Este trabalho trata da formulação de leis constitutivas para meios elásticos, que uma vez danificados passam a apresentar diferentes comportamentos em tração e em compressão e certo grau de anisotropia. Inicialmente é revista uma formulação para meios elásticos anisótropos e bimodulares, sendo a mesma, então, estendida para incorporar os casos de meios elásticos com anisotropia e bimodularidade induzidas pelo dano. Seguindo os conceitos da mecânica do dano contínuo e a extensão mencionada da formulação, propõe-se um modelo constitutivo para o concreto assumindo por hipótese fundamental, a equivalência de energia entre meio danificado real e meio contínuo equivalente. Tal hipótese garante a simetria do tensor constitutivo e a sua consistência termodinâmica. De acordo com o modelo proposto, o material é considerado como um meio elástico inicialmente isótropo que passa a apresentar anisotropia induzida pela evolução do dano. Além disso, a danificação pode também induzir uma resposta bimodular no material, isto é, respostas elásticas diferentes para estados de tensão de tração ou de compressão predominantes. Nesse sentido, dois tensores de dano governando as rigidezes em regimes predominantes de tração ou de compressão são introduzidos. Sugere-se então, um critério afim de caracterizar os estados dominantes. As deformações permanentes induzidas pelo dano são, de uma forma geral, desconsideradas. No entanto, propõe-se uma versão unidimensional do modelo que permite a sua consideração. Por outro lado, os critérios para a ativação inicial dos processos de danificação e de sua posterior evolução são escritos em termos de densidade de energia de deformação. Os parâmetros do modelo podem ser identificados mediante experimentos, onde estados de tensão uniaxial e biaxial são induzidos. Também propõem-se leis de evolução de dano com base nos resultados experimentais. A boa coerência do modelo é ilustrada comparando-se uma série de respostas experimentais e numéricas no concreto relativas a estados de tensão uni, bi e triaxiais. Por fim, o modelo é empregado em análises unidimensionais e planas de vigas e pórtico em concreto armado com o objetivo de mostrar a sua potencialidade. / This thesis deals with the formulation of constitutive laws for elastic media that start to present different behaviours in tension and compression and some anisotropy degree when damaged. Initially a formulation for bimodular and anisotropic elastic media is reviewed; then it is extended to take into account the bimodularity and anisotropy induced by damage. Following the concepts of the continuum damage mechanics and the formulation extension, a constitutive model is proposed here by exploring the fundamental hypothesis of energy equivalence between real and continuous medium. Such hypothesis guarantees symmetry to the constitutive tensor and its thermodynamic consistency. According to the proposed modeling, the material is assumed as an initial elastic isotropic medium presenting anisotropy induced by damage evolution. Moreover, damage can also induce a bimodular response in the material, i.e., distinct elastic responses whether traction or compression stress states prevail. To take into account the bimodularity conveniently, two damage tensors governing the rigidity in traction or compression regimes are introduced. A criterion is proposed in order to characterize the dominant states. In general, the permanent strains induced by damage are disregarded. However, a one-dimensional version of the model that allows considering permanent strains is proposed. On the other hand, damage criteria indicating the initial and further evolution of damage are expressed in terms of strain energy densities. The model parameters can be identified from experiments where one-axial and two-axial stress states are induced. Damage evolution laws are also proposed on the basis of experimental results. The good performance of the model is illustrated by comparing a variety of numerical and experimental responses, from one to three-axial stress states. Finally, the model is used in one-dimensional and plane analysis of reinforced concrete beams and frame in order to show its potentiality.

