Les systèmes mécaniques soumis et excités par vibrations sont les candidats naturels à être modélisé par des systèmes linéaires invariables dans le temps. La localisation de dommages utilisant les paramètres modaux évalués à partir de données de vibration ambiantes mesurées grâce à de capteurs est possible notamment par l'approche nommée Stochastic Dynamic Damage Location Vector (SDDLV), où l'emplacement des dommages est empiriquement relié aux positions où le stress est proche de zéro. La première contribution dans cette thèse montre comment l'incertitude sur les paramètres du système d'état peut être utilisée pour déduire des bornes d'incertitude sur les résidus de localisation de dommages, ceci afin de décider de l'emplacement de dommage utilisant un test d'hypothèse. Dans la deuxième contribution, la méthode de localisation de dommages est étendue pour être robuste au choix des variables de Laplace utilisées dans cette méthode. Ceci est obtenue en agrégeant statistiquement les résultats à valeurs différentes dans le domaine de Laplace. L'influence Line Damage Location (ILDL) est une approche complémentaire du SDDLV où l'angle entre les sous-espaces principaux est calculé et les dommages sont empiriquement localisés aux points près du zéro. L'approche développée pour la SDDLV est étendue à cette nouvelle approche, l'ILDL. Les méthodes proposées sont validées et appliquées avec succès pour la localisation de dommages dans des structures civiles. / Mechanical systems under vibration excitation are prime candidate for being modeled by linear time invariant systems. Damage localization using both finite element information and modal parameters estimated from ambient vibration data collected from sensors is possible by the Stochastic Dynamic Damage Location Vector (SDDLV) approach, where the damage location is empirically related to positions where the stress is close to zero. The first contribution in this thesis shows how the uncertainty in the estimates of the state space system can be used to derive uncertainty bounds on the damage localization residuals to decide about the damage location with a hypothesis test using one chosen Laplace value. In the second contribution, the damage localization method is extended with a statistical framework and robustness of the localization information is achieved by aggregating results at different values in the Laplace domain. The Influence Line Damage Location (ILDL) is a complementary approach of the SDDLV where the subspace angle is computed and damage is empirically located at points near zero. The last contribution describes how robustness of the localization information is achieved by aggregating results at different values in the Laplace domain based on the previous two contributions. The proposed methods are validated and successfully applied to damage localization of several applications in civil structures.

Mechanical systems under vibration excitation are prime candidate for being modeled by linear time invariant systems. Damage localization using both finite element information and modal parameters estimated from ambient vibration data collected from sensors is possible by the Stochastic Dynamic Damage Location Vector (SDDLV) approach, where the damage location is empirically related to positions where the stress is close to zero. The first contribution in this thesis shows how the uncertainty in the estimates of the state space system can be used to derive uncertainty bounds on the damage localization residuals to decide about the damage location with a hypothesis test using one chosen Laplace value. In the second contribution, the damage localization method is extended with a statistical framework and robustness of the localization information is achieved by aggregating results at different values in the Laplace domain. The Influence Line Damage Location (ILDL) is a complementary approach of the SDDLV where the subspace angle is computed and damage is empirically located at points near zero. The last contribution describes how robustness of the localization information is achieved by aggregating results at different values in the Laplace domain based on the previous two contributions. The proposed methods are validated and successfully applied to damage localization of several applications in civil structures.

