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A Mecânica do Dano Contínuo é atualmente uma poderosa ferramenta para se modelar o comportamento não-linear de vários materiais decorrente da evolução de um processo de microfissuração. A perda de rigidez causada pelo processo físico tem sido considerada em modelos constitutivos através de variáveis de dano escalar, vetorial ou tensorial. Quando o carregamento é proporcionalmente crescente as deformações residuais podem ser ignoradas e relações constitutivas simples podem ser obtidas, onde os efeitos do dano aparecem por uma penalização direta das propriedades elásticas. Por outro lado, efeitos de dano podem ser acoplados com deformações residuais levando a relações constitutivas mais gerais. Esse trabalho está relacionado a esses tipos de modelos assumindo que o meio ideal apresenta um comportamento elástico linear com danificação ou elastoplástico com danificação. Um dos principais aspectos discutido relaciona-se à formulação variacional, a qual está baseada em conceitos de Análise Convexa e Não-Convexa. Explorando o fato que a evolução do dano tem correspondência com a idealização de regime de encruamento negativo, a teoria de localização de deformação é abordada e um estudo da condição necessária de singularidade ou perda da condição de elipticidade é realizado. Na sequência, uma proposta preliminar para uma análise de pós-singularidade, baseada na Teoria de Bifurcação, é feita no sentido de caracterizar pontos limite ou pontos de bifurcação de solução, em sistemas conservativos. / Continuum Damage Mechanics is nowadays a powerful tool to model the non-linear behaviour of several materials due to evolution of a microcracking process. The lost of rigidity caused by such physical process has been accounted in the constitutive models through a scalar, vectorial or tensorial damage variables. When proportional loading is considered the residuals strains can be ignored and simple constitutive relations can be obtained in which damage effects appear by direct penalization of the elastic properties. On the other hand, damage effects can be coupled with residual strains leading to more general constitutive relations. This work is related to such kind of models assuming that the ideal medium presents a linear elastic-damage or an elastoplastic-damage behaviour. One of the main topics discussed is related to the variational formulation which is based on Convex and Non-Convex Analysis concepts. Exploring the fact that damage evolution has correspondence with a softening idealised regime, the strain localization theory is treated and a study of a necessary condition for singularity or ellipticity tose condition is developed. In the sequence, a introductory poscritical analysis is proposed, based in the bifurcation theory and aiming to detect if the singularity corresponds to a limit or a bifurcation point solution, in conservative systems.

Commercially available polycrystalline Ni (Ni200; grain size: 32 μm) and electrodeposited nanocrystalline Ni (grain size: 57 nm), Ni-2.6%Fe (grain size: 25 nm) and Ni-8.5%Fe (grain size: 20 nm) were analyzed for the phenomena of stress-induced heat generation and strain localization during plastic deformation at room temperature (i.e. 250C). Tensile specimens according to ASTM E8 standard dimensions were tested at strain rates of 10-2/s and 10-1/s, respectively, to record the amount of heat dissipated and the change of localized strain using a high resolution infrared (IR) detector and digital image correlation (DIC) camera, respectively. Results have shown that the maximum temperatures that were recorded in nanocrystalline Ni and Ni-Fe alloys were at least 300C lower than the onset temperatures for subgrain coalescence previously measured through differential scanning calorimetry. It can be concluded that thermally activated grain growth during tensile testing of nanocrystalline Ni and Ni-Fe alloys is not likely to occur.

Commercially available polycrystalline Ni (Ni200; grain size: 32 μm) and electrodeposited nanocrystalline Ni (grain size: 57 nm), Ni-2.6%Fe (grain size: 25 nm) and Ni-8.5%Fe (grain size: 20 nm) were analyzed for the phenomena of stress-induced heat generation and strain localization during plastic deformation at room temperature (i.e. 250C). Tensile specimens according to ASTM E8 standard dimensions were tested at strain rates of 10-2/s and 10-1/s, respectively, to record the amount of heat dissipated and the change of localized strain using a high resolution infrared (IR) detector and digital image correlation (DIC) camera, respectively. Results have shown that the maximum temperatures that were recorded in nanocrystalline Ni and Ni-Fe alloys were at least 300C lower than the onset temperatures for subgrain coalescence previously measured through differential scanning calorimetry. It can be concluded that thermally activated grain growth during tensile testing of nanocrystalline Ni and Ni-Fe alloys is not likely to occur.