O trabalho trata da formulação, implementação e aplicação de um modelo para análise não-linear de estruturas reticuladas planas em concreto armado, baseado no conceito simplificado de localização dos processos físicos irreversíveis (dano, plasticidade e histerese) em zonas previamente definidas denominadas rótulas que se localizam nas extremidades de um elemento finito de barra. O modelo proposto tem por objetivo reproduzir os deslocamentos residuais relacionados tanto ao comportamento plástico do concreto danificado quanto ao escoamento do aço, além de possibilitar a reprodução de laços de histerese observados experimentalmente em diagramas momento-rotação, ou equivalentemente força-deslocamento, quando a história de carregamento incluir ciclos de descarregamento e recarregamento. A formulação termodinâmica é desenvolvida fazendo-se referência as variáveis de tensão e deformação generalizadas em razão de sua aplicação no âmbito da teoria clássica de flexão de barras. Neste modelo a não-linearidade do elemento estrutural é totalmente decorrente da dissipação de energia localizada nas rótulas e é representada por três variáveis escalares a elas associadas: a variável adimensional de dano, a rotação plástica e a rotação por escorregamento, que representa o fenômeno físico do escorregamento entre as faces das microfissuras no concreto (encaixe e desencaixe dos agregados). Na fase de aplicações as respostas numéricas obtidas com a utilização do modelo proposto foram avaliadas mediante o confronto com diversos resultados experimentais disponíveis na literatura para estruturas de concreto armado sob solicitações estáticas e dinâmicas. Os resultados obtidos evidenciam o bom funcionamento do modelo no caso das solicitações estáticas, tendo sido obtidos resultados limitadamente satisfatórios no caso das solicitações dinâmicas. / This work deals with the formulation, implementation and application of a model for nonlinear analysis of reinforced concrete planed frame structures, based on the simplified concept of localization of the irreversible physical processes (damage, plasticity and hysteresis) in zones previously defined called hinges which are located in the extremities of a bar finite element. The proposed model has as objective to reproduce the residual displacements related to the plastic behavior of the damaged concrete as well as to the steel yielding, moreover making possible the reproduction of hysteresis loops experimentally observed in moment-rotation diagrams, or equivalently force-displacement, when the loading history includes unloading and reloading cycles. The thermodynamic formulation is developed referring to generalized stress and deformation variables due to their application in the scope of the classic theory of bars bending. In this model the nonlinearity of the structural element is totally due to the energy dissipation in the hinges and is represented by three scalar variables associated to them: the non-dimensional damage variable, the plastic rotation and the sliding rotation, which represents the physical phenomenon of sliding between the microcracks faces in the concrete (aggregate interlocking). In the applications phase, the numerical solutions obtained with the use of the proposed model had been evaluated by confrontation with various experimental results available in the literature of reinforced concrete structures under static and dynamic solicitations. The obtained results evidence the good performance of the model in the case of static solicitations, having been obtained limited satisfactory results in the case of dynamic solicitations.

