In the simulation of deformations of plates it is well known that we have to use a special treatment of the thickness dependence. Therewith we achieve a reduction of dimension from 3D to 2D. For linear elasticity and small deformations several techniques are well established to handle the reduction of dimension and achieve acceptable numerical results. In the case of large deformations of plates with non-linear material behaviour there exist different problems. For example the analytical integration over the thickness of the plate is not possible due to the non-linearities arising from the material law and the large deformations themselves. There are several possibilities to introduce a hypothesis for the treatment of the plate thickness from the strong Kirchhoff assumption on one hand up to some hierarchical approaches on the other hand.

Un réseau acrylate amorphe a été fabriqué au laboratoire. Une caractérisation de ses propriétés mécaniques par des essais quasi-statiques et cycliques en traction uniaxiale à différentes températures a été effectuée. Puis, des essais qualifiant et quantifiant la propriété de mémoire de forme de ce matériau ont été menés en appliquant des cycles thermomécaniques de traction uniaxiale. Durant cette étude expérimentale, plusieurs paramètres d'essais ont été variés afin d'estimer leur influence sur la propriété de mémoire de forme. Enfin, afin d'étendre les applications mémoire de forme des réseaux polymères, deux études supplémentaires ont été conduites. La première vise à la réutilisation du matériau pour des applications mémoire de forme. La seconde étude vise à renforcer le matériau obtenant un matériau composite pour améliorer sa propriété de retour de forme sous contrainte (en retour de ‘'force'').Afin d'améliorer la conception d'applications des polymères à mémoire de forme, un modèle grandes déformations, combinant les propriétés viscoélastiques et l'équivalence temps--température du matériau, a été choisi pour prédire le comportement et la mémoire de forme du réseau acrylate et ses composites. Le modèle existant dans les librairies matériaux du code éléments finis Abaqus permet de simuler numériquement les cycles thermomécaniques appliqués expérimentalement de manière exacte. Les résultats issus des simulations ont montré une bonne représentation des mesures expérimentales, reproduisant les effets des paramètres du cycle de mémoire observés expérimentalement. Une analyse des paramètres du modèle est proposée mettant en évidence la sensibilité de la propriété de mémoire de forme aux propriétés d'équivalence temps-température mesurées expérimentalement. / A chemically crosslinked amorphous acrylate network has been prepared in the laboratory. Its mechanical properties were characterized by quasi-static and cyclic uniaxial tensile tests, while varying the temperature. The shape memory property of the polymer was recognized by the application of specific thermomechanical cycles in uniaxial tension (free-length and constrained-length recovery). During the experimental study, the thermomechanical cycle parameters were varied in order to study their influence on the shape memory behavior. Two additional studies were included to improve the potential applications of shape memory polymers. The first study targeted the use of the material shape memory property for subsequent shape memory cycles. The second study aimed at improving the material shape memory properties during fixed length heating (constrained-length recovery) by adding fillers .In order to improve the shape memory polymers application design, a large strain model, combining the material viscoleasticity and its time-temperature superposition property, was chosen to predict the shape memory behavior of the material. The model features, existing in the material behavior libraries of the finite element code Abaqus, allowed simulating numerically the experimental thermomechanical shape memory cycles. Results of the simulations showed good agreements when compared with the experimental results, reproducing the shape memory cycles influence to loading parameters. A parameter sensitivity analysis revealed the shape memory property dependence on the time-temperature superposition.

Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第15312号 / 工博第3191号 / 新制||工||1480(附属図書館) / 27790 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 井合 進, 教授 田村 武, 教授 岡 二三生 / 学位規則第4条第1項該当

