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Purpose. To review the standards and the scientific literature on emergency load calculations that are linked with stability to progressive collapse of building structures and dynamic influence of localized structural component damage (failure) on the building structure. To study the dynamic influence on the building structure of its localized structural component damage by laboratory experiment and numerical simulation. Methodology. To reach the goal the existing standards and the scientific literature of different countries on calculations and design of resistant to progressive collapse buildings and structures were reviewed. The laboratory bench was created. Experimental and numerical studies were conducted by modelling dynamic behaviour of the building structure. The laboratory bench was statically indeterminate system in order to localized structural component damage (failure) did not lead to the hole structure destruction but only to its qualitative reconfiguration. Findings. During the laboratory experiment the vibrational accelerations and displacements for characteristic point of structure were registered. By processing vibrational diagrams, the values of the frequencies and the laboratory bench free vibrations logarithmic decrements were received, as well as the value of the dynamic increase factor by different load levels and different failure types. Experimental results were checked by numerical simulation. Originality. The studies allow to evaluate dynamic effect of localized structural component damage two types. It was also discovered that the values of dynamic displacements and accelerations may be differentby several times by the comparable values of the dynamic increase factors of different failure types. Practical value. The results suggest that in the case of total structural component failure the value of dynamic increase factor (stresses and accelerations) is more than that in the case of structural component damages while retainingpartial functionality. In such a case when carrying out practical engineering calculations it would be sufficient to consider the total structural component failure while the possibility of partial damages would be as reserve of power., Цель. Проанализировать существующие нормативные и научные публикации, содержащие положения расчетов на аварийные нагрузки, связанные с устойчивостью к прогрессирующему обрушению строительных конструкций, а также данные о динамическом влиянии на строительную конструкцию локального структурного повреждения ее элемента (отказа). Исследовать динамическое влияние на строительную конструкцию локального структурного повреждения ее элемента путем лабораторного эксперимента и численного моделирования. Методика. Для достижения поставленной цели был проведен обзор существующих нормативных документов разных стран и научных публикаций по расчету и проектированию зданий и сооружений, устойчивых к прогрессирующему обрушению. Был создан лабораторный стенд и проведены экспериментальные и численные исследования динамического поведения строительной конструкции. Лабораторный стенд был реализован в виде статически неопределимой системы, так, чтобы локальный отказ части конструкции не приводил к разрушению всей структуры, а только к качественному изменению ее конфигурации. Результаты. Во время лабораторного эксперимента регистрировались виброускорения и виброперемещения характерной точки конструкции. Путем обработки виброграмм были получены значения частот и логарифмических декрементов свободных затухающих колебаний экспериментального стенда, а также значения динамического коэффициента при различных уровнях нагрузок и видах отказов. Экспериментальные данные проверялись также числовым моделированием. Научная новизна. Проведенные исследования позволяют оценить динамическое влияние на конструкцию локальных структурных повреждений двух видов. Было выявлено, что даже при сопоставимых значениях динамических коэффициентов при различных видах отказов величины динамических перемещений и ускорений могут отличаться в несколько раз. Практическая значимость. Полученные результаты свидетельствуют о том, что в случаях полных отказов элементов конструкций они получают большие значения динамических коэффициентов (напряжений и ускорений), чем конструкции, у которых отказы дополнительных элементов сопровождаются частичным сохранением их работоспособности. В таком случае в практических инженерных расчетах можно ограничиться рассмотрением именно таких полных отказов критических элементов конструкций, а возможность их неполного выключения из работы может быть отнесено в запас несущей способности., Мета. Проаналізувати наявні нормативні та наукові публікації щодо положень розрахунків на аварійні навантаження, пов’язані зі стійкістю до прогресуючого обвалення будівельних конструкцій, та динамічного впливу на будівельну конструкцію локального структурного пошкодження її елемента (відмови). Дослідити динамічний вплив на будівельну конструкцію локального структурного пошкодження її елемента шляхом лабораторного експерименту і числового моделювання. Методика. Для досягнення поставленої мети було проведено огляд існуючих нормативних документів різних країн і наукових публікацій щодо розрахунку та проєктування будівель і споруд, стійких до прогресуючого обвалення. Було створено лабораторний стенд та проведено експериментальні та числові дослідження динамічної поведінки моделі будівельної конструкції. Лабораторний стенд було реалізовано у вигляді статично невизначуваної системи, так, щоб локальна відмова частини конструкції не призводила до руйнування всієї структури, а лише до якісної зміни її конфігурації. Результати. Під час лабораторного експерименту реєструвалися віброприскорення і вібропереміщення характерної точки конструкції. Шляхом обробки віброграм були отримані значення частот і логарифмічних декрементів вільних затухаючих коливань експериментального стенда, а також значення динамічного коефіцієнта при різних рівнях навантажень і видах відмов. Експериментальні дані перевірялись також числовим моделюванням. Наукова новизна. Проведені дослідження дозволяють оцінити динамічний вплив на конструкцію локальних структурних пошкоджень двох видів. Було виявлено, що навіть при співставних значеннях динамічних коефіцієнтів при різних видах відмов величини динамічних переміщень і прискорень можуть відрізнятися в декілька разів. Практична значимість. Отримані результати свідчать про те, що у випадках повних відмов елементів конструкцій вони отримують більші значення динамічних коефіцієнтів (напружень і прискорень), ніж конструкції, у яких відмови додаткових елементів супроводжуються частковим збереженням їхньої працездатності. У такому разі, в практичних, інженерних розрахунках, можна обмежитися розглядом саме таких повних відмов критичних елементів конструкцій, а можливість їхнього неповного виключення з роботи може бути віднесена в запас несучої здатності.

