Plastic-damage smeared crack model to simulate the behaviour of structures made by cement based materials

This work proposes a constitutive model to simulate nonlinear behaviour of cement based materials subjected to different loading paths. The model incorporates a multidirectional fixed smeared crack approach to simulate crack initiation and propagation, whereas the inelastic behaviour of material between cracks is treated by a numerical strategy that combines plasticity and damage theories. For capturing more realistically the shear stress transfer between the crack surfaces, a softening diagram is assumed for modelling the crack shear stress versus crack shear strain. The plastic damage model is based on the yield function, flow rule and evolution law for hardening variable, and includes an explicit isotropic damage law to simulate the stiffness degradation and the softening behaviour of cement based materials in compression. This model was implemented into the FEMIX computer program, and experimental tests at material scale were simulated to appraise the predictive performance of this constitutive model. The applicability of the model for simulating the behaviour of reinforced concrete shear wall panels submitted to biaxial loading conditions, and RC beams failing in shear is investigated.

2D evaluation of crack openings using smeared and embedded crack models

This work deals with the determination of crack openings in 2D reinforced concrete structures using the Finite Element Method with a smeared rotating crack model or an embedded crack model In the smeared crack model, the strong discontinuity associated with the crack is spread throughout the finite element As is well known, the continuity of the displacement field assumed for these models is incompatible with the actual discontinuity However, this type of model has been used extensively due to the relative computational simplicity it provides by treating cracks in a continuum framework, as well as the reportedly good predictions of reinforced concrete members` structural behavior On the other hand, by enriching the displacement field within each finite element crossed by the crack path, the embedded crack model is able to describe the effects of actual discontinuities (cracks) This paper presents a comparative study of the abilities of these 2D models in predicting the mechanical behavior of reinforced concrete structures Structural responses are compared with experimental results from the literature, including crack patterns, crack openings and rebar stresses predicted by both models

2D evaluation of crack openings using smeared and embedded crack models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Heat transfer in fixed bed: a model non-linearity approach

Studies have been carried out on the heat transfer in a packed bed of glass beads percolated by air at moderate flow rates. Rigorous statistic analysis of the experimental data was carried out and the traditional two parameter model was used to represent them. The parameters estimated were the effective radial thermal conductivity, k, and the wall coefficient, h, through the least squares method. The results were evaluated as to the boundary bed inlet temperature, T-o, number of terms of the solution series and number of experimental points used in the estimate. Results indicated that a small difference in T-o was sufficient to promote great modifications in the estimated parameters and in the statistical properties of the model. The use of replicas at points of high parametric information of the model improved the results, although analysis of the residuals has resulted in the rejection of this alternative. In order to evaluate cion-linearity of the model, Bates and Watts (1988) curvature measurements and the Box (1971) biases of the coefficients were calculated. The intrinsic curvatures of the model (IN) tend to be concentrated at low bed heights and those due to parameter effects (PE) are spread all over the bed. The Box biases indicated both parameters as responsible for the curvatures PE, h being somewhat more problematic. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

An embedded cohesive crack model for finite element analysis of quasi-brittle materials

This paper presents a numerical implementation of the cohesive crack model for the anal-ysis of quasibrittle materials based on the strong discontinuity approach in the framework of the finite element method. A simple central force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need for performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent pro-cedure for the selection of the separated nodes. Such a model is then implemented into a commercial program by means of a user subroutine, consequently being contrasted with the experimental results. The model takes into account the anisotropy of the material. Numerical simulations of well-known experiments are presented to show the ability of the proposed model to simulate the fracture of quasibrittle materials such as mortar, concrete and masonry.

The Cohesive Crack Model Applied To Notched PMMA Specimens Obeying a Non Linear Behaviour Under Torsion Loading

This article presents a new material model developed with the aim of analyzing failure of blunt notched components made of nonlinear brittle materials. The model, which combines the cohesive crack model with Hencky's theory of total deformations, is used to simulate an experimental benchmark carried out previously by the authors. Such combination is achieved through the embedded crack approach concept. In spite of the unavailability of precise material data, the numerical predictions obtained show good agreement with the experimental results.

Comparison of numerical and physical hydraulic models, Masonboro Inlet, North Carolina : Appendix 1, fixed-bed hydraulic model results /

"June 1977."