The present work focuses on the formulation of a Continuum Damage Mechanics model for nonlinear analysis of masonry structural elements. The material is studied at the macro-level, i.e. it is modelled as a homogeneous orthotropic continuum. The orthotropic behaviour is simulated by means of an original methodology, which is based on nonlinear damage constitutive laws and on the concept of mapped tensors from the anisotropic real space to the isotropic fictitious one. It is based on establishing a one-to-one mapping relationship between the behaviour of an anisotropic real material and that of an isotropic fictitious one. Therefore, the problem is solved in the isotropic fictitious space and the results are transported to the real field. The application of this idea to strain-based Continuum Damage Models is rather innovative. The proposed theory is a generalization of classical theories and allows us to use the models and algorithms developed for isotropic materials. A first version of the model makes use of an isotropic scalar damage model. The adoption of such a simple constitutive model in the fictitious space, together with an appropriate definition of the mathematical transformation between the two spaces, provides a damage model for orthotropic materials able to reproduce the overall nonlinear behaviour, including stiffness degradation and strain-hardening/softening response. The relationship between the two spaces is expressed in terms of a transformation tensor which contains all the information concerning the real orthotropy of the material. A major advantage of this working strategy lies in the possibility of adjusting an arbitrary isotropic criterion to the particular behaviour of the orthotropic material. Moreover, orthotropic elastic and inelastic behaviours can be modelled in such a way that totally different mechanical responses can be predicted along the material axes. The aforementioned approach is then refined in order to account for different behaviours of masonry in tension and compression. The aim of studying a real material via an equivalent fictitious solid is achieved by means of the appropriate definitions of two transformation tensors related to tensile or compressive states, respectively. These important assumptions permit to consider two individual damage criteria, according to different failure mechanisms, i.e. cracking and crushing. The constitutive model adopted in the fictitious space makes use of two scalar variables, which monitor the local damage under tension and compression, respectively. Such a model, which is based on a stress tensor split into tensile and compressive contributions that allows the model to contemplate orthotropic induced damage, permits also to account for masonry unilateral effects. The orthotropic nature of the Tension-Compression Damage Model adopted in the fictitious space is demonstrated. This feature, both with the assumption of two distinct damage criteria for tension and compression, does not permit to term the fictitious space as “isotropic”. Therefore, the proposed formulation turns the original concept of “mapping the real space into an isotropic fictitious one” into the innovative and more general one of “mapping the real space into a favourable (or convenient) fictitious one”. Validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry. The model is fully formulated for the 2-dimensional case. However, it can be easily extended to the 3-dimensional case. It provides high algorithmic efficiency, a feature of primary importance when analyses of even large scale masonry structures are carried out. To account for this requisite it adopts a strain-driven formalism consistent with standard displacement-based finite element codes. The implementation in finite element programs is straightforward. Finally, a localized damage model for orthotropic materials is formulated. This is achieved by means of the implementation of a crack tracking algorithm, which forces the crack to develop along a single row of finite elements. Compared with the smeared cracking approach, such an approach shows a better capacity to predict realistic collapsing mechanisms. The resulting damage in the ultimate condition appears localized in individual cracks. Moreover, the results do not suffer from spurious mesh-size or mesh-bias dependence. The numerical tool is finally validated via a finite element analysis of an in-plane loaded masonry shear wall.