abstract: There is a concerted effort in developing robust systems health monitoring/management (SHM) technology as a means to reduce the life cycle costs, improve availability, extend life and minimize downtime of various platforms including aerospace and civil infrastructure. The implementation of a robust SHM system requires a collaborative effort in a variety of areas such as sensor development, damage detection and localization, physics based models, and prognosis models for residual useful life (RUL) estimation. Damage localization and prediction is further complicated by geometric, material, loading, and environmental variabilities. Therefore, it is essential to develop robust SHM methodologies by taking into account such uncertainties. In this research, damage localization and RUL estimation of two different physical systems are addressed: (i) fatigue crack propagation in metallic materials under complex multiaxial loading and (ii) temporal scour prediction near bridge piers. With little modifications, the methodologies developed can be applied to other systems. Current practice in fatigue life prediction is based on either physics based modeling or data-driven methods, and is limited to predicting RUL for simple geometries under uniaxial loading conditions. In this research, crack initiation and propagation behavior under uniaxial and complex biaxial fatigue loading is addressed. The crack propagation behavior is studied by performing extensive material characterization and fatigue testing under in-plane biaxial loading, both in-phase and out-of-phase, with different biaxiality ratios. A hybrid prognosis model, which combines machine learning with physics based modeling, is developed to account for the uncertainties in crack propagation and fatigue life prediction due to variabilities in material microstructural characteristics, crack localization information and environmental changes. The methodology iteratively combines localization information with hybrid prognosis models using sequential Bayesian techniques. The results show significant improvements in the localization and prediction accuracy under varying temperature. For civil infrastructure, especially bridges, pier scour is a major failure mechanism. Currently available techniques are developed from a design perspective and provide highly conservative scour estimates. In this research, a fully probabilistic scour prediction methodology is developed using machine learning to accurately predict scour in real-time under varying flow conditions. / Dissertation/Thesis / Doctoral Dissertation Mechanical Engineering 2016

Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites, stabilized weapon systems and radars may require nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, as the structure will be excited from only a few coordinates, the frequency response function matrices will not be complete. In order to parametrically identify more than one type of nonlinearity which may co-exist at the same location with the above mentioned limitations, a method is proposed where restoring force surface plots are used which are evaluated by describing function inversion. Then, by reformulating this method, a second method is proposed which can directly evaluate the total describing function of more than one type of nonlinearity which may co-exist at the same location without using any linear frequency response function matrix. It is also aimed in this study to use the nonlinearity localization formulations for damage localization purposes. The validation of the methods developed in this study is demonstrated with case studies based on simulated experiments, as well as real experiments with nonlinear structures and it is concluded that the methods are very promising to be used in engineering structures.

Damage and condition identi&amp / #64257 / cation of existing structures using non-destructive tests is a common challenge that has been worked on for a long time. In this study, two di&amp / #64256 / erent methods were developed to &amp / #64257 / nd existing force on cables as well as determine bending characteristics (EI coe&amp / #64259 / cients) of beam like structures (such as bridges). Comparing forces in symmetrically placed cables or against values obtained from design drawings would indicate structural imbalance as well as &amp / #64257 / nding EI coe&amp / #64259 / cients at a number of segments on a bridge girder might indicate weak regions that might possibly have undergone structural damage, having weak connections, lost composite action etc. With the help of the proposed algorithm, the sti&amp / #64256 / ness parameters of bridges can be assessed and the location of any damage that is in the magnitude which can a&amp / #64256 / ect displacement behavior of system can be located. The developed methods are demonstrated using the values analytically obtained from the created models and the e&amp / #64256 / ectiveness of the algorithm is criticized. Furthermore, several damage scenarios on a scaled lab beam was used to test the application using real experimental data / including tests on undamaged beam (for identi&amp / #64257 / cation) and tests on the damaged beam. Additional experiments were conducted on a cable stretched in the laboratory instrumented using a load cell to measure instantaneous axial load on the cable and compare these values against the values obtained from the developed tension measurement device. The results are compared and conclusions are derived.

