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The primary purpose of this work was to evaluate the capability of nanoparticles to transform electromagnetic energy at microwave frequencies into therapeutic heating. Targeted nanoparticles, in conjunction with microwave irradiation, can increase the temperatures of the targeted area over the peripheral region. Therefore, to become clinically viable, microwave absorbing nanoparticles must first be identified, and a system to monitor the treatment must be developed. In this study, ultrasound temperature imaging was used to monitor the temperature of deep lying structures. First, a material-dependent quantity to correlate the temperature induced changes in ultrasound images (i.e. apparent time shifts) to differential temperatures was gathered for a tissue-mimicking phantom, porcine longissimus dorsi muscle, and porcine fat. Then microwave nanoabsorbers were identified using an infrared radiometer. The determined nanoabsorbers were then injected into ex-vivo porcine longissimus dorsi muscle tissue. Ultrasound imaging frames were gathered during microwave treatment of the inoculated tissue. Finally, the ultrasound frames were analyzed using the correlation between temperature and apparent shifts in ultrasound for porcine muscle tissue. The outcome was depth-resolved temperature profiles of the ex-vivo porcine muscle during treatment. The results of this study show that magnetite is a microwave nanoabsorber that increases the targeted temperature of microwave hyperthermia treatments. Overall, there is clinical potential to use microwave nanoabsorbers to increase the efficiency of microwave hyperthermia treatments. / text

A Mecânica do Dano Contínuo é atualmente uma poderosa ferramenta para se modelar o comportamento não-linear de vários materiais decorrente da evolução de um processo de microfissuração. A perda de rigidez causada pelo processo físico tem sido considerada em modelos constitutivos através de variáveis de dano escalar, vetorial ou tensorial. Quando o carregamento é proporcionalmente crescente as deformações residuais podem ser ignoradas e relações constitutivas simples podem ser obtidas, onde os efeitos do dano aparecem por uma penalização direta das propriedades elásticas. Por outro lado, efeitos de dano podem ser acoplados com deformações residuais levando a relações constitutivas mais gerais. Esse trabalho está relacionado a esses tipos de modelos assumindo que o meio ideal apresenta um comportamento elástico linear com danificação ou elastoplástico com danificação. Um dos principais aspectos discutido relaciona-se à formulação variacional, a qual está baseada em conceitos de Análise Convexa e Não-Convexa. Explorando o fato que a evolução do dano tem correspondência com a idealização de regime de encruamento negativo, a teoria de localização de deformação é abordada e um estudo da condição necessária de singularidade ou perda da condição de elipticidade é realizado. Na sequência, uma proposta preliminar para uma análise de pós-singularidade, baseada na Teoria de Bifurcação, é feita no sentido de caracterizar pontos limite ou pontos de bifurcação de solução, em sistemas conservativos. / Continuum Damage Mechanics is nowadays a powerful tool to model the non-linear behaviour of several materials due to evolution of a microcracking process. The lost of rigidity caused by such physical process has been accounted in the constitutive models through a scalar, vectorial or tensorial damage variables. When proportional loading is considered the residuals strains can be ignored and simple constitutive relations can be obtained in which damage effects appear by direct penalization of the elastic properties. On the other hand, damage effects can be coupled with residual strains leading to more general constitutive relations. This work is related to such kind of models assuming that the ideal medium presents a linear elastic-damage or an elastoplastic-damage behaviour. One of the main topics discussed is related to the variational formulation which is based on Convex and Non-Convex Analysis concepts. Exploring the fact that damage evolution has correspondence with a softening idealised regime, the strain localization theory is treated and a study of a necessary condition for singularity or ellipticity tose condition is developed. In the sequence, a introductory poscritical analysis is proposed, based in the bifurcation theory and aiming to detect if the singularity corresponds to a limit or a bifurcation point solution, in conservative systems.