Modeling fracture in geomaterials is essential to the understanding of many physical phenomenon which may posses natural hazards e.g. landslides, faults and iceberg calving or man-made processes e.g. hydraulic fracture and excavations. Continuum Damage Mechanics (CDM) models the crack as a solid region with a degraded stiffness. This continuum definition of cracks in CDM allows more feasible coupling with other forms of material non-linearity and eliminates the need to track complicated crack geometry. Using CDM to analyze fracture for the modeling of fracture in geomaterials encounters several challenges e.g.: 1) the need to model the multiple physical processes occurring in geomaterials, typically: coupled fluid flow and solid deformation, 2) the need to consider non-local damage and transport in order to capture the underlying long range interactions and achieve mesh-independent finite element solutions and 3) the elevated computational cost associated with non-linear mixed finite element formulations. The research presented in this thesis aims at improving the CDM formulations for modeling fracture geomaterials. This research can be divided into three main parts. The first is the introduction of a novel non-local damage transport formulation for modeling fracture in poroelastic media. The mathematical basis of the formulation are derived from thermodynamic equilibrium that considers non-local processes and homogenization principles. The non-local damage transport model leads to two additional regularization equations, one for non-local damage and the other for non-local transport which is reduced to non-local permeability. We consider two options for the implementation of the derived non-local transport damage model. The first option is the four-field formulation which extends the (u/P) formulation widely used in poroelasticity to include the non-local damage and transport phenomena. The second option is the three-field formulation, which is based on the coupling of the regularization equations under the assumptions of similar damage and permeability length scales and similar driving local stress/strain for the evolution of the damage and permeability. The three-field formulation is computationally cheaper but it degrades the physical modeling capabilities of the model. For each of these formulations, a non-linear mixed-finite element solution is developed and the Jacobian matrix is derived analytically. The developed formulations are used in the analysis of hydraulic fracture and consolidation examples. In the second part, a novel approach for CDM modeling of hydraulic fracture of glaciers is pretended. The presence of water-filled crevasses is known to increase the penetration depth of crevasses and this has been hypothesized to play an important role controlling iceberg calving rate. Here, we develop a continuum damage-based poro-mechanics formulation that enables the simulation of water-filled basal and/or surface crevasse propagation. The formulation incorporates a scalar isotropic damage variable into a Maxwell-type viscoelastic constitutive model for glacial ice and the effect of the water pressure on fracture propagation using the concept of effective solid stress. We illustrate the model by simulating quasi-static hydro-fracture in idealized rectangular slabs of ice in contact with the ocean. Our results indicate that water-filled basal crevasses only propagate when the water pressure is sufficiently large and that the interaction between simultaneously propagating water-filled surface and basal crevasses can have a mutually positive influence leading to deeper crevasse propagation which can critically affect glacial stability. In the third part, we propose a coupled Boundary Element Method (BEM) and Finite Element Method (FEM) for modeling localized damage growth in structures. BEM offers the flexibility of modeling large domains efficiently while the nonlinear damage growth is accurately accounted by a local FEM mesh. An integral-type nonlocal continuum damage mechanics with adapting FEM mesh is used to model multiple damage zones and follow their propagation in the structure. Strong form coupling, BEM hosted, is achieved using Lagrange multipliers. Since the non-linearity is isolated in the FEM part of the system of equations, the system size is reduced using Schur complement approach, then, the solution is obtained by a monolithic Newton method that is used to solve both domains simultaneously. The method is applied to multiple fractures growth benchmark problems and shows good agreement with the literature.

No trabalho estudam-se alguns aspectos relativos à formulação teórica e à simulação numérica de modelos constitutivos para o concreto fundamentados na Mecânica do Dano Contínuo, incluindo-se os chamados métodos simplificados de análise estrutural. Inicialmente apresenta-se uma discussão sobre deformações permanentes e anisotropia induzidas pela evolução do dano. A resposta unilateral do concreto submetido a solicitações com inversão de sinal, também é comentada. Cada um dos fenômenos é ilustrado por respostas observadas experimentalmente. O modelo de dano proposto por Mazars para o concreto submetido a carregamento proporcionalmente crescente é então analisado. Em seguida, apresenta-se uma extensão do modelo considerando-se o aspecto unilateral no comportamento do concreto. Na sequência, analisa-se o modelo constitutivo proposto por La Borderie em seus aspectos de formulação e resposta numérica. O modelo é mais completo permitindo levar em conta todos os fenômenos discutidos anteriormente. Um outro aspecto considerado no trabalho é relativo à aplicação dos modelos estudados à análise de estruturas aporticadas. Em termos de discretização destacam-se a técnica de divisão dos elementos estruturais em estratos e os chamados modelos simplificados. Neste último caso, o modelo de Flórez-López é analisado e a simplificação consiste na definição prévia, sobre a estrutura discretizada através de elementos de viga e de coluna, de zonas de localização da plastificação e do dano; no limite com a evolução do processo de carregamento, aquelas zonas passam a se constituir em rótulas. Por último uma generalização do modelo anterior proposta por Álvares é estudada. Os resultados numéricos fornecidos pelos modelos são confrontados com os experimentais de vigas em concreto armado (biapoiadas e com diferentes taxas de armadura) e de um pórtico em concreto armado. / In this work some aspects related to the theoretical formulation and numerical simulation of constitutive models for the concrete based on the Continuum Damage Mechanics are studied, including simplified methods of structural analysis. Initially a discussion about permanent strains and anisotropy induced by the evolution of the damage is presented. The unilateral response of the concrete submitted to loadings with signal inversion is commented as well. Each one of the phenomena is illustrated by experimental tests. The damage model proposed by Mazars for the concrete under proportional increasing load is then analysed. Afterwards, it is shown an extension of the model considering the unilateral aspect ofthe concrete behaviour. In the sequence the constitutive model proposed by La Borderie is presented in its aspects of formulation and numerical response. This model is more complete, allowing to take in to account all the phenomena discussed previously. Another aspect considered in the work is related to the application of the models studied to the analysis of framed structures. Regarding the discretization, the technique of division of the structural elements in layers and the so called simplified models are enhanced. In this last case, the model proposed by Flórez-López is analysed and the simplification consists on previous definition of yielding and damage zones over the assembly of beam and colunm elements, which compose the discretized structure; in the limit evolution of the loading process, these zones become hinges. Finally, a generalization of the previous model proposed by Álvares is studied. The numerical results supplied by the models are compared with the experimental results of reinforced concrete beams (simply supported and with different reinforced rates) and of a reinforced concrete frame.