La localisation de dégâts basée sur les mesures de vibrations est devenue un axe de recherche important pour la surveillance de la santé structurale (SHM). En particulier, la Stochastic Dynamic Damage Locating Vector (SDDLV) est une méthode de localisation des dégâts basée sur le couplage entre un modèle aux éléments finis (FE) de la structure et des paramètres modaux estimés à partir des mesures dynamiques en excitation ambiante dans les états structuraux sain et endommagé, interrogeant les changements dans la matrice de transfert. Dans la première contribution, la méthode SDDLV est étendue avec une approche statistique conjointe utilisant plusieurs ensembles de modes, surmontant la limitation théorique sur le nombre minimal de paramètres. Un autre problème traité est la performance de la méthode en fonction du choix de la variable de Laplace où la fonction de transfert est évaluée. Une attention particulière est accordée à ce choix et à son optimisation. Dans la deuxième contribution, l'approche Influence Line Damage Location (ILDL), complémentaire à l’approche SDDLV est étendue avec un cadre statistique. Dans la dernière contribution, une approche de sensibilité pour les petits dommages est développée en fonction de la différence des matrices de transfert, permettant la localisation des dommages par des tests statistiques dans un cadre gaussien, et en plus la quantification des dommages dans une deuxième étape. Enfin, les méthodes proposées sont validées sur des simulations numériques et leurs performances sont testées dans de nombreuses études de cas sur des expériences de laboratoire. / Vibration-based damage localization has become an important issue for Structural Health Monitoring (SHM). Particularly, the Stochastic Dynamic Damage Locating Vector (SDDLV) method is an output-only damage localization method based on both a Finite Element (FE) model of the structure and modal parameters estimated from output-only measurements in the reference and damaged states of the system, interrogating changes in the transfer matrix. Firstly, the SDDLV method has been extended with a joint statistical approach for multiple mode sets, overcoming the theoretical limitation on the number of modes in previous works. Another problem is that the performance of the method can change considerably depending on the Laplace variable where the transfer function is evaluated. Particular attention is given to this choice and how to optimize it. Secondly, the Influence Line Damage Location (ILDL) approach which is complementary to the SDDLV approach has been extended with a statistical framework. Thirdly, a sensitivity approach for small damages has been developed based on the transfer matrix difference, allowing damage localization through statistical tests in a Gaussian framework, and in addition the quantification of the damage in a second step. Finally, the proposed methods are validated on numerical simulations and their performances are tested extensively in numerous case studies on lab experiments.

Structural Health Monitoring (SHM) is a non-destructive evaluation tool that assesses the functionality of structural systems that are used in the civil, mechanical and aerospace engineering practices. A much desirable objective of a SHM system is to provide a continuous monitoring service at a minimal cost with ability to identify problems even in inaccessible structural components. In this dissertation, several such approaches that utilize the measured dynamic response of structural systems are presented to detect, locate, and quantify the damages that are likely to occur in structures. In this study, the structural damage is identified as a reduction in the stiffness characteristics of the structural elements. The primary focus of this study is on the utilization of measured dynamic strains for damage identification in the framed structures which are composed of interconnected beam elements. Although linear accelerations, being more convenient to measure, are commonly used in most SHM practices, herein the strains being more sensitive to elemental damage are considered. Two different approaches are investigated and proposed to identify the structural element stiffness properties. Both approaches are mode-based, requiring first the identification of system modes from the measured strain responses followed by the identification of the element stiffness coefficients. The first approach utilizes the Eigen equation of the finite element model of the structure, while the second approach utilizes the changes caused by the damage in the structural curvature flexibilities. To reduce size of the system which is primarily determined by the number of sensors deployed for the dynamic data collection, measurement sensitivity-based sensor selection criterion is observed to be effective and thus used. The mean square values of the measurements with respect to the stiffness coefficients of the structural elements are used as the effective measures of the measurement sensitivities at different sensor locations. Numerical simulations are used to evaluate the proposed identification approaches as well as to validate the sensitivity-based optimal sensor deployment approach. / Ph. D. / All modern societies depend heavily on civil infrastructure systems such as transportation systems, power generation and transmission systems, and data communication systems for their day-to-day activities and survival. It has become extremely important that these systems are constantly watched and maintained to ensure their functionality. All these infrastructure systems utilize structural systems of different forms such as buildings, bridges, airplanes, data communication towers, etc. that carry the service and environmental loads that are imposed on them. These structural systems deteriorate over time because of natural material degradation. They can also get damaged due to excessive load demands and unknown construction deficiencies. It is necessary that condition of these structural systems is known at all times to maintain their functionality and to avoid sudden breakdowns and associated ensuing problems. This condition assessment of structural systems, now commonly known as structural health monitoring, is commonly done by visual onsite inspections manually performed at pre-decided time intervals such as on monthly and yearly basis. The length of this inspection time interval usually depends on the relative importance of the structure towards the functionality of the larger infrastructure system. This manual inspection can be highly time and resource consuming, and often ineffective in catching structural defects that are inaccessible and those that occur in between the scheduled inspection times and dates. However, the development of new sensors, new instrumentation techniques, and large data transfer and processing methods now make it possible to do this structural health monitoring on a continuous basis. The primary objective of this study is to utilize the measured dynamic or time varying strains on structural components such as beams, columns and other structural members to detect the location and level of a damage in one or more structural elements before they become serious. This detection can be done on a continuous basis by analyzing the available strain response data. This approach is expected to be especially helpful in alerting the owner of a structure by identifying the iv occurrence of a damage, if any, immediately after an unanticipated occurrence of a natural event such as a strong earthquake or a damaging wind storm.