Um modelo elasto-viscoplástico para análise de peças de concreto estrutural, submetidas a estados planos de tensão, através do método dos elementos finitos

O objetivo deste trabalho é desenvolver um modelo computacional, baseado no método dos elementos finitos, para o estudo de peças de concreto armado e protendido submetidas a estados planos de tensão. O estudo abrange situações de carga de curta e longa duração, onde consideram-se fluência e retração do concreto e relaxação do aço. São utilizados modelos constitutivos elasto-viscoplásticos para descrever o comportamento dos materiais. Implementou-se um modelo de camadas superpostas para melhor representar o comportamento do concreto, onde o material é composto de diversas camadas que sofrem a mesma deformação. Cada camada possui diferentes características materiais e a tensão total é obtida pela soma das diferentes contribuições de cada camada. Para a fissuração da concreto, utilizou-se um modelo de fissuras distribuídas, que leva em conta a contribuição do concreto entre fissuras. Tanto a amadura passiva como a de pratensão são introduzidas no modelo como uma linha de material mais rígido dentro do elemento de concreto. Os deslocamentos ao longo da armadura são referenciados aos deslocamentos nodais do elemento de concreto. Deste modo, obtém-se uma matriz de rigidez para a armadura com as mesmas dimensões que a matriz de rigidez do elemento de concreto, A matriz de rigidez do elemento concreto-aço é a soma das duas matrizes. Considera-se aderência perfeita entre o concreto e o aço. Os resultados obtidos com esse programa computacionai são comparados com valores experimentais disponíveis.

Predição de propagação de fissuras através de modelos constitutivos locais e técnica de construção progressiva da trajetória de descontinuidade

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Creep and damage models for the service behaviour of structural members

Deformability is often a crucial to the conception of many civil-engineering structural elements. Also, design is all the more burdensome if both long- and short-term deformability has to be considered. In this thesis, long- and short-term deformability has been studied from the material and the structural modelling point of view. Moreover, two materials have been handled: pultruded composites and concrete. A new finite element model for thin-walled beams has been introduced. As a main assumption, cross-sections rigid are considered rigid in their plane; this hypothesis replaces that of the classical beam theory of plane cross-sections in the deformed state. That also allows reducing the total number of degrees of freedom, and therefore making analysis faster compared with twodimensional finite elements. Longitudinal direction warping is left free, allowing describing phenomena such as the shear lag. The new finite-element model has been first applied to concrete thin-walled beams (such as roof high span girders or bridge girders) subject to instantaneous service loadings. Concrete in his cracked state has been considered through a smeared crack model for beams under bending. At a second stage, the FE-model has been extended to the viscoelastic field and applied to pultruded composite beams under sustained loadings. The generalized Maxwell model has been adopted. As far as materials are concerned, long-term creep tests have been carried out on pultruded specimens. Both tension and shear tests have been executed. Some specimen has been strengthened with carbon fibre plies to reduce short- and long- term deformability. Tests have been done in a climate room and specimens kept 2 years under constant load in time. As for concrete, a model for tertiary creep has been proposed. The basic idea is to couple the UMLV linear creep model with a damage model in order to describe nonlinearity. An effective strain tensor, weighting the total and the elasto-damaged strain tensors, controls damage evolution through the damage loading function. Creep strains are related to the effective stresses (defined by damage models) and so associated to the intact material.

Experience and lessons learnt from the SMART 2013 Benchmark

The French CEA, together with EDF and the IAEA, recently organised an international benchmark to evaluate the ability to model the mechanical behaviour of a typical nuclear reinforced concrete structure subjected to seismic demands. The participants were provided with descriptions of the structure and the testing campaign; they had to propose the numerical model and the material laws for the concrete (stage #1). A mesh of beam and shell elements was generated; for modelling the concrete a damaged plasticity model was used, but a smeared crack model was also investigated. Some of the initial experimental results, with the mock-up remaining in the elastic range, were provided to the participants for calibrating their models (stage #2). Predictions had to be produced in terms of eigen-frequencies and motion time histories. The calculated frequencies reproduced reasonably the experimental ones; the time histories, calculated by modal response analysis, also reproduced adequately the observed amplifications. The participants were then expected to predict the structural response under strong ground motions (stage #3), which increased progressively up to a history recorded during the 1994 Northridge earthquake, followed by an aftershock. These results were produced using an explicit solver and a damaged plasticity model for the concrete, although an implicit solver with a smeared crack model was also investigated. The paper presents the conclusions of the pre-test exercise, as well as some observations from additional simulations conducted after the experimental results were made available.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

A general linear relaxometry model of R1 using imaging data.

