coesivos, leis de carga-descarga, leis de evolução de dano e efeito de escala. É seguido o modelo coesivo irreversível proposto por Wang e Siegmund (2006). Em particular se dá ênfase aos efeitos de escala não estatísticos. O modelo de zona coesiva irreversível apresenta uma formulação de dano e considera carregamento em fadiga. Quando o tamanho estrutural é reduzido (ou as trinca se extendem), a fratura por fadiga não mais ocorre por propagação de trinca, mas sim por uma decoesão uniforme. O objetivo desde trabalho é implementar este modelo e verificar sua potencialidade na captura de efeitos de escala, comparando com experimentos e dados disponíveis na literatura. / At present work is intended to study crack growth in cyclic and monotonic loading in the case of quasi-brittle materials, introducing a damage mechanism, is reviewed concepts of cohesive models, loading-unloading laws, damage evolution laws and effect of scale. The irreversible cohesive zone model proposed by Wang e Siegmund (2006) is followed. In particular emphasizes in the not statistical size effects. The irreversible cohesive zone model, presents a damage formulation and considers fatigue loading. It is demonstrated in this study that, when the structure size is reduced (or extend cracks), the fatigue fracture no longer occurs by crack propagation, then occurs by uniform decohesion . The objetive of this work is implementing this model and verify its capability to capture the scale effect compared with experiments and data available in literature.

Este estudo analisa a influência do porte empresarial no retorno das ações do mercado brasileiro, lidando com a sobreposição aparentemente existente entre porte da empresa e liquidez das ações e buscando elucidar qual variável é dominante na determinação de retornos acionários. Para tanto, utiliza-se uma análise de dados em painel como ferramenta econométrica para a obtenção de resultados significativos. Os modelos tradicionais de precificação de ativos, notadamente o CAPM, partem de algumas premissas que possuem pouca aderência à realidade dos mercados acionários. Há evidências de que, no Brasil, o CAPM tem sido ineficaz em explicar os retornos do mercado acionário. Por essa razão, algumas variáveis são comumente adicionadas ao modelo original, sendo que o porte empresarial se encontra no topo da lista. Contudo, a legitimidade do porte empresarial reduzido como fator de risco a ser remunerado ao acionista não é consensual em mercados mais maduros como o americano tampouco no mercado brasileiro. O estudo leva em conta um intervalo de tempo de 16 anos (de 1995 até 2011) e analisa a influência dessas variáveis no retorno das ações com diferentes defasagens de tempo entre as variáveis (de 1 a 5 anos). O trabalho conclui que há uma significativa influência do porte empresarial nos retornos das ações. A relação estatística é negativa, isto é, empresas de menor porte tendem a ter custo de capital próprio mais alto. Esse resultado está alinhado com a pesquisa internacional sobre o assunto. O modelo quantitativo sugere que a cada variação de uma unidade logarítmica no porte há uma variação de 4,03% no retorno esperado da ação. Em relação à liquidez não foi encontrada, de forma consistente, relação estatística de que essa variável afeta o retorno das ações quando controlada pelo porte empresarial no mercado brasileiro. / This study analyses the influence of company size in stock returns in Brazilian market, dealing with the apparent superposition between company size and stock liquidity and searching to elucidate which variable is dominant in determining stock returns. With that purpose, panel data analysis has been used as econometric technic, searching to obtain significant results. Traditional pricing models, mainly CAPM, are based on certain premises which have little in common with the stock markets. There is evidence that, in Brazil, CAPM has been unable to explain stock returns properly. For this reason, some variable are commonly added to the original model and the company size is at the top of the list. However, the legitimacy of the size effect as a risk factor to be paid off to the stockholder is neither consensual in more mature markets, as the American one, nor in the Brazilian market. The study takes into account a time span of 16 years (from 1995 to 2011) and analyses the influence of these variables in stock returns with different delays among variables (from 1 to 5 years). The work concludes that there is a significant size effect in stock returns. The statistical relation is negative, that is, smaller companies tend to have higher cost of equity. This result is aligned with the international research on the subject. The quantitative model suggest that for a logarithmic unit variation in company size there is a 4,03% additional cost of equity. Concerning liquidity, it has not been found, consistently, statistical relation that this variable affects stock returns when controlled by company in Brazilian market.