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La mampostería es uno de los materiales de construcción con mayor abanico de usos, ya sea en el pasado como en el presente, así es como hoy en día también se puede encontrar en la construcción de edificaciones modernas. Los materiales utilizados a lo largo de la historia como elementos componentes de la mampostería han sido muchos y muy variados: desde la simple roca unida con mortero de cal (sillería), pasando por los enormes bloques de mármol usados en la construcción de los grandes monumentos del apogeo de la arquitectura del Renacimiento, hasta llegar a elementos cerámicos refractarios como los que se utilizan para la construcción de hornos, centrales nucleares e incluso como aislante térmico de naves espaciales. Los métodos de cálculo avanzado (modelos constitutivos de la mecánica del medio continuo) deben ser el pilar sobre el que desarrollar elementos más objetivos de análisis estructural de la mampostería. Los elementos finitos son una herramienta potente en la que apoyar el cálculo de la obra de fábrica pero, debido a que ésta tiene un tamaño pequeño respecto a las dimensiones globales de la estructura, se hacen inviables desde el punto de vista computacional. La necesidad de encontrar un método que equilibre sencillez, objetividad y rapidez de cálculo es la que motiva el desarrollo de formulaciones con tratamiento al nivel de macromodelo de la mampostería. La inquietud por conseguir este equilibrio hace a Jacob Lubliner y Sergio Oller sentar las bases que permitirán el desarrollo del modelo constitutivo homogeneizado que se presenta en este trabajo.

In order to ensure that a building structure do not collapse when subjected to the action of strong ground motions, modern codes include prescriptions in order to guarantee the ductile behavior of the elements and of the whole structure. Obviously, it is of special importance for the designer to know during the design process the extent of damage that the structure will suffer under the seismic action specified by the design spectrum and also the probability of occurrence of different states of behaviour. The incremental nonlinear static analysis procedure used in this paper allows formulating a new, simplified, seismic damage index and damage thresholds associated with five limit states. The seismic behavior of a set of regular reinforced concrete buildings designed according to the EC-2/EC-8 prescriptions for a high seismic hazard level is then studied using the proposed damage index and damage states. Fragility curves and damage probability matrices corresponding to the performance point are calculated for the studied buildings. The obtained results show that the collapse damage state is not reached in the buildings designed according the prescriptions of EC-2/EC-8 and also that the damage does not exceed the irreparable damage limit state.

In this chapter, we present a procedure to evaluate the local damage and global damage in structures subjected to static and dynamic actions, with special emphasis on the seismic problem. In addition to the formulation for the evaluation of damage, we introduce the concept of reinforcement and structural repair by using laminated epoxy matrix composites with carbon fiber reinforcement. For this purpose, the theory of mixtures is used to define a composite material from its basic components. Damage is also evaluated in these reinforced and/or repaired structures and the influence of these improvements on the overall damage assessment of the structure is discussed.

In this work, the nonlinear dynamic response of RC buildings with energy dissipating devices is studied using advanced computational techniques. A fully geometric and constitutive nonlinear model is used for describing the dynamic behavior of structures. The equations of motion are expressed in terms of cross sectional forces and strains and its weak form is solved using the displacement based finite element method. A suitable version of Newmark’s scheme is used in updating the kinematics variables in a classical Newton type iterative scheme. Material points of the cross section are assumed to be composed of several simple materials with their own constitutive laws. The mixing theory is used to treat the resulting composite. A specific finite element based on the beam theory is proposed for the dissipators including constitutive relations. Finally, several numerical tests are carried out to validate the proposed model.

The monograph begins with a review of the usual seismic analysis procedures and presents the problem of seismic-resistant projects. The required structurual analyses can be elastic or inelastic, but the latter have been used mostly during the last decade thanks to advances in numerical methods and in the area of ​​computers. It also presents a summary of the most common seismic codes prescriptions for reinforced concrete elements and examines aspects of conceptual design that often come from code recommendations. Next, an introduction to the theme of performance based design is made. A method for linear seismic dimensioning is then developed, but with displacement amplification factors obtained from research performed on the nonlinear behavior of the structures. This method allows the displacements, and not the strength, to govern the project, is simple to apply, compatible with most of the rules required by the earthquake resistant structures and is illustrated by the application to a group of reinforced concrete framed buildings. Once the buildings designed, they be subjected to seismic actions of the pseudostatic or dynamic type and will undergo a non-linear behaviour. The response of the structures is evaluated by applying a set of limit states formulated in accordance with the principles of performance based design. The non-linear response allows to calibrate some of the factors applied in the seismic project, such as the global ductility, the behavior factor and the redundancy factor and resistance reserve. From the non-linear response, damage indices are obtained, both local and global, that allow the rapid evaluation of the seismic behavior, as well as the identification of the areas in which the damage is concentrated and which must be reinforced. Finally, using a series of thresholds that allow the definition of the limit states, a mixed procedure (deterministic-probabilistic) is applied by means of which the exceedance probabilities of the mentioned states are calculated. These procedure allows calculating fragility curves and damage probability matrices that applied according to the conceptual framework of the performance based design, allow obtaining earthquake resistant buildings.