PURPOSE: The longitudinal relaxation rate (R1 ) measured in vivo depends on the local microstructural properties of the tissue, such as macromolecular, iron, and water content. Here, we use whole brain multiparametric in vivo data and a general linear relaxometry model to describe the dependence of R1 on these components. We explore a) the validity of having a single fixed set of model coefficients for the whole brain and b) the stability of the model coefficients in a large cohort. METHODS: Maps of magnetization transfer (MT) and effective transverse relaxation rate (R2 *) were used as surrogates for macromolecular and iron content, respectively. Spatial variations in these parameters reflected variations in underlying tissue microstructure. A linear model was applied to the whole brain, including gray/white matter and deep brain structures, to determine the global model coefficients. Synthetic R1 values were then calculated using these coefficients and compared with the measured R1 maps. RESULTS: The model's validity was demonstrated by correspondence between the synthetic and measured R1 values and by high stability of the model coefficients across a large cohort. CONCLUSION: A single set of global coefficients can be used to relate R1 , MT, and R2 * across the whole brain. Our population study demonstrates the robustness and stability of the model. Magn Reson Med, 2014. © 2014 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. Magn Reson Med 73:1309-1314, 2015. © 2014 Wiley Periodicals, Inc.

Statistical characterization of soft tissue inelastic parameters and application to the material failure of the aortic ach

Caracterización de los procesos de disipación mecánica basándose en la microestructura de los tejidos blandos. We present a continuous damage model with regularized softening (smeared crack models) for fiber reinforced soft tissues. Material parameters of the continuous model derive from the mesoscopic scale. In the mesoscopic scale continuum is considered as a collagenous fibrilreinforced composite. We want to study the continnumlevel response as a function of the nanoscale properties of the collagen and the adherent forces between the tropocollagen molecules.

A study of the mechanical behaviour of the human aortic artery by means of non-linear finite element models

En la presente tesis desarrollamos una estrategia para la simulación numérica del comportamiento mecánico de la aorta humana usando modelos de elementos finitos no lineales. Prestamos especial atención a tres aspectos claves relacionados con la biomecánica de los tejidos blandos. Primero, el análisis del comportamiento anisótropo característico de los tejidos blandos debido a las familias de fibras de colágeno. Segundo, el análisis del ablandamiento presentado por los vasos sanguíneos cuando estos soportan cargas fuera del rango de funcionamiento fisiológico. Y finalmente, la inclusión de las tensiones residuales en las simulaciones en concordancia con el experimento de apertura de ángulo. El análisis del daño se aborda mediante dos aproximaciones diferentes. En la primera aproximación se presenta una formulación de daño local con regularización. Esta formulación tiene dos ingredientes principales. Por una parte, usa los principios de la teoría de la fisura difusa para garantizar la objetividad de los resultados con diferentes mallas. Por otra parte, usa el modelo bidimensional de Hodge-Petruska para describir el comportamiento mesoscópico de los fibriles. Partiendo de este modelo mesoscópico, las propiedades macroscópicas de las fibras de colágeno son obtenidas a través de un proceso de homogenización. En la segunda aproximación se presenta un modelo de daño no-local enriquecido con el gradiente de la variable de daño. El modelo se construye a partir del enriquecimiento de la función de energía con un término que contiene el gradiente material de la variable de daño no-local. La inclusión de este término asegura una regularización implícita de la implementación por elementos finitos, dando lugar a resultados de las simulaciones que no dependen de la malla. La aplicabilidad de este último modelo a problemas de biomecánica se estudia por medio de una simulación de un procedimiento quirúrgico típico conocido como angioplastia de balón. In the present thesis we develop a framework for the numerical simulation of the mechanical behaviour of the human aorta using non-linear finite element models. Special attention is paid to three key aspects related to the biomechanics of soft tissues. First, the modelling of the characteristic anisotropic behaviour of the softue due to the collagen fibre families. Secondly, the modelling of damage-related softening that blood vessels exhibit when subjected to loads beyond their physiological range. And finally, the inclusion of the residual stresses in the simulations in accordance with the opening-angle experiment The modelling of damage is addressed with two major and different approaches. In the first approach a continuum local damage formulation with regularisation is presented. This formulation has two principal ingredients. On the one hand, it makes use of the principles of the smeared crack theory to avoid the mesh size dependence of the structural response in softening. On the other hand, it uses a Hodge-Petruska bidimensional model to describe the fibrils as staggered arrays of tropocollagen molecules, and from this mesoscopic model the macroscopic material properties of the collagen fibres are obtained using an homogenisation process. In the second approach a non-local gradient-enhanced damage formulation is introduced. The model is built around the enhancement of the free energy function by means of a term that contains the referential gradient of the non-local damage variable. The inclusion of this term ensures an implicit regularisation of the finite element implementation, yielding mesh-objective results of the simulations. The applicability of the later model to biomechanically-related problems is studied by means of the simulation of a typical surgical procedure, namely, the balloon angioplasty.