The past 30 years have witnessed major developments in vibration based damage detection and identification, also collectively referred to as damage diagnosis. Moreover, the past 10 years have seen a rapid increase in the amount of research related to Structural Health Monitoring (SHM) as quantified by the significant escalation in papers published on this subject. Thus, the increased interest in this engineering field and its associated potential constitute the main motive for this thesis. The goal of the thesis is the development and introduction of novel advanced functional and sequential statistical time series methods for vibration based damage diagnosis and SHM. After the introduction of the first chapter, Chapter II provides an experimental assessment and comparison of vibration based statistical time series methods for Structural Health Monitoring (SHM) via their application on a lightweight aluminum truss structure and a laboratory scale aircraft skeleton structure. A concise overview of the main non-parametric and parametric methods is presented, including response-only and excitation-response schemes. Damage detection and identification are based on univariate (scalar) versions of the methods, while both scalar (univariate) and vector (multivariate) schemes are considered. The methods' effectiveness for both damage detection and identification is assessed via various test cases corresponding to different damage scenarios, multiple experiments and various sensor locations on the considered structures. The results of the chapter confirm the high potential and effectiveness of vibration based statistical time series methods for SHM. Chapter III investigates the identification of stochastic systems under multiple operating conditions via Vector-dependent Functionally Pooled (VFP) models. In many applications a system operates under a variety of operating conditions (for instance operating temperature, humidity, damage location, damage magnitude and so on) which affect its dynamics, with each condition kept constant for a single commission cycle. Typical examples include mechanical structures operating under different environmental conditions, aircrafts under different flight conditions (altitude, velocity etc.), structures under different structural health states (various damage locations and magnitudes). In this way, damage location and magnitude may be considered as parameters that affect the operating conditions and as a result the structural dynamics. This chapter's work is based on the novel Functional Pooling (FP) framework, which has been recently introduced by the Stochastic Mechanical Systems \& Automation (SMSA) group of the Mechanical Engineering and Aeronautics Department of University of Patras. The main characteristic of Functionally Pooled (FP) models is that their model parameters and innovations sequence depend functionally on the operating parameters, and are projected on appropriate functional subspaces spanned by mutually independent basis functions. Thus, the fourth chapter of the thesis addresses the problem of identifying a globally valid and parsimonious stochastic system model based on input-output data records obtained under a sample of operating conditions characterized by more than one parameters. Hence, models that include a vector characterization of the operating condition are postulated. The problem is tackled within the novel FP framework that postulates proper global discrete-time linear time series models of the ARX and ARMAX types, data pooling techniques, and statistical parameter estimation. Corresponding Vector-dependent Functionally Pooled (VFP) ARX and ARMAX models are postulated, and proper estimators of the Least Squares (LS), Maximum Likelihood (ML), and Prediction Error (PE) types are developed. Model structure estimation is achieved via customary criteria (Bayesian Information Criterion) and a novel Genetic Algorithm (GA) based procedure. The strong consistency of the VFP-ARX least squares and maximum likelihood estimators is established, while the effectiveness of the complete estimation and identification method is demonstrated via two Monte Carlo studies. Based on the postulated VFP parametrization a vibration based statistical time series method that is capable of effective damage detection, precise localization, and