A Mecânica do Dano Contínuo é atualmente uma poderosa ferramenta para se modelar o comportamento não-linear de vários materiais decorrente da evolução de um processo de microfissuração. A perda de rigidez causada pelo processo físico tem sido considerada em modelos constitutivos através de variáveis de dano escalar, vetorial ou tensorial. Quando o carregamento é proporcionalmente crescente as deformações residuais podem ser ignoradas e relações constitutivas simples podem ser obtidas, onde os efeitos do dano aparecem por uma penalização direta das propriedades elásticas. Por outro lado, efeitos de dano podem ser acoplados com deformações residuais levando a relações constitutivas mais gerais. Esse trabalho está relacionado a esses tipos de modelos assumindo que o meio ideal apresenta um comportamento elástico linear com danificação ou elastoplástico com danificação. Um dos principais aspectos discutido relaciona-se à formulação variacional, a qual está baseada em conceitos de Análise Convexa e Não-Convexa. Explorando o fato que a evolução do dano tem correspondência com a idealização de regime de encruamento negativo, a teoria de localização de deformação é abordada e um estudo da condição necessária de singularidade ou perda da condição de elipticidade é realizado. Na sequência, uma proposta preliminar para uma análise de pós-singularidade, baseada na Teoria de Bifurcação, é feita no sentido de caracterizar pontos limite ou pontos de bifurcação de solução, em sistemas conservativos. / Continuum Damage Mechanics is nowadays a powerful tool to model the non-linear behaviour of several materials due to evolution of a microcracking process. The lost of rigidity caused by such physical process has been accounted in the constitutive models through a scalar, vectorial or tensorial damage variables. When proportional loading is considered the residuals strains can be ignored and simple constitutive relations can be obtained in which damage effects appear by direct penalization of the elastic properties. On the other hand, damage effects can be coupled with residual strains leading to more general constitutive relations. This work is related to such kind of models assuming that the ideal medium presents a linear elastic-damage or an elastoplastic-damage behaviour. One of the main topics discussed is related to the variational formulation which is based on Convex and Non-Convex Analysis concepts. Exploring the fact that damage evolution has correspondence with a softening idealised regime, the strain localization theory is treated and a study of a necessary condition for singularity or ellipticity tose condition is developed. In the sequence, a introductory poscritical analysis is proposed, based in the bifurcation theory and aiming to detect if the singularity corresponds to a limit or a bifurcation point solution, in conservative systems.

Phenomenological material models such as Johnson-Cook plasticity are often used in finite element simulations of large deformation processes at different strain rates and temperatures. Since the material constants that appear in such models depend on the material, experimental data, fitting method, as well as the mathematical representation of strain rate and temperature effects, the predicted material behavior is subject to uncertainty. In this dissertation, evidence theory is used for modeling uncertainty in the material constants, which is represented by separate belief structures that are combined into a joint belief structure and propagated using impact loading simulation of structures. Yager’s rule is used for combining evidence obtained from more than one source. Uncertainty is quantified using belief, plausibility, and plausibility-decision functions. An evidence-based design optimization (EBDO) approach is presented where the nondeterministic response functions are expressed using evidential reasoning. The EBDO approach accommodates field material uncertainty in addition to the embedded uncertainty in the material constants. This approach is applied to EBDO of an externally stiffened circular tube under axial impact load with and without consideration of material field uncertainty caused by spatial variation of material uncertainties due to manufacturing effects. Surrogate models are developed for approximation of structural response functions and uncertainty propagation. The EBDO example problem is solved using genetic algorithms. The uncertainty modeling and EBDO results are presented and discussed.

Les matériaux composites à matrice céramique (CMC) sont élaborés à partir de constituants fragiles. Le comportement mécanique et le développement de la fissuration dépendent des propriétés des constituants élémentaires des CMC. La connaissance de l’influence de ces propriétés sur l’évolution de la fissuration et du comportement mécanique fournit une aide au concepteur de matériaux composites.L’objectif de ce travail est de modéliser l’évolution du réseau de fissures au sein du CMC sollicité en traction, à l’échelle du fil et à l’échelle du composite tissé. L’approche proposée est une alternative aux principaux modèles de comportement des CMC.A l’échelle du fil, l’endommagement intervient d’abord sous forme de fissures matricielles accompagnées de décohésions à l’interface fibre/matrice. Les analyses de ces deux mécanismes ont permis d’exprimer leur évolution au sein du fil en traction. Le comportement en traction résultant de l’endommagement et l’ouverture de la fissure matricielle sont aussi exprimés semi-analytiquement.Les comparaisons avec un modèle numérique de zones cohésives et avec les essais expérimentaux montrent une bonne corrélation des résultats.Enfin ces expressions à l’échelle du fil sont utilisées pour modéliser l’endommagement du fil longitudinal au sein du composite tissé en traction. De plus, un outil numérique est développé pour modéliser la fissuration matricielle inter-fil dans le composite tissé. / Ceramic matrix composite materials (CMC) are elaborated from fragile constituents. Their mechanical behaviour and crack growing depend on the properties of the CMC elementary constituent. Knowing the influence of these properties on crack development and mechanical behaviour provides support to the composite material designer.This work aims at modelling the crack networks development within the CMC under axial tension, at the yarn scale as well as at the woven composite scale. The proposed approach is an alternative to the main CMC behaviour models.At the yarn scale, matrix cracking with interfacial debonding between fiber and matrix first happen. Both mechanisms are analysed and their development are expressed. The mechanical behaviour resulting from damage and the crack opening displacement are also described using semi-analytical equations. Comparisons with numerical cohesive zone model and also with experimental testing shows good correlation between results.These semi-analytical expressions are then used for modelling damage within each yarns at the woven composite scale. In addition, a numerical tool is developed for matrix cracking and interfacial debonding between yarns of the woven composite.