xv, 95 p. : ill. (some col.), maps (some col.) Plate 1. Geologic Map of the Sierra Bacha, Coastal Sonora, Mexico (1:30,000 scale) attached as a separate file. / The Gulf of California is an active rift basin formed by late Cenozoic dextral-oblique extension along the Pacific-North America plate boundary. Well exposed volcanic and sedimentary rocks in the Sierra Bacha, coastal Sonora, Mexico, preserve a history of proto-Gulf (late Miocene) deformation and offer insight into the structures and kinematics responsible for localization of the plate boundary and inception of the Gulf at about 6 Ma. Geologic mapping, fault kinematic analysis, and paleomagnetic data suggest that proto-Gulf deformation in the Sierra Bacha occurred primarily by ENE-WSW extension and that vertical-axis rotation related to dextral strain was minor. Lack of significant dextral shear supports an emerging model for proto-Gulf deformation in which dextral strain was not ubiquitous across Sonora but instead became localized during latest Miocene time in a narrow coastal shear zone that mechanically weakened the lithosphere and helped facilitate continental rupture. This thesis includes the "Geologic Map of the Sierra Bacha, Coastal Sonora, Mexico" as supplemental material. / Committee in charge: Dr. Rebecca J. Dorsey, Chairperson; Dr. Marli B. Miller, Member; Dr. Ray J. Weldon II, Member

Doctor of Philosophy / Department of Civil Engineering / Dunja Peric / A low ratio between the compressive strength of concrete and its cost makes concrete one of the most widely used construction materials in civil engineering. Despite of a very good response to compressive stress, concrete exhibits a low tensile strength and limited tensile strain capacity. Adding short discrete fibers to a cementitious matrix can significantly improve its performance under tensile stress, thus ultimately exhibiting a ductile behavior. Nevertheless, in spite of their beneficial properties fiber reinforced cementitious composites remain underutilized in engineering practice. One of the main reasons for this is a lack of an adequate characterization of the tensile behavior as well as a lack of analysis methods that would allow engineers to incorporate fiber reinforced structural concrete elements into their design. Therefore, this dissertation has four key objectives: 1) to computationally model a stress-strain response of high performance fiber reinforced cementitious composites in uniaxial tension and uniaxial compression prior to macro-crack localization, 2) to develop and perform a diagnostic strain localization analysis for high performance fiber reinforced cementitious composites, the results of which can characterize effects of fibers on failure precursors, 3) to devise and perform an experimental program for characterization of ultra-high performance fiber reinforced cementitious composites, and 4) to characterize a full-fledged behavior including stress-strain and stress-crack opening displacement responses of ultra-high performance fiber reinforced cementitious composites in uniaxial tension. To quantify effects of fibers on onset of strain localization in fiber reinforced cementitious composites a combined computational/analytical models have been developed. To this end, linear-elastic multi-directional fibers were embedded into a cementitious matrix. The resulting composite was described by different types of two-invariant non-associated Drucker-Prager plasticity models. In order to investigate effects of a shape of a yield surface and hardening type linear and nonlinear yield surfaces, and linear and nonlinear hardening rules were considered. Diagnostic strain localization analyses were conducted for several plane stress uniaxial tension and uniaxial compression tests on non-reinforced cementitious composites as well as on high performance fiber-reinforced cementitious composites. It was found that presence of fibers delayed the inception of strain localization in all tests on fiber-reinforced composites. Furthermore, presence of fibers exerted a more significant effect on the strain localization direction and mode in uniaxial compression than in uniaxial tension. The main objective of experimental program was to facilitate characterization of the post-cracking tensile behavior of ultra-high performance fiber reinforced cementitious composites. To this end, five different mixes of fiber-reinforced cementitious composites were cast, whereby volumetric fiber content, fiber shape and water to binder ratio were the experimental variables. Two testing methods were adopted, a direct uniaxial tension test and four-point prism bending test. Two different post-cracking behaviors were observed in direct tension tests, softening and strain hardening accompanied with multiple cracking. On the other hand, the response from prism bending tests was less scattered. Several different inverse analyses were carried out to predict stress-strain and stress-crack opening displacement responses in uniaxial tension based on the prism bending tests. The analyses resulted in worthy correlations with the experimental data, thus suggesting that the prism bending test is a viable alternative to a much more challenging to perform direct tension test for ultra-high performance fiber reinforced composites.