The monograph highlights the way in which, in the long term, the application of design standards can lead to a reduction of seismic risk in urban areas. The seismic design standards make recommendations regarding the seismic loads to be used, the simplified methods of structural analysis, the criteria that must be applied to ensure a good overall behavior of the same, as well as the design details that must be incorporated. The structural analysis procedures foreseen in all the world standards are based on concepts generally used in the static and dynamic calculation of structures. However, the concepts considered when using these simplified procedures of dynamic analysis and the approximate formulas for the determination of the dynamic characteristics of buildings, are not explained. For this reason, the monograph analyzes the content of the seismic-resistant design regulations in relation to the analysis methods they propose, explaining the concepts of structural analysis that are applied in each case, with special reference to the Spanish regulations in vigor, NCSE-02. Since many design codes include rules that are not justified in the text of the regulations, this monograph also deals with aspects of the so-called conceptual design that requires decisive decisions in the initial phases of the design of structures, which condition the seismic behavior of the same. To facilitate the application of the dynamic analysis of buildings, a program developed in Matlab ® has been incorporated, which can be obtained from the web page www.cimne.com/is-56/modal, together with the data files and results, which are described in the Annex to this monograph.

In this monograph, a complete review of the state of the art of the seismic vulnerability of motorway bridges is carried out. The work begins with a review of the damage caused by the last major earthquakes in the world. Next, the theoretical framework of the methods of evaluation of the seismic vulnerability of structures is described. Then, different methodologies for the evaluation of the seismic vulnerability of bridges are examined in detail. Advances in assessing their seismic vulnerability should be sought using expert judgment, the study of damage data associated with past earthquakes and the numerical simulation of bridge response. For this reason, in the monograph the seismic vulnerability evaluation methods are classified into the following groups: (1) methods based on vulnerability indexes; (2) methods that use structural analysis; (3) methods based on statistical evaluations and expert opinion; and (4) methods that use the observed damage statistics. Finally, some of the main methods for obtaining the indices that characterize the importance of motorway bridges are described, as well as indices for the evaluation of the liquefaction effect.

The standards make recommendations regarding the seismic loads, the simplified methods of structural analysis, the criteria that must be applied to ensure its good global seismic behavior, as well as the earthquake resistant design details that must be applied. The structural analysis procedures included in all the seismic design standards are based on concepts generally used in the static and dynamic analysis of structures. However, when considering the possibility of using simplified procedures of dynamic calculation and of formulas that allow approximating the values of the dynamic characteristics of buildings, the mentioned concepts are not explained in a clear way. For this reason, the present monograph analyzes the content of the earthquake-resistant design codes in relation to the calculation methods they propose, explaining the concepts of structural analysis that are applied in each case, with special reference to Spanish regulations in force, NCSE-02. In addition, this monograph deals with aspects of conceptual design, which provides qualitative descriptions of design solutions based on the designer's experience. In this phase, the structural typology, the plan form of the structure, the distribution of the masses in height and the rigidities are chosen, the organization of the resistant system is specified, etc. It should be mentioned that in many regulations the conceptual design is specified in rules that are not justified in the text. All this implies taking decisive decisions in the initial phases of the design of structures, which condition the seismic behavior of the structures to such an extent that all the subsequent calculations, as well as the design details that are applied, may not have the expected effect.

In this monograph, a numerical model based on the finite element method is developed to analyze buildings with base seismic isolation, discretizing the structure-isolator system. In this way, the response of such systems is estimated with greater precision and, thus, the tasks of designing and verifying them is facilitated. The development of the model requires the resolution of the following problems: • Development of an appropriate constitutive model for elastomers that considers large elastic deformations, incompressibility, visco-elasticity and elasto-plasticity in large strains. • Incorporation of the constitutive model developed in a general model of dynamic analysis of structures using the finite element method that combines bar elements with plane elements; appropriate constitutive models for the numerical simulation of the structural materials; mixing theory; discretization by layers. • Application of damage indices that facilitate the evaluation of the global state of the structure after a seismic ground motion. • Numerical study of the behavior of structures with elastomeric isolation system subjected to earthquakes and their comparison with the corresponding fixed base structures.