The objective of this work is to develop an evolution equation for the ductile growth of a spherical void in a highly strain rate and temperature dependent material. The material considered in this work is stainless steel 304L at 982 °C. The material is characterized by a physically-based internal state variable model derived within consistent kinematics and thermodynamics — Evolving Microstructure Model for Inelasticity. Through this formulation, the degradation of the elastic moduli due to damage has been naturally acquired. An elastoviscoplasticity user material subroutine has also been developed and implemented into a commercially available finite element software ABAQUS. The subroutine utilizes a return mapping algorithm, where a purely elastic trial state (elastic predictor) is followed by a plastic corrector phase (return mapping). A conditionally stable fully-implicit scheme, derived from the backward Euler integration method, has been employed to calculate the values of the internal state variables in the elastoviscoplasticity integration routine. A repeating unit cell problem is set up by introducing a spherical void inside a matrix material that simulates a periodic array of voids in a component. Using finite element analysis, a database is generated by recording the responses of the unit cell under various combinations of loading conditions, porosity, and state variables. Functional forms of the void growth equations are constructed by utilizing normalization techniques to collapse all the data into master curves. The evolution equations are converted to a form consistent with the continuum damage variable in the complete thermal-elastic-plastic-damage version of the physically-based internal state variable model.

This project addresses characterization of the material properties of aortic tissue. Understanding of these properties is important for a variety of studies including tissue engineering, effects of aging and diseases, stents engineering, and traumatic aorta rupture. The goal of the presented research was to characterize the stress-strain relationship of aorta in dynamic oscillatory biaxial loading. A setup was developed that supplied pressure loading from the physiological to sub-failure levels (between 7 and 76 kPa) to porcine aorta at frequencies ranging from 0.50Hz to 5.00Hz. Samples tested were constrained at both ends while the deformation and the pressure were recorded. Volumetric strain versus pressure was used to characterize the structural behavior of the material which showed frequency dependency and hysteresis indicating viscoelastic response. An offset method was developed to account for drifting behavior exhibited by some of the samples. The structural behavior of aorta was modeled using a quasi-linear viscoelastic (QLV) creep theory. The QLV model included a logarithmic steady state elastic function v = 0.663 +/- 0.040 + 0.241 +/- 0.011 ln(P) for pressure in kPa, and a Prony series creep function ( J0 = 0.472 +/- 0.021, J2 = 0.109 +/- 0.060, J3 = 0.419 +/- 0.056). Modeling results were then used to determine the relationships between the circumferential and longitudinal stresses and strains of the material. The results exhibited that the stress in the transverse direction was about 1.5 times larger than in the axial direction. However, in the axial direction material was stiffer and the deformation was 30% less. The relaxation function of the material was determined by linearizing the non-linear component of the QLV model and applying to it the linear viscoelastic theory. Furthermore, literature comparison revealed that aorta's creep function, as well as its elastic modulus, is within the range of what has been reported in the literature. In conclusion, an experimental model was developed that can be used to predict the behavior of porcine aorta under physiological and sub-failure conditions at quasi-static and dynamic loading. / Mechanical Engineering

Der Grenzwert kleiner Deformationen in Anwesenheit eines gegebenen Risses wird in drei verschiedenen kontinuumsmechanischen Modellen betrachtet. Erstens wird für rein statische Elastizität mit finiter Spannung im Grenzwert kleiner Belastung bewiesen, dass die Nebenbedingung globaler Injektivität im Sinne der Gamma-Konvergenz eine lokale Nichtdurchdringungsbedingung auf dem Riss ergibt. Zweitens wird Deformationsplastizität mit finiten Spannungen und multiplikativer Zerlegung des Spannungstensors behandelt und die Gamma-Konvergenz zu linearisierter Deformationsplastizität mit Rissbedingungen gezeigt. Drittens wird die ratenunabhängige Evolution der Elastoplastizität betrachtet mit einer allgemeineren Klasse globaler Injektivitätsbedingungen für den finiten Fall. Hierbei wird einerseits die evolutionäre Gamma-Konvergenz unter Vernachlässigung der Nebenbedinung gezeigt, andererseits eine Vermutung aufgestellt, unter deren Voraussetzung die evolutionäre Gamma-Konvergenz auch mit Rissbedingungen gilt. / The small-deformation limit in presence of a given crack is considered in three distinct continuummechanical models. First, a purely static finite-strain elasticity model is considered in the limit of small loading, where the constraint of global injectivity is shown to converge in the sense of Gamma-convergence to a local constraint of non-interpenetration along the crack. Second, finitestrain deformation plasticity based on the multiplicative decomposition of the strain tensor is shown to Gamma-converge to linearized deformation elastoplasticity with crack conditions. Third, the rate-independent evolution of elastoplasticity is considered with a generalized class of global injectivity constraints for the finite-strain model. On the one hand, neglecting the constraints the evolutionary Gamma-converge to linearized elastoplasticity is proven. On the other hand, a conjecture is made, subject to which the evolutionary Gamma-convergence with constraints still holds.