Une bonne tenue mécanique des structures du génie civil en béton armé sous chargements dynamiques sévères est primordiale pour la sécurité et nécessite une évaluation précise de leur comportement en présence de propagation dynamique de fissures. Dans ce travail, on se focalise sur la modélisation constitutive du béton assimilé à un matériau élastique-fragile endommageable. La localisation des déformations sera régie par un modèle d'endommagement à gradient où un champ scalaire réalise une description régularisée des phénomènes de rupture dynamique. La contribution de cette étude est à la fois théorique et numérique. On propose une formulation variationnelle des modèles d'endommagement à gradient en dynamique. Une définition rigoureuse de plusieurs taux de restitution d'énergie dans le modèle d'endommagement est donnée et on démontre que la propagation dynamique de fissures est régie par un critère de Griffith généralisé. On décrit ensuite une implémentation numérique efficace basée sur une discrétisation par éléments finis standards en espace et la méthode de Newmark en temps dans un cadre de calcul parallèle. Les résultats de simulation de plusieurs problèmes modèles sont discutés d'un point de vue numérique et physique. Les lois constitutives d'endommagement et les formulations d'asymétrie en traction et compression sont comparées par rapport à leur aptitude à modéliser la rupture fragile. Les propriétés spécifiques du modèle d'endommagement à gradient en dynamique sont analysées pour différentes phases de l'évolution de fissures : nucléation, initiation, propagation, arrêt, branchement et bifurcation. Des comparaisons avec les résultats expérimentaux sont aussi réalisées afin de valider le modèle et proposer des axes d'amélioration. / In civil engineering, mechanical integrity of the reinforced concrete structures under severe transient dynamic loading conditions is of paramount importance for safety and calls for an accurate assessment of structural behaviors in presence of dynamic crack propagation. In this work, we focus on the constitutive modeling of concrete regarded as an elastic-damage brittle material. The strain localization evolution is governed by a gradient-damage approach where a scalar field achieves a smeared description of dynamic fracture phenomena. The contribution of the present work is both theoretical and numerical. We propose a variationally consistent formulation of dynamic gradient damage models. A formal definition of several energy release rate concepts in the gradient damage model is given and we show that the dynamic crack tip equation of motion is governed by a generalized Griffith criterion. We then give an efficient numerical implementation of the model based on a standard finite-element spatial discretization and the Newmark time-stepping methods in a parallel computing framework. Simulation results of several problems are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. Specific properties of the dynamic gradient damage model are investigated for different phases of the crack evolution: nucleation, initiation, propagation, arrest, kinking and branching. Comparisons with experimental results are also performed in order to validate the model and indicate its further improvement.

Cette thèse traite de processus de détérioration en théorie du risque et en biomathématique. En théorie du risque, le processus de détérioration étudié est celui des sinistres supportés par une compagnie d'assurance. Le premier chapitre examine la distribution de Markov-Polya comme loi possible pour modéliser le nombre de sinistres et établit certains liens avec la famille de lois de Katz/Panjer. Nous construisons la loi de Markov-Polya sur base d'un modèle de survenance des sinistres et nous montrons qu'elle satisfait une récurrence élégante. Celle-ci permet notamment de déduire un algorithme efficace pour la loi composée correspondante. Nous déduisons la famille de Katz/Panjer comme famille limite de la loi de Markov-Polya. Le second chapitre traite de la famille dite "Lagrangian Katz" qui étend celle de Katz/Panjer. Nous motivons par un problème de premier passage son utilisation comme loi du nombre de sinistres. Nous caractérisons toutes les lois qui en font partie et nous déduisons un algorithme efficace pour la loi composée. Nous examinons également son indice de dispersion ainsi que son comportement asymptotique. Dans le troisième chapitre, nous étudions la probabilité de ruine sur horizon fini dans un modèle discret avec taux d'intérêt positifs. Nous déterminons un algorithme ainsi que différentes bornes pour cette probabilité. Une borne particulière nous permet de construire deux mesures de risque. Nous examinons également la possibilité de faire appel à de la réassurance proportionelle avec des niveaux de rétention égaux ou différents sur les périodes successives. Dans le cadre de processus épidémiques, la détérioration étudiée consiste en la propagation d'une maladie de type SIE (susceptible - infecté - éliminé). La manière dont un infecté contamine les susceptibles est décrite par des distributions de survie particulières. Nous en déduisons la distribution du nombre total de personnes infectées à la fin de l'épidémie. Nous examinons en détails les épidémies dites de type Markov-Polya et hypergéométrique. Nous approximons ensuite cette loi par un processus de branchement. Nous étudions également un processus de détérioration similaire en théorie de la fiabilité où le processus de détérioration consiste en la propagation de pannes en cascade dans un système de composantes interconnectées.