There is a general interest in civil engineering to quantify the damage produced in structures by catastrophic actions. It would be convenient, from a practical point of view, to describe the state of a structure by means of a single figure that clarifies whether the structure is capable of supporting the service charges or not; if it will survive to another extraordinary load in the future; how does the present damaged state influence in its future behavior; where the most damaged points are located; what capacity of resistance remains in each point; and, in general, all kind of information that help to make design or repair decisions. The authors have proposed a solution to this problem in the specific case of earthquakes acting upon reinforced concrete building structures. A methodology has been formulated for the definition of an index of damage that can be typified for all the structures belonging to the same class and that allows classifying them according to their seismic vulnerability. In the monograph, simple beam structures are first studied in order to better describe the concepts involved and the parameters that influence the solution to the problem. The developed methodology, which models the structures using the finite element method, is directly and easily extended to shells, plates or 3D solids. The fundamental idea of ​​this work is to apply constitutive equations formulated in 3D at a material point instead of using constitutive laws formulated in generalized forces-displacements such as, for example, bending moment-curvature, shear force-angular distortion, etc. This allows modeling the behavior of composite materials directly since for each component material its own constitutive law is considered. In this way, it is sufficient to have a single 3D constitutive model and a methodology to calculate the components of the stress and strain tensors at any point of the beam section.

The poor performance of some reinforced concrete (RC) structures during strong earthquakes has alerted about the need of improving their seismic behavior, especially when they are designed according to obsolete codes and show low structural damping, important second-order effects and low ductility, among other defects. These characteristics allow proposing the use of energy-dissipating devices for improving their seismic behavior. In this work, the non-linear dynamic response of RC buildings with energy dissipators is studied using advanced computational techniques. A fully geometric and constitutive non-linear model for the description of the dynamic behavior of framed structures is developed. The model is based on the geometrically exact formulation for beams in finite deformation. Points on the cross section are composed of several simple materials. The mixing theory is used to treat the resulting composite. A specific type of element is proposed for modeling the dissipators including the corresponding constitutive relations. Special attention is paid to the development of local and global damage indices for describing the performance of the buildings. Finally, numerical tests are presented for validating the ability of the model for reproducing the non-linear seismic response of buildings with dissipators.

The purpose of this paper is to develop an improved analytical model for predicting the damage response of multi-storey reinforced concrete frames modelled as an elastic beam-column with two inelastic hinges at its ends. The damage is evaluated in the hinges, using the concentrated damage concepts and a new member damage evaluation method for frame members, which leads to a meaningful global damage index of the structure. A numerical procedure for predicting the damage indices of the structures using matrix structural analysis, plastic theory and continuum damage model is also developed. The method is adequate for the prediction of the failure mechanisms. Using the proposed framework, various numerical examples are included. Based on the obtained results, advantages and limitation of the proposed model are observed. The proposed numerical model is useful to solve multi-storey reinforced concrete frames using a procedure that combines structural finite elements (beams) with moment-curvature constitutive models derived from classic stress-strain ones. It is an inexpensive and reliable procedure to model the frame structures.

Living biological tissues are complex structures that have the capacity of evolving in response to external loads and environmental stimuli. The adequate modelling of soft biological tissue behaviour is a key issue in successfully reproducing biomechanical problems through computational analysis. This study presents a general constitutive formulation capable of representing the behaviour of these tissues through finite element simulation. It is based on phenomenological models that, used in combination with the generalized mixing theory, can numerically reproduce a wide range of material behaviours. First, the passive behaviour of tissues is characterized by means of hyperelastic and finite-strain damage models. A generalized damage model is proposed, providing a flexible and versatile formulation that can reproduce a wide range of tissue behaviour. It can be particularized to any hyperelastic model and requires identifying only two material parameters. Then, the use of these constitutive models with generalized mixing theory in a nite strain framework is described and tools to account for the anisotropic behaviour of tissues are put forth. The active behaviour of tissues is characterized through constitutive models capable of reproducing the growth and remodelling phenomena. These are built on the hyperelastic and damage formulations described above and, thus, represent the active extension of the passive tissue behaviour. A growth model considering biological availability is used and extended to include directional growth. In addition, a novel constitutive model for homeostatic-driven turnover remodelling is presented and discussed. This model captures the stiffness recovery that occurs in healing tissues, understood as a recovery or reversal of damage in the tissue, which is driven by both mechanical and biochemical stimuli. Finally, the issue of correctly identifying the material parameters for computational modelling is addressed. An inverse method using optimization techniques is developed to facilitate the identification of these parameters.

