Constitutive models for the material nonlinear analysis of concrete structures including time-dependent effects

Abstract

In recent years concrete technology has been improved significantly due, mainly, to the development of self-compacting concrete, ultra-fluid cement based materials, high performance fiber reinforced concrete and engineered cement composites. These developments have their main applicability in the pre-casting industry, where the earliest demoulding of the pre-cast elements is an important aim for economic reasons. Due to the relatively high cost of these advanced cement based materials, optimization of the behavior of structural elements made with these materials is a fundamental issue for their competitiveness. As a consequence, these materials are, in general, applied to relatively thin elements that require special attention in terms of shear and punching resistance. With the aim of studying these types of structures, a multi-directional fixed smeared crack model for plane shells has been developed. This model implements an innovative approach for capturing the behavior of laminar structures failing in punching, which is based on the adoption of a softening diagram to simulate the behavior of the out-of-plane shear stress components. Since most advanced cement based materials have relatively high binder content, the risk of cracking at an early age should be evaluated using models that can estimate the heat generated by the hydration of pozolanic components and the induced stress fields. For this purpose, a FEM-based heat transfer model has been developed and integrated into a mechanical model that can simulate the crack initiation and propagation in structures discretized with solid finite elements. The mechanical model is a 3D multi-directional smeared crack model with the capability of simulating the behavior of structures failing in punching and shear. Shrinkage and creep are also a concern mainly for service limit states due to crack opening limits. In the last two decades fiber reinforced polymer composite materials have also been used for the structural rehabilitation of concrete structures, mainly for the flexural and shear strengthening of reinforced concrete beams. The prediction of the behavior of the shear viii Abstract strengthened beams requires the use of crack constitutive models to simulate the decrease of the shear stress degradation with the crack opening evolution, in agreement. Two numerical approaches are proposed to simulate this phenomenon. One is based on the use of a softening crack shear stress versus crack shear strain diagram to model the fracture mode II, while in the other the total crack shear stress is obtained from the total crack shear strain adopting a crack shear modulus that decreases with the crack normal strain. Fiber reinforcement mechanisms are more effectively mobilized when support redundancy of a structure is high, since the stress redistribution capacity provides to this type of structure an ultimate load that is much higher than the load at crack initiation. However, the supporting conditions of a structure can change during the loading process, and even a loss of contact can occur. To simulate accurately these situations, linear, nonlinear and unilateral support conditions are numerically implemented. To increase the robustness of the developed numerical models, innovative numerical strategies are implemented in the stress update phase of the nonlinear finite element analysis process. Furthermore, to improve the convergence performance of the finite element nonlinear analyses an arc-length algorithm is implemented. All the numerical models are implemented in the FEMIX 4.0 FEM package, using the ANSI-C computer language.

Fiber reinforcement mechanisms are more effectively mobilized when support redundancy of a structure is high, since the stress redistribution capacity provides to this type of structure an ultimate load that is much higher than the load at crack initiation. However, the supporting conditions of a structure can change during the loading process, and even a loss of contact can occur. To simulate accurately these situations, linear, nonlinear and unilateral support conditions are numerically implemented. To increase the robustness of the developed numerical models, innovative numerical strategies are implemented in the stress update phase of the nonlinear finite element analysis process. Furthermore, to improve the convergence performance of the finite element nonlinear analyses an arc-length algorithm is implemented. All the numerical models are implemented in the FEMIX 4.0 FEM package, using the ANSI-C computer language. Estes materiais avançados de matriz cimentícia têm uma quantidade de ligante relativamente elevado, pelo que a possibilidade de ocorrência de fendilhação nas primeiras idades deve ser avaliada usando modelos que permitam estimar o calor gerado pela hidratação do ligante durante o seu processo de cura, bem como a determinação das correspondentes tensões. Para o efeito, no presente trabalho é desenvolvido um modelo de transferência de calor baseado no método dos elementos finitos, o qual é integrado num modelo mecânico que permite simular o início de fendilhação e a sua propagação em estruturas discretizadas por elementos finitos de volume. Este modelo de fendilhação 3D tem a possibilidade de simular a ocorrência de múltiplas fendas fixas distribuídas, bem como o comportamento de estruturas cujo modo de ruptura é condicionado pelas componentes de corte. A retracção e a fluência também são fenómenos de relevância em estruturas constituídas por estes tipos de materiais, principalmente em estados limites de serviço por abertura de fenda, pelo que a sua modelação foi também integrada no modelo termo-mecânico. Nas últimas duas décadas, materiais de matriz polimérica reforçados com fibras contínuas têm sido utilizados na reabilitação estrutural de estruturas de betão, principalmente para o reforço à flexão e ao corte de vigas de betão armado. A previsão do comportamento das vigas reforçadas ao corte requer o uso de modelos constitutivos capazes de simular a diminuição da capacidade de transferência de tensão de corte com a evolução da abertura de fenda. Duas abordagens numéricas são propostas para este fim. Uma delas baseia-se na utilização de um diagrama de amolecimento para a modelação do modo II de fractura. A outra suporta-se numa formulação total para a relação entre a tensão e a extensão de corte na fenda, adoptando um módulo de rigidez correspondente ao modo II de fractura que diminui com a extensão normal à fenda. De forma a aumentar a robustez dos modelos numéricos desenvolvidos, foram implementadas algumas estratégias de actualização do estado de tensão no material durante o processo de análise não linear. Com o objectivo de melhorar as características de convergência dos métodos numéricos utilizados foram introduzidos algoritmos baseados na técnica arc-length. Condições de apoio com comportamento linear, não linear e unilateral também foram numericamente implementadas. Todos os modelos numéricos foram implementados no software de elementos finitos FEMIX usando a linguagem de programação ANSI-C.