We study natural vibration of elastic parabolic arches, modeled as plane curved beams susceptible to elongation, shear, and bending, exhibiting small concentrated cracks. The crack is simulated by springs between regular chunks, with stiffness evaluated following stress concentration in usual crack opening modes. We evaluate and compare the linear dynamic response of the undamaged and damaged arch in nondimensional form. The governing equations are turned into a system of first-order differential equations that are solved numerically by the so-called matricant. The original contribution of this study lies in highlighting the dependence of the variation of the first natural frequencies on the crack location not only along the axis but also on opposite sides of the cross-section. We obtain the relative variations of the first frequencies in terms of the two crack locations. The result of this direct problem provides information on the possibility to detect such locations, and gives indications on structural monitoring and damage identification.

Free vibration and Ljapounov stability of compressed open thin-walled beams with a cross-section reduction are studied by a in-house finite differences numerical code, based on a refined direct beam model and allowing for investigating elastic stability of non-trivial equilibrium paths in a dynamic setting. The benchmark is a beam with doubly symmetric cross-section and non-zero warping rigidity, under free, semi-, and fully restrained warping at its ends. In all cases, the results of the direct model are compared to finite element and/or experimental ones. The reduction in the cross-section rigidity induces a weakening that may model a local damage; thus, the present investigation may be useful with an outlook to damage monitoring and identification.

The aim of this paper is to present a modelling of mechanical behaviour of concrete on a mesoscopic scale. Concrete is considered as a bi-phasic material where the cement paste and the aggregates are described with their own mechanical characteristics. Firstly, the model is studied in two dimensions in order to optimize the geometrical model of the inner structure of concrete in terms of the meshing strategy and the smallest size of the aggregate to be taken into account. The model shows interesting results on the transition from diffuse to localized damage and is able to reproduce dilatancy in compression. Finally, results of the three-dimensional model are shown in tension. © 2010 Taylor & Francis Group, LLC.

An study of the damage induced in dental materials and model multilayer systems by masticatory contact stresses, simulated by hertzian indentation test, have been performed. In particular, the nature of induced damage has been identified, and quantified from stressstrain curves and critical loads for yielding or crack initiation. For multilayer systems, test have been numerically simulated using finite element techniques (FEM). FEM simulations complement indentation test, allowing to justify the observed fracture modes from calculated stress fields. Practical implications can be derived from our results, relevant to the design of multilayer structures tolerant to contact damage.En este trabajo se ha realizado un estudio del daño introducido en materiales dentales y en sistemas multicapa prototipo cuando soportan las tensiones de contacto que se generan en la boca del paciente, simuladas mediante ensayos de indentación Hertz. En particular, se ha determinado la naturaleza del daño introducido, y se ha procedido a su cuantificación a partir de la obtención de curvas tensión-deformación y cargas críticas para el inicio de la deformación plástica y/o fractura. Además, en el caso del sistema multicapa, los ensayos se han simulado numéricamente mediante el método de elementos finitos (FEM). La simulación FEM es el complemento perfecto a los ensayos Hertz, ya que permite cuantificar el campo de tensiones y por consiguiente justificar los diferentes modos de fractura observados. A partir de los resultados de este estudio se deducen implicaciones de interés práctico para el diseño de materiales multicapa resistentes al daño por contacto.