Most of the existing materials around us can be considered composite materials, since they are composed by several phases or components at certain spatial scale. The physical and chemical properties of composites, as occurs with structures composed by two or more materials, is defined by the response provided by their constituents. Therefore, a good characterization of the composite requires considering the performance of its components. In the last decades, several methods have been proposed with this approach to characterize composite materials, most of them based on multiscale techniques. Nowadays, multiscale homogenization analysis is a popular topic in the simulation of composite materials. This is because the complexity of new composites demands of advanced analysis techniques for their correct characterization, and thanks to the continuous increase of computational capacity. However, the computational cost when multiscale procedures are taken to the non-linear range and are applied to real-size structures is still excessively high. In this context, this monograph presents a comprehensive homogenization formulation for an efficient non-linear multiscale modeling of composite structures. The development of a composite multiscale constitutive model is addressed from two different homogenization approaches. The first one corresponds to a phenomenological homogenization procedure for the non-linear analysis of carbon nanotubes reinforced composites. The second one is a general two-scale homogenization procedure to analyze three-dimensional composite structures. Carbon nanotubes (CNTs) have been regarded as ideal reinforcements for high-performance composites. The formulation developed takes into account explicitly the performance of the interface between the matrix and the CNTs. The load is transferred to the nanotubes through the considered interface. The composite non-linear behavior results from the non-linearities of its constituents, and in case of interface damage, it also becomes non-linear the law defined to couple the interface with the CNTs. The formulation is validated studying the elastic response and non-linear behavior of several composites. In the context of multiscale homogenization, a first-order and an enhanced-first-order formulation is developed. The results obtained for laminate composites using the first-order formulation are compared with other microscopic formulations, showing that the homogenization method is an excellent alternative when microstructural effects must be taken into account. Then, a strategy to conduct non-linear multiscale analysis in an efficient way is proposed. The procedure conserves the dissipated energy through the scales and is mesh independence. The analysis of academic examples is used to show the capacity of the non-linear strategy. Finally, the simulation of an industrial composite component proves the performance and benefits of the non-linear homogenization procedure developed.

The present work aims at advancing an innovative computational methodology that simulates steel and composite material fracture under cyclic loading following a phenomenological approach, with calibration from both small scale and large scale testing. This work addresses fatigue processes ranging from High Cycle to Ultra-Low-Cycle Fatigue. An assessment of the current state of the art is done for all the di erent fatigue types. Following, for Ultra-Low Cycle Fatigue a new constitutive law is proposed and validated with experimental results obtained on small scale samples. Industrial applications are shown for a large diameter straight pipe under monotonic loading conditions and for a bent pipe under cyclic loading. Emphasis is made on the capacity of the model to represent di erent failure modes depending on the loading conditions. The research regarding this part has been used in the frame of the European Project: \Ultra low cycle fatigue of steel under cyclic high-strain loading conditions" (ULCF). Regarding High Cycle Fatigue, a classic damage model is presented in combination with an automatic load advancing strategy that saves computational time when dealing with load histories of millions of cycles. Numerical examples are shown in order to demonstrate the capabilities of the advancing strategy and a validation of the model is done on small scale samples. A new constitutive model is presented for Low Cycle Fatigue that uses the classic plasticity and damage theories and simultaneously integrates both processes in the softening regime. The capabilities of the model are shown in numerical examples. Finally, the High Cycle Fatigue damage model is applied to the constituents of a composite material and the structural behaviour is obtained by means of the serial/parallel rule of mixtures. Validation of the constitutive formulation is done on pultruded glass ber reinforced polymer pro les.