This thesis has two parts. In the first part, we use the results of new fatigue experiments conducted with variable load levels as well as variable stress ratios to critically assess three (two old and one relatively new) cumulative fatigue damage models. These models are deterministic. Such models are usually tested using multiple blocks of periodic loading with differing amplitudes. However, available data pertains to zero-mean loading, and does not investigate the role of variable stress ratio (Smin/Smax). Here, we present experimental results for variable stress ratios. Two specimen geometries and two materials (Al 2014and Al 2024)are tested. Manson’s double linear damage rule (DLDR)gives the highest accuracy in predicting the experimental outcome, even in the presence of variable stress ratios, whereas predictions of the newer model (“A constructive empirical theory for metal fatigue under block cyclic loading,” Proceedings of the Royal Society A, 464 (2008), 1161-1179) are slightly inferior. The widely used Miner’s rule is least accurate in terms of prediction. The merits and drawbacks of these models, in light of the experimental results, are as follows. The DLDR, though accurate, has minor scientific inconsistencies and no clear generalization. The constructive model has possible generalizability and more appealing scientific consistency, but presently has poorer accuracy. Miner’s rule, least accurate, lies within the constructive approach for special parameter values. The DLDR can guide the new (constructive)approach through new parameter fitting criteria. In the second part of this thesis, we consider the scatter in fatigue life and use the Weibull distribution to describe ‘S-N-P’ curves. We first assume homoscedasticity (load-independent or constant variance) and present a way to draw a p-percentile line on a log-log load-life plot. Then heteroscedasticity (load-dependent variance) in fatigue life is incorporated and a simple statistical model is proposed, to obtain a straight line percentile plot at a pre-specified probability of survival ps. The proposed method is illustrated for Al 2014-T6 and Al 2024-T4 data sets (extracted manually) from MMPDS-01 (a data handbook).

Κίνητρο της παρούσας διατριβής αποτέλεσε η αποτίμηση της δομικής ακεραιότητας κελυφοειδών κατασκευών από σύνθετα υλικά που παρουσιάζουν ανοχή στη βλάβη, με τη χρήση ακουστικών τεχνικών μη καταστροφικού ελέγχου. Στόχος ήταν η πειραματική και θεωρητική μελέτη επίδρασης της αστοχίας, που αναπτύσσεται σε μια πολύστρωτη μετά από φόρτιση, σε μετρήσιμα χαρακτηριστικά της κυματικής διάδοσης. Χωρίζεται σε δύο τμήματα, στη μοντελοποίηση της βλάβης και στη μελέτη επίδρασης αυτής στην κυματική διάδοση. Η έρευνα εστιάστηκε σε μορφές αστοχίας που συναντώνται σε πολύστρωτες υπό επίπεδη εντατική κατάσταση και συσσωρεύεται κατά το πάχος τους στη διάρκεια φόρτισης. Για την προσομοίωση της δημιουργήθηκαν διαφορετικά μηχανικά μοντέλα. Έμφαση δόθηκε στην προσέγγιση της συμπεριφοράς του υλικού υπό μονότονη στατική φόρτιση. Γι’ αυτό αναπτύχθηκε ένα φαινομενολογικό πρότυπο προοδευτικής αστοχίας για gl/ep πολύστρωτες. Η δομή του στηρίχθηκε σε τέσσερις πυλώνες. Πρώτον στην πειραματική διαδικασία χαρακτηρισμού μηχανικών ιδιοτήτων της μονοαξονικής στρώσης, ως το βασικό δομικό υλικό μιας πολύστρωτης. Ο ενδελεχής χαρακτηρισμός του υλικού σπάνια συναντάται σε τέτοια έκταση. Δεύτερον από τις δοκιμές προέκυψαν οι καταστατικές εξισώσεις της στρώσης. Η προσέγγιση της ανισότροπης μη – γραμμικότητας του υλικού έγινε με βηματική, γραμμική ανά βήμα, τασική ανάλυση στο επίπεδο της στρώσης χρησιμοποιώντας εφαπτομενική ελαστικότητα. Ο τρίτος πυλώνας αφορά στον προσδιορισμό έναρξης αστοχίας. Υιοθετήθηκαν κριτήρια ευρείας αποδοχής στο σχεδιασμό με σύνθετα υλικά, όπως π.χ. του Puck, των Shokrieh και Lessard κ.