No description available.

Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a novel plasticity model for plain concrete is proposed in this research. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations, the strain equivalence hypothesis is adopted. The proposed constitutive model has been shown to satisfy the thermodynamics requirements, and detailed numerical algorithms are developed for the Finite Element implementation of the proposed model. Moreover, the numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus, and the overall performance of the proposed model is verified by comparing the model predictions to various experimental data on macroscopic level. Using the proposed coupled plasticity-damage constitutive model, the effect of the micromechanical properties of concrete, such as aggregate shape, distribution, and volume fraction, the ITZ thickness, and the strength of the ITZ and mortar matrix on the tensile behavior of concrete is investigated on 2-D and 3-D meso-scale. As a result of simulation, the tensile strength and thickness of the ITZ is the most important factor that control the global strength and behavior of concrete, and the aggregate shape and volume fraction has somewhat effect on the tensile behavior of concrete while the effect of the aggregate distribution is negligible. Furthermore, using the proposed constitutive model, the pull-out analysis of the single straight and curved CNT embedded in cement matrix is carried out. In consequence of the analysis, the interfacial fracture energy is the key parameter governing the CNT pull-out strength and ductility at bonding stage, and the Young's modulus of the CNT has also great effect on the pull-out behavior of the straight CNT. In case of the single curved CNT, while the ultimate pull-out force of the curved CNT at sliding stage is governed by the initial sliding force when preexisting normal force is relatively high, the ultimate pull-out force, when the preexisting normal force is not significant, is increased linearly proportional to the curvature and the Young's modulus of the CNT due to the additionally induced normal force by the bending stiffness of the curved CNT.