This monograph focuses on an eminently practical issue, which allows to take advantage of the characteristics associated with high ductility steels: the confinement of concrete. An adequate disposition, not only of the transversal reinforcement, but also of the longitudinal reinforcement itself, can considerably increase the performance of the structures. This fact is something fundamental when the structures are subjected to actions close to the collapse situations, as it happens in the case of some earthquakes. Given the importance of this last aspect, as well as the increasing importance that issues related to the earthquake are beginning to have in Spain, this monograph analyzes which are the most appropriate structural typologies in these situations, and what is the contribution of high ductility steel to the improvement of its behavior. The result does not shows excessive surprises. The structurally "more robust" typologies are those constituted by moment resisting frames, consisting of a network of beams and columns. Other typologies, commonly used in our country, such as the structures with columns and slabs, or with flat beams, remain on the side of insecurity. The contribution of high ductility steels is very favorable in the case of the appropriate typologies, while it is insufficient to resolve the bad seismic behaviour of the "more sensitive" typologies.

In this monograph, we study the definition of possible damage in bridges by using simplified structural models. The state-of-the-art of the seismic vulnerability of bridges is first discussed and the theoretical background of the methods to evaluate their vulnerability is commented. The existing methodologies to evaluate the vulnerability of bridges are then described in detail; The methods are classified as: (1) methods based on the vulnerability index; (2) methods based on structural analyses; (3) methods based on expert opinion and statistical evaluations; and (4) methods based on statistical evaluations of the observed damages. A simplified methodology to estimate the seismic vulnerability of reinforced concrete bridges with simple pier bent and elastic girders is then proposed. The methodology is applied to an existing bridge, built 30 years ago. The elastic and the non-linear procedures of evaluation are first discussed. The non-linear procedure includes an analytical methodology to estimate the local damage in the piers, using a continuous damage model, and the global damage of the bridge. Thereinafter, a numerical process allows considering artificial seismic actions compatible with the velocity spectrum of deterministic records. Finally, an application of the proposed analytical procedure to estimate the seismic vulnerability of the real bridge is given. The obtained damage results show that the studied bridge would suffer only a minor damage when a seismic action similar to that of the expected seismic scenario is considered. The proposed methodology is compared with previous experimental results and with analytical results obtained by using commercial codes. It is shown that the proposed simplified methodology is less computational time consuming and that it provides reliable values of the maximum damage suffered by the bridge piers.

In this work, a formulation for rod structures, able to consider coupled geometric and constitutive sources of nonlinearity in both the static and the dynamic range, is developed. It is extended for allowing the inclusion of passive energy dissipating elements as a special rod element and geometric irregularities as a full three-dimensional body connected to the framed structure by means of a two-scale model. The proposed formulation is based on the Reissner-Simo geometrically exact formulation for rods considering an initially curved reference configuration and extended to include arbitrary distribution of composite materials in the cross sections. Each material point of the cross section is assumed to be composed of several simple materials with their own thermodynamically consistent constitutive laws. The simple mixing rule is used for treating the resulting composite. Cross sections are meshed into a grid of quadrilaterals, each of them corresponding to a fiber directed along the axis of the beam. A mesh independent response is obtained by means of the regularization of the energy dissipated at constitutive level considering the characteristic length of the mesh and the fracture energy of the materials. Local and global damage indices have been developed based on the ratio between the visco-elastic and nonlinear stresses. The consistent linearization of the weak form of the momentum balance equations is performed considering the effects of rate dependent inelasticity. Due to the fact that the deformation map belongs to a nonlinear manifold, an appropriated version of Newmark's scheme and of the iterative updating procedure of the involved variables is developed. The space discretization of the linearized problem is performed using the standard Galerkin finite element approach. A Newton-Raphson type of iterative scheme is used for the step-by-step solution of the discrete problem. A specific element for energy dissipating devices is developed, based on the rod model but releasing the rotational degrees of freedom. Appropriated constitutive relations are given for a wide variety of possible dissipative mechanisms. Several numerical examples have been included for the validation of the proposed formulation. The examples include elastic and inelastic finite deformation response of framed structures with initially straight and curved beams. Comparisons with existing literature is performed for the case of plasticity and new results are presented for degrading and composite materials. Those examples show how the present formulation is able to capture different complex mechanical phenomena such as the uncoupling of the dynamic response from resonance due to inelastic incursions and suppression of the high frequency content. The study of realistic flexible pre-cast and cast in place reinforced concrete framed structures subjected to static and dynamic actions is also carried out. Detailed studies regarding to the evolution of local damage indices, energy dissipation and ductility demands are presented. The studies include the seismic response of concrete structures with energy dissipating devices. Advantages of the use of passive control are verified.