magnitude estimation within a unified stochastic framework is introduced in Chapter IV. The method constitutes an important generalization of the recently introduced Functional Model Based Method (FMBM) in that it allows, for the first time in the statistical time series methods context, for complete and precise damage localization on continuous structural topologies. More precisely, the proposed method can accurately localize damage anywhere on properly defined continuous topologies on the structure, instead of pre-defined specific locations. Estimator uncertainties are taken into account, and uncertainty ellipsoids are provided for the damage location and magnitude. To achieve its goal, the method is based on the extended class of Vector-dependent Functionally Pooled (VFP) models, which are characterized by parameters that depend on both damage magnitude and location, as well as on proper statistical estimation and decision making schemes. The method is validated and its effectiveness is experimentally assessed via its application to damage detection, precise localization, and magnitude estimation on a prototype GARTEUR-type laboratory scale aircraft skeleton structure. The damage scenarios considered consist of varying size small masses attached to various continuous topologies on the structure. The method is shown to achieve effective damage detection, precise localization, and magnitude estimation based on even a single pair of measured excitation-response signals. Chapter V presents the introduction and experimental assessment of a sequential statistical time series method for vibration based SHM capable of achieving effective, robust and early damage detection, identification and quantification under uncertainties. The method is based on a combination of binary and multihypothesis versions of the statistically optimal Sequential Probability Ratio Test (SPRT), which employs the residual sequences obtained through a stochastic time series model of the healthy structure. In this work the full list of properties and capabilities of the SPRT are for the first time presented and explored in the context of vibration based damage detection, identification and quantification. The method is shown to achieve effective and robust damage detection, identification and quantification based on predetermined statistical hypothesis sampling plans, which are both analytically and experimentally compared and assessed. The method's performance is determined a priori via the use of the analytical expressions of the Operating Characteristic (OC) and Average Sample Number (ASN) functions in combination with baseline data records, while it requires on average a minimum number of samples in order to reach a decision compared to most powerful Fixed Sample Size (FSS) tests. The effectiveness of the proposed method is validated and experimentally assessed via its application on a lightweight aluminum truss structure, while the obtained results for three distinct vibration measurement positions prove the method's ability to operate based even on a single pair of measured excitation-response signals. Finally, Chapter VI contains the concluding remarks and future perspectives of the thesis. / Κατά τη διάρκεια των τελευταίων 30 ετών έχει σημειωθεί σημαντική ανάπτυξη στο πεδίο της ανίχνευσης και αναγνώρισης βλαβών, το οποίο αναφέρεται συνολικά και σαν διάγνωση βλαβών. Επίσης, κατά την τελευταία δεκαετία έχει σημειωθεί σημαντική πρόοδος στον τομέα της παρακολούθησης της υγείας (δομικής ακεραιότητας) κατασκευών. Στόχος αυτής της διατριβής είναι η ανάπτυξη εξελιγμένων συναρτησιακών και επαναληπτικών μεθόδων χρονοσειρών για τη διάγνωση βλαβών και την παρακολούθηση της υγείας κατασκευών υπό ταλάντωση. Αρχικά γίνεται η πειραματική αποτίμηση και κριτική σύγκριση των σημαντικότερων στατιστικών μεθόδων χρονοσειρών επί τη βάσει της εφαρμογής τους σε πρότυπες εργαστηριακές κατασκευές. Εφαρμόζονται μη-παραμετρικές και παραμετρικές μέθοδοι που βασίζονται σε ταλαντωτικά σήματα διέγερσης και απόκρισης των κατασκευών. Στη συνέχεια αναπτύσσονται στοχαστικά συναρτησιακά μοντέλα για την στοχαστική αναγνώριση κατασκευών υπό πολλαπλές συνθήκες λειτουργίας. Τα μοντέλα αυτά χρησιμοποιούνται για την αναπαράσταση κατασκευών σε διάφορες καταστάσεις βλάβης (θέση και μέγεθος βλάβης), ώστε να είναι δυνατή η συνολική μοντελοποίσή