Cette thèse a pour objectif de développer une modélisation robuste pour l’endommagement ductile. En raison de l’adoucissement et du niveau de déformation élevé, les principales difficultés pratiques dans la simulation de l’endommagement ductile sont la dépendance au maillage et le verrouillage volumique. Dans ce travail, on choisit tout d’abord le cadre de grandes déformations en se basant sur un formalisme logarithmique. Puis, partant de la loi de Gurson-Tvergaard-Needleman transcrite en grandes déformations, on adopte une formulation non locale à gradient d’une variable interne qui permet de contrôler la localisation du dommage et traiter ainsi la dépendance au maillage. Ensuite, le modèle non local est couplé avec des éléments finis mixtes pour limiter le verrouillage volumique relatif à l’incompressibilité plastique. On aboutit ainsi à la construction d’un cadre de modélisation de l’endommagement ductile, indépendant du maillage et exonéré du verrouillage volumique. Les propriétés mathématiques et la performance numérique du modèle sont étudiées avec attention. Enfin, après une identification des paramètres sur un acier nucléaire, on réalise des simulations sur des éprouvettes (AE, CT, SENT) et sur une tuyauterie de réelle dimension afin de les confronter à des résultats d’essais. / The major goal of this dissertation is to develop a robust model for ductile damage simulation. Because of the softening behavior and the significantly large deformation in ductile damage, two principle difficulties should be dealt with carefully: mesh-dependency and volumetric locking. In this thesis, we adopt a logarithmic finite strain framework in which the Gurson-Tvergaard-Needleman constitutive law is reformulated. Then a non-local formulation with regularization of hardening variable is applied so as to solve mesh dependency and strain localization problem. In addition, the non-local model is combined with mixed “displacement-pressure-volume variation” elements to avoid volumetric locking. Thereby we establish a mesh-independent and locking-free finite strain framework for ductile damage modelling. Attention is paid to mathematical properties and numerical performance of the model. Finally, after an identification work of a nuclear steel,we carry out simulations on normalized specimens (NT, CT, SENT) as well as an industrial tube in order to compare with experimental results.

Ce travail concerne l'étude théorique, expérimentale et numérique du comportement mécanique de matériaux tissés et de toiles laminées à base de fibres synthétiques, destinés à la fabrication des voiles, comme le polyester ou le Kevlar. Une approche théorique originale a été proposée ; elle permet une prise en compte du comportement spécifique des fils, de l'enduction et de leurs interactions. La modélisation, qui en résulte, permet de décrire le comportement biaxial des matériaux tissés et des toiles, en chargements cycliques complexes, avec une prise en compte des déformations finies, des effets visqueux non linéaires, de l'irréversibilité indépendante du temps et de l'anisotropie. Une mise en œuvre de cette modélisation a été effectuée dans un code d'Eléments Finis, afin de produire un outil opérationnel pour le calcul des voiles. L'approche théorique proposée a été validée grâce à une étude expérimentale détaillée, qui a été réalisée sur le Dacron SF HTP Plus. Ainsi, nous avons réalisé sur ce matériau différents essais de tractions monotones et de tractions ondulées, contrôlés en déformation et en force. Certains de ces essais comportent des séquences de relaxation. Ces essais ont été réalisés dans les axes du matériau, dans le sens chaîne ou dans le sens trame, ainsi qu'en hors axes avec des orientations par rapport à la direction chaîne allant de 5° à 45°. Des résultats expérimentaux complémentaires ont également été obtenus sur une toile laminée en Kevlar X15 et sur un Dacron SF HTM simple. Enfin, une simulation de l'essai de traction biaxiale a été réalisée et a permis d'étudier l'homogénéité des champs de contrainte et de déformation de trois formes d'éprouvette différentes. / This work deals with theoretical, experimental and numerical studies of the mechanical behavior of woven materials and laminated fabrics, made with synthetic fibers, for the manufacture of sails, such as polyester or Kevlar. An original theoretical approach was proposed, it allows taking into account the specific behavior of yarns, of coating and their interactions. The resulting modeling allows describing the behavior of woven materials and laminated fabrics, in the case of complex cyclic biaxial loadings, taking into account finite deformations, nonlinear viscous effects, time-independent irreversibility and anisotropy. The implementation of this modeling was performed in a finite element code, in order to produce an operational tool for the design and calculation of sails. The proposed theoretical approach has been validated through a detailed experimental study, which was conducted on material “Dacron SF HTP Plus”. Thus, we performed various monotonous and cyclic tensile tests, which were strain or load-controlled. Some of these tests include relaxation sequences. These tests were conducted in the axes of the material, in the warp and weft directions, as well as off-axis or bias orientations, from 5 ° to 45 ° with respect to the warp direction. Further experimental results were also obtained on a laminated “Kevlar X15” and a woven “Dacron SF HTM simple” fabrics. Finally, numerical simulations of the biaxial tensile test were performed and were used for studying homogeneity of the stress and the strain fields in the cases of three different contours of biaxial-tensile samples.