This paper is an analytical/experimental investigation of the effect of damage on the nodes of free vibration modes of a thin rod in longitudinal vibration. The damage, a notch, is simulated by a simple spring. It is shown that nodes move toward the notch. The direction and amount by which they move may be used to estimate the position and severity of the damage. Analytical results agree well with experimental tests.

For the last few decades, we have obtained tremendous insight into underlying microscopic mechanisms of degrading quasi-brittle materials from persistent and near-saintly efforts in laboratories, and at the same time we have seen unprecedented evolution in computational technology such as massively parallel computers. Thus, time is ripe to embark on a novel approach to settle unanswered questions, especially for the earthquake engineering community, by harmoniously combining the microphysics mechanisms with advanced parallel computing technology. To begin with, it should be stressed that we placed a great deal of emphasis on preserving clear meaning and physical counterparts of all the microscopic material models proposed herein, since it is directly tied to the belief that by doing so, the more physical mechanisms we incorporate, the better prediction we can obtain. We departed from reviewing representative microscopic analysis methodologies, selecting out “fixed-type” multidirectional smeared crack model as the base framework for nonlinear quasi-brittle materials, since it is widely believed to best retain the physical nature of actual cracks. Microscopic stress functions are proposed by integrating well-received existing models to update normal stresses on the crack surfaces (three orthogonal surfaces are allowed to initiate herein) under cyclic loading. Unlike the normal stress update, special attention had to be paid to the shear stress update on the crack surfaces, due primarily to the well-known pathological nature of the fixed-type smeared crack model–spurious large stress transfer over the open crack under nonproportional loading. In hopes of exploiting physical mechanism to resolve this deleterious nature of the fixed crack model, a tribology-inspired three-dimensional (3d) interlocking mechanism has been proposed. Following the main trend of tribology (i.e., the science and engineering of interacting surfaces), we introduced the base fabric of solid particle-soft matrix to explain realistic interlocking over rough crack surfaces, and the adopted Gaussian distribution feeds random particle sizes to the entire domain. Validation against a well-documented rough crack experiment reveals promising accuracy of the proposed 3d interlocking model. A consumed energy-based damage model has been proposed for the weak correlation between the normal and shear stresses on the crack surfaces, and also for describing the nature of irrecoverable damage. Since the evaluation of the consumed energy is directly linked to the microscopic deformation, which can be efficiently tracked on the crack surfaces, the proposed damage model is believed to provide a more physical interpretation than existing damage mechanics, which fundamentally stem from mathematical derivation with few physical counterparts. Another novel point of the present work lies in the topological transition-based “smart” steel bar model, notably with evolving compressive buckling length. We presented a systematic framework of information flow between the key ingredients of composite materials (i.e., steel bar and its surrounding concrete elements). The smart steel model suggested can incorporate smooth transition during reversal loading, tensile rupture, early buckling after reversal from excessive tensile loading, and even compressive buckling. Especially, the buckling length is made to evolve according to the damage states of the surrounding elements of each bar, while all other dominant models leave the length unchanged. What lies behind all the aforementioned novel attempts is, of course, the problem-optimized parallel platform. In fact, the parallel computing in our field has been restricted to monotonic shock or blast loading with explicit algorithm which is characteristically feasible to be parallelized. In the present study, efficient parallelization strategies for the highly demanding implicit nonlinear finite element analysis (FEA) program for real-scale reinforced concrete (RC) structures under cyclic loading are proposed. Quantitative comparison of state-of-the-art parallel strategies, in terms of factorization, had been carried out, leading to the problem-optimized solver, which is successfully embracing the penalty method and banded nature. Particularly, the penalty method employed imparts considerable smoothness to the global response, which yields a practical superiority of the parallel triangular system solver over other advanced solvers such as parallel preconditioned conjugate gradient method. Other salient issues on parallelization are also addressed. The parallel platform established offers unprecedented access to simulations of real-scale structures, giving new understanding about the physics-based mechanisms adopted and probabilistic randomness at the entire system level. Particularly, the platform enables bold simulations of real-scale RC structures exposed to cyclic loading–H-shaped wall system and 4-story T-shaped wall system. The simulations show the desired capability of accurate prediction of global force-displacement responses, postpeak softening behavior, and compressive buckling of longitudinal steel bars. It is fascinating to see that intrinsic randomness of the 3d interlocking model appears to cause “localized” damage of the real-scale structures, which is consistent with reported observations in different fields such as granular media. Equipped with accuracy, stability and scalability as demonstrated so far, the parallel platform is believed to serve as a fertile ground for the introducing of further physical mechanisms into various research fields as well as the earthquake engineering community. In the near future, it can be further expanded to run in concert with reliable FEA programs such as FRAME3d or OPENSEES. Following the central notion of “multiscale” analysis technique, actual infrastructures exposed to extreme natural hazard can be successfully tackled by this next generation analysis tool–the harmonious union of the parallel platform and a general FEA program. At the same time, any type of experiments can be easily conducted by this “virtual laboratory.”