τους για όλες τις συνθήκες λειτουργίας. Τα μοντέλα αυτά αποτελούν τη βάση στην οποία αναπτύσσεται μια συναρτησιακή μέθοδος η οποία είναι ικανή να αντιμετωπίσει συνολικά και ενιαία το πρόβλημα της ανίχνευσης, εντοπισμού και εκτίμησης βλαβών σε κατασκευές. Η πειραματική αποτίμηση της μεθόδου γίνεται με πολλαπλά πειράματα σε εργαστηριακό σκελετό αεροσκάφους. Στο τελευταίο κεφάλαιο της διατριβής προτείνεται μια καινοτόμος στατιστική επαναληπτική μέθοδο για την παρακολούθηση της υγείας κατασκευών. Η μέθοδος κρίνεται αποτελεσματική υπό καθεστώς λειτουργικών αβεβαιοτήτων, καθώς χρησιμοποιεί επαναληπτικά και στατιστικά τεστ πολλαπλών υποθέσεων. Η αποτίμηση της μεθόδου γίνεται με πολλαπλά εργαστηριακά πειράματα, ενώ η μέθοδος κρίνεται ικανή να λειτουργήσει με τη χρήση ενός ζεύγους ταλαντωτικών σημάτων διέγερσης-απόκρισης.

This thesis focuses on the development of a new method for the continuous<p>monitoring of civil engineering structures in order to locate small damages automatically. A<p>review of the very wide literature on Structural Health Monitoring (SHM) points first out that<p>the methods can be grouped in four categories based on their need or not of a numerical model,<p>as well as their need or not of information of the damaged structure to be applied. This state<p>of the art of the SHM methods highlights the requirement to reach each levels of SHM, which<p>is in particular for the localization of small damages in civil engineering structures the needs<p>for a non-model based output-only damage sensitive feature extraction technique. The origin of<p>the local sensitivity of strains to damages is also analyzed, which justifies their use for damage<p>localization.<p>A new method based on the modal filtering technique which consists in combining linearly<p>the sensor responses in a specific way to mimic a single degree of freedom system and which<p>was previously developed for damage detection is proposed. A very large network of dynamic<p>strain sensors is deployed on the structure and split into several independent local sensor networks.<p>Low computational cost and fast signal processing techniques are coupled to statistical<p>control charts for robust and fully automated damage localization.<p>The efficiency of the method is demonstrated using time-domain simulated data on a simply<p>supported beam and a three-dimensional bridge structure. The method is able to detect and<p>locate very small damages even in the presence of noise on the measurements and variability<p>of the baseline structure if strain sensors are used. The difficulty to locate damages from acceleration<p>sensors is also clearly illustrated. The most common classical methods for damage<p>localization are applied on the simply supported beam and the results show that the modal filtering<p>technique presents much better performances for an accurate localization of small damages<p>and is easier to automate.<p>An improvement of the modal filters method referred to as adaptive modal filters is next<p>proposed in order to enhance the ability to localize small damages, as well as to follow their<p>evolution through modal filters updating. Based on this study, a new damage sensitive feature<p>is proposed and is compared with other damage sensitive features to detect the damages with<p>modal filters to demonstrate its interest. These expectations are verified numerically with the<p>three-dimensional bridge structure, and the results show that the adaptation of the modal filters<p>increases the sensitivity of local filters to damages.<p>Experimental tests have been led first to check the feasibility of modal filters to detect damages<p>when they are used with accelerometers. Two case studies are considered. The first work<p>investigates the experimental damage detection of a small aircraft wing equipped with a network<p>of 15 accelerometers, one force transducer and excited with an electro-dynamic shaker. A<p>damage is introduced by replacing inspection panels with damaged panels. A modified version<p>of the modal filtering technique is applied and compared with the damage detection based principal<p>component analysis of FRFs as well as of transmissibilities. The three approaches succeed<p>in the damage detection but we illustrate the advantage of using the modal filtering algorithm as<p>well as of the new damage sensitive feature. The second experimental application aims at detecting<p>both linear and nonlinear damage scenarios using the responses of four accelerometers<p>installed on the three-storey frame structure previously developed and studied at Los Alamos<p>National Labs. In particular, modal filters are shown to be sensitive to both types of damages,<p>but cannot make the distinction between linear and nonlinear damages.