A Mecânica do Dano Contínuo é atualmente uma poderosa ferramenta para se modelar o comportamento não-linear de vários materiais decorrente da evolução de um processo de microfissuração. A perda de rigidez causada pelo processo físico tem sido considerada em modelos constitutivos através de variáveis de dano escalar, vetorial ou tensorial. Quando o carregamento é proporcionalmente crescente as deformações residuais podem ser ignoradas e relações constitutivas simples podem ser obtidas, onde os efeitos do dano aparecem por uma penalização direta das propriedades elásticas. Por outro lado, efeitos de dano podem ser acoplados com deformações residuais levando a relações constitutivas mais gerais. Esse trabalho está relacionado a esses tipos de modelos assumindo que o meio ideal apresenta um comportamento elástico linear com danificação ou elastoplástico com danificação. Um dos principais aspectos discutido relaciona-se à formulação variacional, a qual está baseada em conceitos de Análise Convexa e Não-Convexa. Explorando o fato que a evolução do dano tem correspondência com a idealização de regime de encruamento negativo, a teoria de localização de deformação é abordada e um estudo da condição necessária de singularidade ou perda da condição de elipticidade é realizado. Na sequência, uma proposta preliminar para uma análise de pós-singularidade, baseada na Teoria de Bifurcação, é feita no sentido de caracterizar pontos limite ou pontos de bifurcação de solução, em sistemas conservativos. / Continuum Damage Mechanics is nowadays a powerful tool to model the non-linear behaviour of several materials due to evolution of a microcracking process. The lost of rigidity caused by such physical process has been accounted in the constitutive models through a scalar, vectorial or tensorial damage variables. When proportional loading is considered the residuals strains can be ignored and simple constitutive relations can be obtained in which damage effects appear by direct penalization of the elastic properties. On the other hand, damage effects can be coupled with residual strains leading to more general constitutive relations. This work is related to such kind of models assuming that the ideal medium presents a linear elastic-damage or an elastoplastic-damage behaviour. One of the main topics discussed is related to the variational formulation which is based on Convex and Non-Convex Analysis concepts. Exploring the fact that damage evolution has correspondence with a softening idealised regime, the strain localization theory is treated and a study of a necessary condition for singularity or ellipticity tose condition is developed. In the sequence, a introductory poscritical analysis is proposed, based in the bifurcation theory and aiming to detect if the singularity corresponds to a limit or a bifurcation point solution, in conservative systems.

Comme tous les milieux amorphes, lorsque les milieux granulaires sont soumis à une contrainte suffisamment importante, ils présentent de la localisation de la déformation. Lors de la rupture d'un matériau granulaire, on assiste ainsi à la formation de bandes de cisaillement. Cette transition solide-liquide est encore largement incomprise. Dans le but de caractériser cette dynamique et d'observer des précurseurs à la rupture, nous avons développé un dispositif expérimental original de test biaxial en déformation plane. Il consiste à appliquer une compression uni-axiale quasi-statique à un échantillon granulaire modèle constitué de micro-billes de verre soumis à une pression de confinement. La compréhension des mécanismes physiques mis en jeu nécessite d'observer de très faibles déformations, pour cela nous utilisons une méthode interférométrique basée sur la diffusion multiple de la lumière. Lors des expériences, nous avons mis en évidence deux types de déformation distincts caractérisés par une dynamique et des angles caractéristiques différents. Avant la rupture, on observe une dynamique intermittente de micro-bandes organisées en réseau. Il s'agit de la première observation de ce type de dynamique que nous interprétons comme une cascade de réarrangements localisés de type Eshelby. Cette dynamique collective émergente ne fait pas intervenir la friction et s'inscrit dans le cadre de la plasticité des amorphes. À la rupture, nous observons des bandes permanentes dont l'inclinaison est donnée par l'angle de friction interne (Mohr-Coulomb). Au cours de la charge, ces deux types de déformation cohabitent, révélant une transition complexe d'un écoulement plastique à une localisation sur des bandes frictionnelles. / Granular materials belong to amorphous media and display localization of deformation when submitted to a large enough stress. Indeed, shear bands appear at the failure of a granular medium and this solid/liquid transition is still an open question. In order to characterize this dynamics and to observe rupture precursors, we developed an experimental device of plane strain biaxial test. It consists in a quasistatic uniaxial compression of a model granular sample made of glass microbeads under confinement pressure. We used an original interferometric method based on multiple light scattering to probe tiny deformations. Our experiments evidenced two types of deformation, those two behaviors differ in their dynamics and their characteristic angle. We observed for the first time an organization of the deformation in an intermittent microbands network from the early stage of the loading. We interpreted this behavior as a cascade of Eshelby-like localized rearrangements. This emerging collective dynamics is not due to friction and can be understood in the framework of amorphous media plasticity. At the failure, permanent shear bands of inclination governed by internal friction angle (Mohr-Coulomb) appear. During the loading, both types of strain coexist displaying a complex transition between plastic flow and frictional shear bands.