α., προτείνοντας και έναν νέο συνδυασμό τους. Τέλος, στρατηγικές υποβάθμισης των μηχανικών ιδιοτήτων της στρώσης προσομοίωσαν το αποτέλεσμα της συσσώρευσης αστοχίας μετά την έναρξή της. Το πρότυπο προοδευτικής αστοχίας ενσωματώθηκε σε στοιχείο κελύφους εμπορικού κώδικα πεπερασμένων στοιχείων. Ακολούθησε αξιολόγηση του, συγκρίνοντας τα αριθμητικά αποτελέσματα με πλειάδα μονοαξονικών και πρωτότυπων διαξονικών πειραμάτων. Η διαδικασία αυτή οδήγησε αφενός στην σημαντική για τον σχεδιασμό παρατήρηση εξάρτησης του μέτρου διάτμησης από το υπάρχον επίπεδο εντατικό πεδίο και αφετέρου στην εξέλιξη του προτύπου ώστε παρά τον περιορισμό των καταστατικών εξισώσεων που το διέπουν να μπορεί να προσομοιώσει τη διαστρωματική αποκόλληση. Έχοντας αναπτύξει τα εργαλεία περιγραφής της βλάβης, η διατριβή ολοκληρώνεται με τη μελέτη δομικής ακεραιότητας, χρησιμοποιώντας τη μη – καταστροφική τεχνική των ακουστό - υπέρηχων. Παρουσιάζεται το πειραματικό και θεωρητικό υπόβαθρο της διάδοσης τασικών κυμάτων σε κελύφη. Πρότυπα πολύστρωτων που υπέστησαν αριθμητική βλάβη υποβλήθηκαν σε αριθμητικές μη – καταστροφικές δοκιμές, καταλήγοντας σε συμπεράσματα όπως π.χ. τη μείωση της φασικής ταχύτητας με τη συσσώρευση βλάβης. / The motivation for the present research was the integrity estimation of shell – like structures made of damage tolerant composite materials, using acoustic non destructive testing techniques. An experimental and theoretical study was held aiming to investigate the influence of the damage, accumulated in a loaded laminate, in measurable wave propagation characteristics. The thesis is separated in two major parts. One described with detail the damage simulation model and the other the damage effects on the wave propagation and the wave mechanics. The study was focused on damage modes developed in composite laminates under in – plane complex stress fields due to several loading conditions and various mechanical models were developed for simulation purposes. Emphasis was given in the description of the material performance under monotonic static loading. Thus, a phenomenological progressive damage model for gl/ep multiaxial laminates was developed. This was structured based on four pillars. Primarily, as the laminate basic building block, the unidirectional layer was mechanically characterized. Such an extended experimental procedure can hardly be found. Secondly, the test results defined the ply constitutive equation laws. The highly anisotropic material non – linearity was approximated with piece – wise linear incremental layer by layer stress analysis using tangential elasticity. The third pillar regarded the damage initiation conditions. Thus, well defined criteria widely accepted in composite design were implemented i.e. Puck, Shokrieh and Lessard, etc. Finally post failure strategies were deployed, simulating material mechanical properties degradation emerging during damage accumulation. The progressive damage model was incorporated in a shell element of a commercial finite element code. An extended validation procedure took place comparing numerical results with several uniaxial and innovative biaxial test data. During this procedure the G12 shear modulus dependence on the developed plane stress field was thoroughly studied, resulting in recommendations for the designer and the selection of the appropriate modulus value. Additionally, the material model was further enhanced, taking into account incompatible failures with its constitutive equations e.g. delamination. Having developed several tools that described damage existence or accumulation, this dissertation was finished with the structural integrity study, using the acousto – ultrasonics non destructive testing technique. The experimental and theoretical background for stress wave propagation in waveguides was presented. Numerically damaged material models were additionally inspected with numerical non – destructive tests, resulting in specific conclusions for damage effect on measurable wave propagation characteristics, e.g. phase velocity reduction with damage growth.