<p>Finally, the new method is tested experimentally to locate damages by considering cheap<p>piezoelectric patches (PVDF) for dynamic strain measurements. Again, two case studies are investigated.<p>The first work investigates a small clamped-free steel plate equipped with 8 PVDFs sensors, and excited with a PZT patch. A small damage is introduced at different locations by<p>fixing a stiffener. The modal filters are applied on three local filters in order to locate damage.<p>Univariate control charts allow to locate automatically all the damage positions correctly.<p>The last experimental investigation is devoted to a 3.78m long I-steel beam equipped with 20<p>PVDFs sensors and excited with an electro-dynamic shaker. Again, a small stiffener is added to<p>mimic the effect of a small damage and five local filters are defined to locate the damage. The<p>damage is correctly located for several positions, and the interest of including measurements<p>under different environmental conditions for the baseline as well as overlapping the local filters<p>is illustrated.<p>The very nice results obtained with these first experimental applications of modal filters<p>based on strains show the real interest of this very low computational cost method for outputonly<p>non-model based automated damage localization of real structures. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

In der vorliegenden Arbeit wird die Frage untersucht, ob effektive Eigenschaften von Verbunden auch nach dem Auftreten einer Dehnungslokalisierung aufgrund von entfestigendem Materialverhalten noch durch numerische Homogenisierungsmethoden berechnet werden können. Ihr Nutzen für diesen Anwendungsfall wird in der Literatur kritisch beurteilt. Aus diesem Grund werden hier systematisch alle Teilaufgaben betrachtet, die zu diesem Zweck gelöst werden müssen. Die erste dieser Aufgaben ist die Charakterisierung der einzelnen Verbundbestandteile. Zur Demonstration einer experimentell gestützten Charakterisierung wird ein glasfaserverstärktes Epoxidharz als Beispielmaterial gewählt. Neben der Beschreibung von Faser- und Matrixmaterial wird besonderes Augenmerk auf die Charakterisierung der Grenzschicht zwischen beiden gelegt. Die für die Glasfasern vorliegenden Festigkeitsmessungen entsprechen nicht der Kettenhypothese. Daher werden zahlreiche Verallgemeinerungen der Weibull-Verteilung untersucht, um störende Effekte zu erfassen. Schließlich werden Wahrscheinlichkeitsverteilungen hergeleitet, die Faserbrüche im Bereich der Einspannung einbeziehen. Die Messwerte können von diesen Verteilungen gut wiedergegeben werden. Zusätzlich macht ihre Anwendung das aufwändige Aussortieren und Wiederholen jener Experimente unnötig, bei denen der Faserbruch im Klemmbereich auftritt. Zur Modellierung der Grenzfläche wird ein Kohäsivzonengesetz entwickelt. Die Bestimmung seiner Parameter erfolgt anhand von Daten aus Pullout- und Einzelfaserfragmentierungsversuchen. Aus diesen ermittelte Festigkeiten und Energiefreisetzungsraten weisen eine sehr gute Übereinstimmung zwischen beiden Versuchen auf. Dabei erfolgt die Parameteridentifikation mithilfe von Finite-Elemente-Modellen anstatt der häufig genutzten vereinfachten analytischen Modelle, welche üblicherweise eine schlechtere Übereinstimmung erreichen. Sobald eine Dehnungslokalisierung auftritt, ist neben der Materialmodellierung auch das Homogenisierungsschema zu verallgemeinern. Zu diesem gehören die Generierung repräsentativer Volumenelemente, Randbedingungen (RB) und ein Mittelungsoperator. Anhand des aktuellen Standes der Literatur werden die Randbedingungen als ein signifikanter Schwachpunkt von Homogenisierungsverfahren erkannt. Daher erfolgt die Untersuchung periodischer RB, linearer Verschiebungsrandbedingungen und minimal kinematischer RB sowie zweier adaptiver RB, nämlich Lokalisierungspfad-ausgerichteter RB und generalisiert periodischer RB. Unter