Les intrusions magmatiques au sein d’une lithosphère soumise aux contraintes tectoniques sont souvent considérées comme des instabilités thermomécaniques à même de stimuler transitoirement et localement la localisation de la déformation. Dans le but de tester ce modèle et de déterminer les possibles mécanismes gouvernant l’initiation d’une déformation localisée au contact et au sein de corps magmatiques en cours de consolidation, ce travail de thèse se propose de coupler une étude de terrain à une approche expérimentale. Les Cyclades (Mer Égée, Grèce) constituent un domaine de croûte continentale en extension dans lequel se sont mises en place au cœur de cinq dômes métamorphiques extensifs (MCCs) des intrusions magmatiques, elles-mêmes coiffées par des systèmes de détachements. Les diverses campagnes de terrain, combinées aux données de la bibliographie, ont permis de proposer un modèle d’interaction régional dans lequel ces corps magmatiques impactent l’évolution tardive de MCCs cycladiques. Au vu des âges de mise en place des intrusions (15-9 Ma), soit plusieurs millions d’années après le début de l’extension et les premiers stades d’exhumation de roches métamorphiques, le magmatisme dans les Cyclades ne peut être considéré comme un candidat réel pour la genèse de MCCs. Néanmoins, les continuums de la déformation enregistrés en bordure des intrusions (depuis l’état magmatique jusqu’aux conditions ductile/cassant) et les relations géométriques avec les détachements laissent supposer un rôle majeur des complexes magmatiques dans les processus de redistribution et de localisation de la déformation, notamment sur le développement séquentiel de détachements. Les vecteurs de localisation de la déformation au sein de magmas partiellement cristallisés ont été en parallèle recherchés par la voie expérimentale. L’étude du comportement structural de magmas, chimiquement et texturalement proches de systèmes naturels, a permis d’une part de confirmer que la déformation se localise préférentiellement le long d’interfaces à rhéologie contrastée tels aux abords de filons syn-plutoniques. Il est d’autre part montré que la présence initiale d’inhomogénéités texturales (e.g. concentration de cristaux en amas) au sein de magmas moyennement cristallisés peut de manière drastique influencer le degré de localisation de la déformation au cours des stades de refroidissement ultérieurs. / Magma intrusions within the lithosphere are often considered as thermomechanical instabilities capable to locally and transiently stimulate strain localization. With the aim of testing this model and determining possible mechanisms that govern the initiation of localized deformation at the contact and within magmatic bodies, this thesis combine a fieldwork with an experimental approach. The Cyclades (Aegean Sea, Greece) form a highly extended continental domain in which five metamorphic core complexes (MCCs) were intruded by magmatic complexes, themselves capped by detachment systems. All collected structural and kinematic data, combined with previous investigations, converge toward a regional scheme in which magmatic bodies dynamically impacted the late evolution of the Cycladic MCCs. Granitoids were emplaced in relatively short time period (15-9 Ma) while metamorphic domes were largely exhumed after more than 10 Myrs of extension. None of those intrusions thereby proves to be a real candidate for the genesis of MCCs. However, continuums of deformation recorded within granitoids (magmatic to ductile/brittle states) as well as geometrical relationships with detachments suggest a pivotal role of magmatic complexes in redistribution and localization processes of the deformation, with in particular the sequential development of detachments. Precursors of strain localization within partially cristallized magmas have been concurrently deciphered by an experimental study. The investigation of the structural behavior of magmas, chemically and texturally similar to natural systems, corroborates that strain localization is efficiently activated along interfaces with contrasting rheology such as in the vicinity of synplutonic dikes. It has been also shown that the initial presence of textural inhomogeneities (e.g. like clusters) in medium-crystallized magmas can drastically influence the degree of strain localization during subsequent cooling stages.