At present, most of the energy power consumed in the world is produced by fossil fuel combustion, which has raised increasing interest in renewable energy technologies, non-conventional oil and gas reservoirs, and nuclear power. Innovative nuclear fuels and reactors depend on the economical and environmental impacts of waste management. Disposals in mined geological formations are viewed as potential consolidated storage facilities before final disposition. Different stress paths during construction result in different kinds of failure mechanisms, which alter rock strength and induce anisotropy of rock elastic properties. Crack propagation in rock can be originated by these engineering activities (excavation, drilling, mining, building overburden), or by changes of the natural environment (tectonic processes, erosion or weathering). Damage is a mathematical variable that can represent a variety of microstructure changes, such as crack density, length, aspect ratio and orientation. The framework of Continuum Damage Mechanics allows modeling the resulting reduction in strength and stiffness, as well as the associated stress-induced anisotropy and irreversible deformation. This work presents a modeling framework for anisotropic crack propagation in rock, in conditions of stress typical of geological storage and oil and gas extraction. Emphasis is put on the prediction of the damage zone around cavities and ahead of pressurized fracture tips. An original model of anisotropic damage, the Differential Stress Induced Damage (DSID) model, is explained. The Drucker-Prager yield function is adapted to make the damage threshold depend on damage energy release rate and to distinguish between tension and compression strength. Flow rules are derived with the energy release rate conjugate to damage, which is thermodynamically consistent. The positivity of dissipation is ensured by using a non-associate flow rule for damage, while nonelastic deformation due to damage is computed by an associate flow rule. Stress paths simulated at the material point illustrate damaged stiffness and deformation variations in classical rock mechanics tests. The maximum likelihood method was employed to calibrate and verify the DSID model against stress-strain curves obtained during triaxial compression tests and uniaxial compression tests performed on clay rock and shale. Logarithmic transformation, normalization and forward deletion allowed optimizing the formulation of the DSID model, and reduce the number of damage constitutive parameters from seven to two for clay rock. The DSID model was implemented in ABAQUS Finite Element (FE) software. The iterative scheme was adapted in order to account for the non-linearities induce both by damage and damage-induced deformation. FE simulations of laboratory tests capture size an intrinsic anisotropy effects on the propagation of damage in rock. Smeared DSID zones representing shale delamination planes avoid some convergence problems encountered when modeling discontinuities with debonded contact surface elements. FE simulations of tunnel excavation, fracture propagation and borehole pressurization were performed to illustrate the evolution of the damage zone and the impact on energy dissipation, anisotropy of deformation, and loss of stiffness. Future work will focus on coupling the propagation of fractures with the evolution of the damage process zone, and on the transition from continuum damage to discrete fracture upon crack coalescence.

The main objective of this study is to develop and validate a framework for microstructural modeling of asphalt composite materials using a coupled thermo-viscoelastic, thermo-viscoplastic, and thermo-viscodamage constitutive model. In addition, the dissertation presents methods that can be used to capture and represent the two-dimensional (2D) and three-dimensional (3D) microstructure of asphalt concrete. The 2D representative volume elements (RVEs) of asphalt concrete were generated based on planar X-ray Computed Tomography (CT) images. The 2D RVE consists of three phases: aggregate, matrix, and interfacial transmission zone (ITZ). The 3D microstructures of stone matrix asphalt (SMA) and dense-graded asphalt (DGA) concrete were reconstructed from slices of 2D X-ray CT images; each image consists of the matrix and aggregate phases. The matrix and ITZ were considered thermo-viscoelastic, thermo-viscoplastic, and thermo-viscodamaged materials, while the aggregate is considered to be a linear, isotropic elastic material. The 2D RVEs were used to study the effects of variation in aggregate shape, distribution, volume fraction, ITZ strength, strain rate, and temperature on the degradation and micro-damage patterns in asphalt concrete. Moreover, the effects of loading rate, temperature, and loading type on the thermo-mechanical response of the 2D and 3D microstructures of asphalt concrete were investigated. Finally, the model parameters for Fine Aggregate Mixture (FAM) and full asphalt mixture were determined based on the analysis of repeated creep recovery tests and constant strain rate tests. These material parameters in the model were used to simulate the response of FAM and full asphalt mixture, and the results were compared with the responses of the corresponding experimental tests. The microstructural modeling presented in this dissertation provides the ability to link the microstructure properties with the macroscopic response. This modeling combines nonlinear constitutive model, finite element analysis, and the unique capabilities of X-ray CT in capturing the material microstructure. The modeling results can be used to provide guidelines for designing microstructures of asphalt concrete that can achieve the desired macroscopic behavior. Additionally, it can be helpful to perform 'virtual testing' of asphalt concrete, saving numerous resources used in conducting real experimental tests.

No description available.

Thesis (Ph..D.), Memorial University of Newfoundland, 1998. / Restricted until June 1999. Bibliography: leaves 179-187.