This paper presents a numerical study of Mallorca Cathedral carried out by means of a FE approach devised for the study of this complex historical construction. Previous studies, including inspection and historical research, have shown that part of the existing damage and deformation might have been experienced during the construction process itself, while later historical processes causing long-term deformation, may also have contributed significantly to the final deformation. In order to analyse the possible influence of the construction process and long term deformation on the deformation of the structure, a numerical tool has been developed to carry out sequential-evolutionary analyses, involving the superposition of consecutive construction stages. A constitutive model has been implemented accounting for both viscoelasticity and mechanical damage by means of an enhanced continuum damage model. This tool has been used to carry out the sequential FE analysis of a typical bay structure of the main nave of the building. The proposed numerical tool has been also used to assess the seismic performance of the typical bay, in the transverse direction, through a nonlinear static analysis. The proposed numerical strategy seems effective to describe deformation and damage and could be applied to other similar historical masonry constructions.

cited By 57; International audience; This study is intended to characterize the evolution in triaxial behavior of a standard concrete subjected to confining pressures varying from 0 to 600 MPa. Hydrostatic and triaxial tests, with several unloading-reloading cycles, are carried out on concrete samples using a high-capacity triaxial press. These tests serve to identify the evolution of the elastic unloading characteristics of concrete, depending on both confining pressure and axial strain. A number of optical observations are also provided to allow visualizing the evolution in concrete damage mode in the middle of the sample. Experimental results indicate a sizable change in concrete behavior with confining pressure. At low pressure values, Young's modulus decreases and Poisson's ratio rises sharply with axial strain. The concrete exhibits brittle behavior with failure caused by a localized damage mechanism. In contrast, at high confining pressures, the concrete becomes a ductile material, and the evolution in its unloading characteristics is negligible. Failure is thus associated with diffuse material damage. The concrete behaves like a granular material controlled by plasticity, meaning that the damage phenomenon observed at low confinement is completely inhibited. © 2009 RILEM.

cited By 26; This study focuses on identifying concrete behavior under severe loading (near field detonation or ballistic impacts). In order to reproduce high stress levels with well-controlled loading paths, static tests are carried out on concrete samples by mean of a very high-capacity triaxial press. Experimental results indicate a sizeable change in concrete behavior with confining pressure. At low pressure values, the concrete exhibits brittle behavior with failure caused by a localized damage mechanism. In contrast, at high confining pressures, the concrete becomes a ductile material, and failure is associated with diffuse material damage. These tests also show an evolution of the elastic characteristics of concrete. A numerical modeling of these previous experiments is performed at a mesoscopic scale. It provides a reproduction of the main characteristics of concrete behavior under high confinement, both qualitatively and quantitatively. © 2010 Taylor & Francis Group, LLC.