The earthquake resistant design codes in force in the different countries are applied to the field of building structures. However, some of the standards give a certain appearance of "generality" that can give the impression that these are mandatory for any type of structure. In fact, the rules are general only in the definition of the seismic hazard of the area to which they apply, that is, in relation to the maximum ground acceleration. However, in each country, there are other specific codes for the design of non-building structures. This chapter describes the dynamic calculations foreseen in the building seismic design standards; the use of simplified, shear building models; the usual procedure of dynamic calculation of structures based on modal analysis; and, finally, the use of linear and non-linear response seismic spectra, which provides only the maximum response of the structure.

When solving dynamic problems, it is necessary to define in some way the damping of the structure. Generally, a damping term that depends on the velocities is incorporated directly into the dynamic equilibrium equation. To do this, we define a structural damping matrix, such as Rayleigh's, which is quite difficult to estimate. Once the damping has been defined, the problem is solved as a linear elastic one, what enters in contradiction with the fact that a dissipative phenomenon is being treated. In this chapter, an alternative with greater conceptual basis is described, which considers the structural damping based on a viscoelastic constitutive models in which the stress depends in some way on the strain velocity. In this way, the term of structural damping arises directly in the dynamic equilibrium equation, where the properties of the materials can be determined through simple laboratory tests.

The main objective of this thesis is to present a novel methodology for the analysis of post-tensioned concrete structures, based on the potential offered by the use of the Serial-Parallel Rule of Mixtures when modelling composite materials. The advantages of this methodology are studied in comparison to the available approaches, i.e. the formulation proposed by the standards used in the design of structures and the mechanism used in numerical simulation based on the finite element method (FEM). The Serial-Parallel Rule of Mixtures allows the modelization of each component material in depth, working as a constitutive model manager in order to simulate the composite material being studied. The prestressed concrete is modelled as a composite material with long fibres where the fibre orientation is defined by the steel tendon direction. Therefore, the most suitable constitutive model can be used in each case. In the present thesis this is: for the matrix - concrete an isotropic damage model and for the fibre - steel a viscoelasticity model, achieving an extraordinary accuracy in the micro-scale. The analysis is based on the FEM, which combined with the Serial-Parallel Rule of Mixtures theory allows the study of large-scale structures, taking into account the specific geometric requirements of the construction. Three application examples are included which are used for validating the methodology and the potential of this approach. The first two cases are two isostatic beams that allow the comparison with the results obtained through the study using analytical methods. Finally, the third case shows the results obtained recently for the analysis of a Benchmark, in which the behaviour of a mock-up of a reactor containment building has been studied.

Although laminated materials have been used for decades, their employment has increased nowadays in the last years as a result of the gained confidence of the industry on these materials. This has provided the scientific community many reasons to dedicate considerable amount of time and efforts to address a better understanding of their mechanical behavior. With this objective both, experimental and numerical simulation have been working together to give response to a variety of problems related with these materials. Regarding numerical simulation, a correct modeling of the kinematics of laminated materials is essential to capture the real behavior of the structure. Moreover, once the kinematics of the structure has been accurately predicted other non-linear phenomena such as damage and/or plasticity process could be also studied. In consequence, in order to contribute to the constant development of simpler and more efficient numerical tools to model laminated materials, a numerical method for modeling mode II/III delamination in advanced composite materials using one-and two-dimensional finite elements is proposed inthis work. In addition, two finite elements base on a zigzag theory for simulating higly heterogeneous multilayered beams and plates structures are developed here. The document is written based on results of four papers published in indexed journals. Copies of all these papers are included in Appendix. The main body of this thesis is constituted by Chapters 2 to 4. Chapter 2 deals with the numerical treatment of laminated beams and plates. Chapter 3 presents the formulation of the LRZ beam and the QLRZ plate finite elements based on the Refined Zigzag theory. Finally, the main contribution of this thesis, the LRZ/QLRZ delamination model, is developed in Chaptert 4.

The main purpose of this paper is to develop a reliable method based on a three-dimensional (3D) finite-element (FE) model to simulate the constitutive behaviour of reinforced concrete structures strengthened with post-tensioned tendons. A 3D FE model was used, where the nonlinear material behaviour and geometrical analysis based on incremental–iterative load methods were adopted. The pre-tensioned concrete is modelled as a composite material whose behaviour is described with the serial-parallel rule of mixtures (S/P RoM) [1-3]. The effective pre-tensioning stress was applied as an initial strain imposition in the steel material used to model the tendons. The methodology is valid for both straight and curvilinear steel tendons. Examples of both cases will be shown. Validation by comparison with the analytic solution is done for the case of a concrete beam with a straight pre-tensioned steel tendon embedded. Other examples are also included.