der Bezeichnung Tesselationsrandbedingungen wird ein weiterer Typ adaptiver RB vorgeschlagen. Zunächst erfolgt der Beweis, dass alle drei adaptiven RB die Hill-Mandel-Bedingung erfüllen. Des Weiteren wird mittels einer Modifikation der Hough-Transformation ein systematischer Fehler derselben bei der Bestimmung der Richtung von Lokalisierungszonen eliminiert. Schließlich werden die Eigenschaften aller Randbedingungen an verschiedenen Beispielen demonstriert. Dabei zeigt sich, dass nur Tesselationsrandbedingungen sowohl beliebige Richtungen von Lokalisierungszonen erlauben als auch fehlerhafte Lokalisierungen in Eckbereichen ausschließen. Zusammengefasst können in der Literatur geäußerte grundlegende Einschränkungen hinsichtlich der Anwendbarkeit numerischer Homogenisierungsverfahren beim Auftreten von Dehnungslokalisierungen aufgehoben werden. Homogenisierungsmethoden sind somit auch für entfestigendes Materialverhalten anwendbar. / The thesis at hand is concerned with the question if numerical homogenization schemes can be of use in deriving effective material properties of composite materials after the onset of strain localization due to strain softening. In this case, the usefulness of computational homogenization methods has been questioned in the literature. Hence, all the subtasks to be solved in order to provide a successful homogenization scheme are investigated herein. The first of those tasks is the characterization of the constituents, which form the composite. To allow for an experimentally based characterization an exemplary composite has to be chosen, which herein is a glass fiber reinforced epoxy. Hence the constituents to be characterized are the epoxy and the glass fibers. Furthermore, special attention is paid to the characterization of the interface between both materials. In case of the glass fibers, the measured strength values do not comply with the weakest link hypothesis. Numerous generalizations of the Weibull distribution are investigated, to account for interfering effects. Finally, distributions are derived, that incorporate the possibility of failure inside the clamped fiber length. Application of such a distribution may represent the measured data quite well. Additionally, it renders the cumbersome process of sorting out and repeating those tests unnecessary, where the fiber fails inside the clamps. Identifying the interface parameters of the proposed cohesive zone model relies on data from pullout and single fiber fragmentation tests. The agreement of both experiments in terms of interface strength and energy release rate is very good, where the parameters are identified by means of an evaluation based on finite element models. Also, the agreement achieved is much better than the one typically reached by an evaluation based on simplified analytical models. Beside the derivation of parameterized material models as an input, the homogenization scheme itself needs to be generalized after the onset of strain localization. In an assessment of the current state of the literature, prior to the generation of representative volume elements and the averaging operator, the boundary conditions (BC) are identified as a significant issue of such a homogenization scheme. Hence, periodic BC, linear displacement BC and minimal kinematic BC as well as two adaptive BC, namely percolation path aligned BC and generalized periodic BC are investigated. Furthermore, a third type of adaptive BC is proposed, which is called tesselation BC. Firstly, the three adaptive BC are proven to fulfill the Hill-Mandel condition. Secondly, by modifying the Hough transformation an unbiased criterion to determine the direction of the localization zone is given, which is necessary for adaptive BC. Thirdly, the properties of all the BC are demonstrated in several examples. These show that tesselation BC are the only type, that allows for arbitrary directions of localization zones, yet is totally unsusceptible to spurious localization zones in corners of representative volume elements. Altogether, fundamental objections, that have been raised in the literature against the application of homogenization in situations with strain localization, are rebutted in this thesis. Hence, the basic feasibility of homogenization schemes even in case of strain softening material behavior is shown.