WITHIN THE FRAMEWORK OF FEASABILITY STUDIES OF UNDERGROUND REPOSITORIES FOR RADIOACTIVE WASTE, THE STUDY OF PERMEABILITY EVOLUTION WITH DAMAGE OF THE HOST LAYER IS CRUCIAL. THE GOALS OF THIS WORK WERE : (i) TO CHARACTERIZE EXPERIMENTALLY THE DAMAGE OF TWO CLAYEY ROCKS (BEAUCAIRE MARL AND EAST SHALE) WITH X-RAY MICRO TOMOGRAPHY, (ii) TO DEVELOPP A HIGH PRESSURE TRIAXIAL SET-UP ADAPTED TO PERMEABILITY MEASUREMENT ON VERY LOW PERMEABILITY ROCKS.A NUMBER OF ORIGINAL TRIAXIAL DEVICES HAVE BEEN REALISED TO CHARACTERIZE DAMAGE OF CLAYEY ROCKS, UNDER DEVIATORIC LOADING, WITH X-RAY MICRO TOMOGRAPHY ON A SYNCHROTRON BEAMLINE AT THE ESRF (GRENOBLE). LOCALIZED DAMAGE AND ITS EVOLUTION HAVE BEEN CHARACTERIZED AT A FINE SCALE (OF ORDER OF TEN MICRONS). DIGITAL IMAGE CORRELATION TECHNIQUES, EXTENDED TO 3D IMAGES, HAVE BEEN USED TO MEASURE INCREMENTAL STRAIN FIELDS FROM TOMOGRAPHIC IMAGES. WE DEMONSTRATED THAT THESE TECHNIQUES ARE VERY USEFUL IN THE STUDY OF THE LOCALIZED DAMAGE OF GEOMATERIALS AND ESPECIALLY FOR THE INITIATION.A HIGH PRESSURE TRIAXIAL DEVICE HAS BEEN REALISED TO MEASURE PERMEABILITY EVOLUTION OF THE EAST SHALE AS A FUNCTION OF APLLIED STRESS (ISOTROPIC AND DEVIATORIC). THE PARTICULARITY OF THIS SET-UP IS THE SMALL SIZE OF THE TEST SPECIMEN (CYLINDER OF 10MM IN DIAMETER AND 20MM IN HEIGHT) WHICH ALLOWS SIGNIFICANT REDUCTION OF TEST DURATION.; DANS LE CADRE DES ETUDES DE FAISABILITE DU STOCKAGE DES DECHETS RADIOACTIFS EN COUCHES GEOLOGIQUES PROFONDES, L'ETUDE DE L'EVOLUTION DE LA PERMEABILITE DE LA COUCHE HOTE EN FONCTION DE L'ENDOMMAGEMENT EST PRIMORDIALE. CE TRAVAIL A CONSISTE D'UNE PART, A ETUDIE EXPERIMENTALEMENT L'ENDOMMAGEMENT DE DEUX ROCHES ARGILEUSES (MARNE DE BEAUCAIRE ET ARGILITE DE L'EST) A L'AIDE DES TECHNIQUES DE MICRO TOMOGRAPHIE A RAYONS X, ET D'AUTRE PART, A DEVELOPPER UNE INSTALLATION TRIXIALE HAUTE PRESSION ADAPTEE AUX MESURES DE PERMEABILITE SUR DES ROCHES DE TRES FAIBLES PERMEABILITES.DES INSTALLATIONS TRIAXIALES ORIGINALES ONT ETE REALISEES AFIN DE CARACTERISER SOUS CHARGEMENT DEVIATOIRE L'ENDOMMAGEMENT DES ROCHES ARGILEUSES A L'AIDE DE LA MICRO TOMOGRAPHIE A RAYONS X SUR UNE LIGNE SYNCHROTRON A L'ESRF (GRENOBLE). L'ENDOMMAGEMENT LOCALISE ET SON EVOLUTION EN COURS D'ESSAI, ONT AINSI PU ETRE CARACTERISES A UNE ECHELLE FINE (DE L'ORDRE DE LA DIZAINE DE MICRONS). LES TECHNIQUES DE CORRELATION D'IMAGES NUMERIQUES ETENDUES AUX IMAGES TRIDIMENSIONNELLLES ONT ETE UTILISEES POUR MESURER LES CHAMPS INCREMENTAUX DE DEFORMATION ET ONT MONTRE LEUR INTERET DANS L'ETUDE DE L'ENDOMMAGEMENT LOCALISE DANS LES GEOMATERIAUX ET NOTAMMENT DE SON EVOLUTION.ENFIN, UNE INSTALLATION TRIAXIALE HAUTE PRESSION A ETE REALISEE POUR MESURER L'EVOLUTION DE LA PERMEABILITE DE L'ARGILITE DE L'EST EN FONCTION DU NIVEAU DE CONTRAINTES (ISOTROPE ET DEVIATOIRE) APPLIQUEES. SA PARTICULARITE EST LA PETITE TAILLE DES ECHANTILLONS (CYLINDRES DE 10MM DE DIAMETRE ET 20MM DE HAUTEUR) AFIN DE REDUIRE LES TEMPS D'ESSAIS.