In this paper we derive the field of displacements and strains for thin-walled open composite beams with composite laminated material including in their kinematics flexural and torsional shear deformations effects. The equilibrium equations are defined through the variational formulation and show that is possible to formulate Co finite elements taking into account the torsional shear deformation. Stress-strain relationships for the cross-section of thin-walled composite beams are obtained by extending first-order laminate (FSDT: first-order shear deformation) theory and using a «free stress resultant condition at the boundary». Three different one-dimensional finite elements with Co continuity are formulated for the study of thin-walled open composite beams and they are labelled as BSW (beam with shear and warping). The influence of the integration strategy in the BSW elements is evaluated via the shear-locking phenomenon and the rate of convergence for displacements and rotations. The stiffness matrix integration is compared using exact and reduced integration methods. Examples of pure torsion and flexo-torsion in a cantilever composite beam are performed. Numerical results are compared to those reported by other authors.

This work presents a numerical model of the cyclic structural behavior of dissipative buckling-restrained braces, commonly used as an alternative to classical concentric braces for seismic protection of building frames and other structures. Such devices are usually composed of a slender steel core embedded in a stockiest casing that is intended to prevent its buckling when it is under compression. The casing is made either of mortar or steel, and a sliding interface is interposed between the core and the casing to prevent excessive shear stress transfer. The behavior of the steel core is described by a damage and plasticity model, the behavior of the mortar casing is described by an isotropic damage model and the sliding behavior of the interface is described by a contact penalty model. These 3 models are implemented in the Abaqus software package following an explicit formulation. In a previous article (published in an earthquake engineering journal) the model was briefly described, its ability to reproduce the cyclical behavior of buckling-restrained braces was preliminarily pointed out and their results were satisfactorily compared with those of experimental tests. The aim of this paper is to describe the model thoroughly and to present new judgments about its usefulness.

This paper presents a new algorithm for solving the equations of motion of multi-storey buildings that incorporate frictional energy dissipators as seismic protection. The behavior of the dissipators is represented by Coulomb dry friction models, they introduce severe nonlinearities in the dynamic behavior of the structure every time that the contact conditions (stick or slip) change in the dissipators. These nonlinearities complicate the resolution of the equations of motion as it usually is described by lumped masses models whose degrees of freedom are the displacements of the floors and, as the stick or slip conditions change, the degrees of freedom must be modified: for blocking conditions they are only the displacements of the storeys while under sliding conditions the displacements of the dissipators have to be also considered. In previous articles the accuracy of the proposed algorithm has been verified by comparison with experimental results, as well, the computational efficiency of the algorithm has been confirmed by comparing the required resources (in terms of computation time and of memory allocation) with those of other algorithms. The objectives of this paper are to describe in detail the numerical solution of the equations of motion and present representative examples confirming the ability of the algorithm to reproduce the dynamic behavior of buildings with friction dissipators and reporting preliminarily about the usefulness of such devices to reduce the oscillations of the structure to be protected.

Este artículo presenta un nuevo procedimiento con el que simular el fallo por delaminación en materiales compuestos. El método propuesto utiliza la teoría de mezclas serie/paralelo, desarrollada por Fernando Rastellini, para la caracterización constitutiva del material compuesto. Esta formulación obtiene el comportamiento del compuesto acoplando la respuesta constitutiva de los materiales componentes, fibra y matriz, imponiendo una relación de iso-deformación en la dirección de la fibra (dirección en paralelo) y una relación de iso-tensión en el resto de direcciones (direcciones en serie). Si bien la teoría de mezclas serie/paralelo permite simular los materiales componentes con cualquier ecuación constitutiva, el presente trabajo utiliza una formulación de daño para caracterizar la matriz y una formulación elástica para la fibra. Se mostrará que es posible, utilizando la teoría de mezclas serie/paralelo y una formulación de daño, simular el fallo del compuesto por delaminación. Además, éste se obtiene de forma natural, sin necesidad de definir elementos especiales en los que propagar la fractura, ni ser necesario utilizar costosas técnicas numéricas como el remallado o elementos de contacto. Con el procedimiento propuesto el fallo constitutivo de la matriz conduce a una reducción de la capacidad portante del compuesto en las direcciones en serie (entre otras, la dirección de las tensiones tangenciales) sin eliminar la capacidad resistente en la dirección de la fibra. Se probará que un material compuesto con este comportamiento corresponde a un material delaminado. La última sección de este artículo muestra la simulación del End Notch Failure Test y los resultados obtenidos son comparados con resultados experimentales. La similitud de los resultados numéricos y experimentales demuestra la validez del método propuesto para resolver problemas de delaminación en materiales compuestos.

