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)

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.

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.

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.

Inverse analysis FOR two-dimensional structures using the boundary element method

Inverse analysis is currently an important subject of study in several fields of science and engineering. The identification of physical and geometric parameters using experimental measurements is required in many applications. In this work a boundary element formulation to identify boundary and interface values as well as material properties is proposed. In particular the proposed formulation is dedicated to identifying material parameters when a cohesive crack model is assumed for 2D problems. A computer code is developed and implemented using the BEM multi-region technique and regularisation methods to perform the inverse analysis. Several examples are shown to demonstrate the efficiency of the proposed model. (C) 2010 Elsevier Ltd. All rights reserved,

Evolution of stress deficit and changing rates of seismicity in cellular automaton models of earthquake faults

We investigate the internal dynamics of two cellular automaton models with heterogeneous strength fields and differing nearest neighbour laws. One model is a crack-like automaton, transferring ail stress from a rupture zone to the surroundings. The other automaton is a partial stress drop automaton, transferring only a fraction of the stress within a rupture zone to the surroundings. To study evolution of stress, the mean spectral density. f(k(r)) of a stress deficit held is: examined prior to, and immediately following ruptures in both models. Both models display a power-law relationship between f(k(r)) and spatial wavenumber (k(r)) of the form f(k(r)) similar tok(r)(-beta). In the crack model, the evolution of stress deficit is consistent with cyclic approach to, and retreat from a critical state in which large events occur. The approach to criticality is driven by tectonic loading. Short-range stress transfer in the model does not affect the approach to criticality of broad regions in the model. The evolution of stress deficit in the partial stress drop model is consistent with small fluctuations about a mean state of high stress, behaviour indicative of a self-organised critical system. Despite statistics similar to natural earthquakes these simplified models lack a physical basis. physically motivated models of earthquakes also display dynamical complexity similar to that of a critical point system. Studies of dynamical complexity in physical models of earthquakes may lead to advancement towards a physical theory for earthquakes.

Accelerating seismic energy release and evolution of event time and size statistics: Results from two heterogeneous cellular automaton models

The evolution of event time and size statistics in two heterogeneous cellular automaton models of earthquake behavior are studied and compared to the evolution of these quantities during observed periods of accelerating seismic energy release Drier to large earthquakes. The two automata have different nearest neighbor laws, one of which produces self-organized critical (SOC) behavior (PSD model) and the other which produces quasi-periodic large events (crack model). In the PSD model periods of accelerating energy release before large events are rare. In the crack model, many large events are preceded by periods of accelerating energy release. When compared to randomized event catalogs, accelerating energy release before large events occurs more often than random in the crack model but less often than random in the PSD model; it is easier to tell the crack and PSD model results apart from each other than to tell either model apart from a random catalog. The evolution of event sizes during the accelerating energy release sequences in all models is compared to that of observed sequences. The accelerating energy release sequences in the crack model consist of an increase in the rate of events of all sizes, consistent with observations from a small number of natural cases, however inconsistent with a larger number of cases in which there is an increase in the rate of only moderate-sized events. On average, no increase in the rate of events of any size is seen before large events in the PSD model.

Caracterização geológico-geofísica do meio aqüífero fissural : uma contribuição aos modelos de fluxo e armazenamento de água subterrânea