The possibility to detect the structural damage affecting a narrow zone of a doubly hinged plane circular arch by means of a few measured natural frequencies is considered. Such localised damage induces a discontinuity in the bending stiffness of the arch, modelled as a torsion spring joining two adjacent sections and characterised by the location and the stiffness of the spring. The direct problem in the damaged and undamaged case is examined; the inverse problem is then considered. Two different procedures to identify the damage parameters are introduced: the first is based on the search of an intersection point of curves obtained by the modal equation; the second is based on the comparison between the analytical and experimental values of the variation of frequencies passing from the undamaged to the damaged state. In conclusion, the possibility of identifying the damage parameters by means of pseudo-experimental data is examined.

The paper deals with the prediction of global and localized damage and the future reliability estimation of partly damaged reinforced concrete (RC) structures under seismic excitation. Initially, a global maximum softening damage indicator is considered based on the variation of the eigenfrequency of the first mode due to the stiffness and strength deterioration of the structure. The hysteresis of the first mode is modelled by a Clough and Johnston hysteretic oscillator with a degrading elastic fraction of the restoring force. The linear parameters of the model are assumed to be known, measured before the arrival of the first earthquake from non-destructive vibration tests or via structural analysis. The previous excitation and displacement response time series is employed for the identification of the instantaneous softening using an ARMA model. The hysteresis parameters are updated after each earthquake. The proposed model is next generalized for the MDOF system. Using the adapted models for the structure and the global damage state, the global damage in a future earthquake can then be estimated when a suitable earthquake model is applied. The performance of the model is illustrated on RC frames which were tested by Sözen and his associates.

From the theoretical point of view, systems composed by masonry arches or vaults would require, during construction, the simultaneous activation of all structural elements in order to reach the optimum balance of thrusts. This is not obviously the case of complex ancient masonry constructions, whose long and gradual building process may have contributed to their deformed condition and even to damage. In this paper, the possible influence of the construction process as well as that of later long-term deformation on the final condition of the building is investigated in the case of a complex and large historical structure, namely Mallorca Cathedral. A FE code has been specifically developed for the present study. The code is able to account for construction processes through sequential-evolutionary analyses, with the description of masonry mechanical damage and long-term deformation. The representative bay of the cathedral is analyzed taking into account different construction phases, as emerged from historical research. The response of such substructure to transverse earthquake equivalent forces is then investigated. In this case, the damage model is improved with a local crack-tracking algorithm. This numerical strategy models the tensile damage as distinct cracks, leading to a better prediction of realistic collapsing mechanisms.

An study of the damage induced in dental materials and model multilayer systems by masticatory contact stresses, simulated by hertzian indentation test, have been performed. In particular, the nature of induced damage has been identified, and quantified from stressstrain curves and critical loads for yielding or crack initiation. For multilayer systems, test have been numerically simulated using finite element techniques (FEM). FEM simulations complement indentation test, allowing to justify the observed fracture modes from calculated stress fields. Practical implications can be derived from our results, relevant to the design of multilayer structures tolerant to contact damage. En este trabajo se ha realizado un estudio del daño introducido en materiales dentales y en sistemas multicapa prototipo cuando soportan las tensiones de contacto que se generan en la boca del paciente, simuladas mediante ensayos de indentación Hertz. En particular, se ha determinado la naturaleza del daño introducido, y se ha procedido a su cuantificación a partir de la obtención de curvas tensión-deformación y cargas críticas para el inicio de la deformación plástica y/o fractura. Además, en el caso del sistema multicapa, los ensayos se han simulado numéricamente mediante el método de elementos finitos (FEM). La simulación FEM es el complemento perfecto a los ensayos Hertz, ya que permite cuantificar el campo de tensiones y por consiguiente justificar los diferentes modos de fractura observados. A partir de los resultados de este estudio se deducen implicaciones de interés práctico para el diseño de materiales multicapa resistentes al daño por contacto.