In this article a new methodology is presented for the mechanical characterization of the asphalt mixes, specially the recycled asphalt mixes, which leads to define the adequate laboratory tests and to formulate a new constitutive model able to integrate the mechanical properties and reproduce the response of the material in a more complex context. The addition of asphaltic recycled material over a conventional mix, change in a significant way the properties of this mix. The design of recycled asphalt mixes requires additional information far away the properties of this mix. The design of recycled asphalt mixes requires additional information far away from the usual test used in the design of conventional mixes, to pick up the evolution of the tenacity of the cracking resistance, determinant variables in the recycled asphalt mix’s behavior. For thid purpose, the direct tensile test in proposed as the experimental reference for the characterization of the material. A new constitutive model in formulated considering in a explicit shape, the influence of the strain shape, the influence of the strain rate of the material in the simulation of its response. The direct tensile test is used to calibrate the parameters of the model, and so characterize its structural response. The main objective of this development is the simulation of the behavior of the recycled asphalt mixture in a fleexible pavement. The results obtained reach a good approximation to the experimental measures with the proposed model.

The numerical simulation of composite materials is a field under continuous development. Its application to structural design has shown important improvements, leading to a better simulation of strengthened structures. This paper uses the serial/parallel mixing theory to predict the mechanical behavior of composites. This theory uses the constitutive equations of the component materials to obtain the composite performance. The advantages provided by this formulation to simulate concrete structures reinforced or retrofitted with Fiber Reinforced Polymers (FRP) will be shown from the analysis of several finite element models, consisting of a set of concrete frames with different strengthening configurations. The results obtained will show that the use of this theory to simulate FRP reinforced structures improves their analysis and design.

En este trabajo se propone un modelo hiperelástico generalizado para el análisis de elastómeros multi-fase. El modelo se desarrolla en grandes deformaciones en función de los estiramientos principales. Debido a la cuasi-incompresibilidad de los elastómeros, se supone un comportamiento diferente para las partes volumétrica y desviadora de la deformación. Se utiliza teoría de mezclas para incorporar las expresiones constitutivas básicas propuestas para cada material, viscoelasticidad para el caucho y elastoplasticidad para las partículas agregadas, en una formulación de sólido compuesto. La resolución numérica del modelo se implementa en una formulación lagrangeana total con elementos de presión constante. Mediante condensación estática se elimina el grado de libertad de presión del elemento. La contribución del modelo propuesto es su capacidad para capturar el comportamiento elástico fuertemente no lineal con deformaciones extremas de los cauchos naturales y de alto amortiguamiento y sus características disipativas. El comportamiento de la formulación propuesta y su aplicación numérica se ilustra por medio de resultados numéricos y su comparación con resultados experimentales.

Los sistemas de aislamiento sísmico de base desacoplan parcialmente una estructura de los movimientos del terreno por medio de dispositivos colocados entre la estructura y su cimentación. De los diversos tipos de dispositivos desarrollados, los más utilizados son los de elastómero laminado que están constituidos por capas alternadas de elastómero y acero. Este artículo es una contribución al tratamiento numérico conjunto de las estructuras con sus dispositivos de aislamiento de base de elastómeros laminados. La no linealidad en la respuesta material no está limitada a la componente elastomérica del sistema, puesto que el comportamiento de la estructura de hormigón armado se representa mediante modelos constitutivos elasto-plásticos y de daño. Como ejemplo se analiza la respuesta sísmica de una estructura de seis plantas con aislamiento de base y se compara con la de una estructura similar de base fija.

A numerical model, based on large strain plasticity, to simulate the uniaxial compaction of powder materials is presented. The elastic response is obtained from a hyperelastic model. The plastic response represents the loss of voids and the plastic deformation oY the grains. Two parameters that evolve in terms of the relative density control the modified, Von Mises type, yield surface. A visco-plastic model to include the rate load dependency is proposed. This regularization prevents the loss of ellipticity that could occur with wrong compaction processes. Two different friction models are studied: 1 a Norton-Hoff type model and 2. a Coulomb friction model. Penalization and Lagrange multipliers methods are studied to solve the last one as well as a mixed algorithm, to implement the last model in a robust way.