Northeastern Brazil is mainly formed by crystalline terrains (around 60% in area). Moreover, this region presents a semi-arid climate so that it is periodically subject to drought seasons. Furthermore, ground water quality extracted fromwells usually presents poor quality because of their high salinity contents. Nevertheless, ground water is still a very important source of water for human and animal consumption in this region. Well sitting in hard rocks terrains in Northeastern Brazil offers a mean success index of aboul 60%, given that a successful siting is defined by a well producing at least 0.5 m³/h. This low index reveals lack of knowledga about the true conditions of storage and percolation of ground water in crystalline rocks. Two models for structures storing and producing ground water in crystalline rocks in Northeastem Brazil have been proposed in the literature. The first model,tradnionally used for well sitting since the sixties are controlled by faults or fractures zones. This model is commonly referred, in Brazilian hydrogeological literature, as the "creek-crack" model (riacho-fenda in Portuguese). Sites appearing to present dense drainage network are preferred for water well siting - particularly at points where the drainages cross-cul each other. Field follow up work is usually based only on geological criteria. The second model is the "eluvio-alluvial through" (calha eluvio-aluvionar in Portuguese); it is also described in the literature but it is not yet incorporated in well sitting practice. This model is based on the hypothesis that reclilinear drainages can also be controlled by the folietion of the rock. Eventually, depending upon the degree of weathering, a through-shaped structure filled with sediments (alluvium and regolith) can be developed which can store and water can be produced from. Using severalfield case studies, this Thesis presents a thorough analysis ofthe two above cited models and proposes a new model. The analysis is based on an integrated methodological approach using geophysics and structural geology. Both land (Resitiviy and Ground Penetrating Radar- GPR) and aerogeophysical (magnetics and frequency domain eletromagnetics) surveys were used. Slructural analysis emphasized neolectonic aspects; in general, itwas found that fractures in the E-W direction are relatively open, as compared to fracturas inthe N-S direction, probably because E-W fractures were opened by the neotectonic stress regime in Northeastern Brazil, which is controlled by E-W compression and N-S extension. The riacho-fenda model is valid where drainages are controlled by fractures. The degree of fracturing and associated weathering dictale the hydrogeological potential of the structure. Field work in structural analogues reveals that subvertical fractures show consistent directions both in outcrop and aerophotograph scales. Geophysical surveys reveal subvertical conductive anomalies associated to the fracture network controlling the drainage; one of the borders of the conductive anomaly usually coincide wih the drainage. An aspect of particular importance to the validation of fracture control are the possible presence of relalively deep conductive anomalies wihoul continuation or propagalion to the surface. The conductive nature of lhe anomaly is due to the presence of wealhered rock and sedirnenls (alluvium and/or regolilh) storing ground waler which occur associated to the fracture network. Magnetic surveys are not very sensisnive to these structures.lf soil or covering sedirnents are resislive (> 100 Ohm.m), GPR can ba used to image precisely lhe fracture network. A major limialion of riacho-fenda model, revealed by GPR images, is associated to the fact thal subhorizontal fractures do play a very important role in connecting the fracture network, besides connect shallow recharge zones to relalively deep subvertical frecture zones. Iffractures play just a secondary control on the drainage, however, r/acho-fenda model may have a very limiled validny; in these cases, large portions oflhe drainage do nol coincide wilh frectures and mosl oflhewells localed in lhe drainage surrounding would resull dry. Usually, a secondary conlrol on lhe drainage by Ihefraclure networkcan be revealed only wilh detailed geophysical survey. The calha elClv1o-aluvlonarmodel is valid where drainages are conlrolled by folialion. The degree 01 wealhering 01 lhe lolialion planes dictales lhe hydrogeological polenlial 01 lhe slruclure. Outcrop analysis reveals Ihal lolialion and drainage direclions are parallel and Ihal no Iraclures, orfraclures wilh diflerent directions 01 lhe drainage direclion occur. Geophysical surveys reveal conduclive anomalies in a slab lorm associaled 10 lhe Ihrough 01 lhe wealhered rock and sedimenls (alluvium and/or regolith). Magnelic surveys can ofler a very good conlrol on lolialion direclion. An importanl aspect 10 validale lolialion conlrol are lhe presence 01 conductive anomalies showing shallow and deep portions area which are linked. Illhere is an exlensive soil cover, r/acho-fenda and calha eIClv1o-aluv/onar conlrols can be easily misinlerpreled in lhe absence 01 geophysical conlrol. Certainly, Ihis lacl could explain at leasl a part of lhe failure index in well sitting. The model wealhering sack (bolsllo de Intempertsmo in Portuguese) is proposed to explain cases where a very inlensive wealhering occur over lhe crystalline rock so Ihal a secondary inlerslilial porosity is crealed. The waler is Ihen stored in lhe porous of lhe regolilh in a similar mannerlo sedimentary rocks. A possible example ofthis model was delecled by using land geophysical survey where a relalivelyvery deep isolaled conduclive anomaly, in a slab form, was delected. Iflhis structure does store ground waler, certainly Ihere must be a link 01 lhe deep slructure wilh lhe surface in orderlo provide walerfeeding. This model mighl explain anomalous waler yields as greal as 50 m³/h Ihalsomelimescan occur in crystalline rocks in Northeaslern Brazil