Grâce à leurs bonnes propriétés mécaniques spécifiques, les matériaux cellulaires architecturés présentent un fort intérêt pour répondre aux problématiques du secteur aéronautique. Cependant, la modélisation d'une structure macroscopique incluant un matériau cellulaire nécessite, soit de modéliser complètement l'architecture à l'échelle mésoscopique - ce qui est coûteux en temps de calcul - soit d'utiliser un Milieu Homogène Equivalent (MHE). Ainsi, cette thèse propose de caractériser un matériau cellulaire modèle constitué d'un empilement de tubes, selon un motif carré ou hexagonal, puis d'identifier un modèle phénoménologique rendant compte du comportement mécanique inélastique du matériau. Dans un premier temps, le matériau est caractérisé sous chargements multi-axiaux à l'aide de simulations éléments finis périodiques en petites déformations. Le comportement homogénéisé en petites déformations est ensuite utilisé pour l'identification d'une Loi Homogène Equivalente (LHE) compressible et anisotrope, qui permet la modélisation de structures sandwichs en remplaçant le coeur cellulaire par son MHE. Une comparaison est réalisée entre les réponses mécaniques des simulations de référence complètement maillées et celles utilisant l'approche par MHE, validant ainsi la pertinence de la méthode multi-échelle de modélisation proposée. La caractérisation en grandes déformations des deux types d'empilement est ensuite menée. D'abord, les effets de bords et les instabilités qui gouvernent le comportement macroscopique sont étudiés. Puis, après une étude du volume élémentaire représentatif des empilements, la caractérisation du comportement inélastique par la technique de l'homogénéisation périodique est réalisée. Le comportement adoucissant en compression de l'empilement hexagonal est ainsi étudié. Finalement, une extension des LHE identifiées en petites déformations est proposée pour rendre compte du comportement en compression du matériau observé en grandes déformations. / Cellular materials have excellent specific properties, which make them attractive for aeronautical applications. However, modelling macroscopic structures including a cellular material is either very costly in terms of computational time if the whole mesoscopic structure is considered or a Homogeneous Equivalent Medium (HEM) has to be used. This Ph.D. dissertation presents, the characterisation of a cellular material built from a stacking of tubes with a square or hexagonal based pattern and the identification of a phenomenological model of their inelastic mechanical behaviour. First, the material is characterised for multi-axial loadings through a periodic finite element model in small deformations for each tube stacking pattern. The macroscopic behaviour is then used to identify a compressible anisotropic Homogeneous Equivalent Law (HEL). Within the infinitesimal strain hypothesis, a comparison is carried out between reference full scale models and HEM based ones of sandwich structures with a cellular core, confirming the relevance of the proposed multi-scale method. Then, the mechanical behaviour of each tube stacking is characterised for large deformations in order to study the influence of the boundary size effects and the instabilities in the core on the macroscopic behaviour of sandwich structures. After a study on the representative volume element, the macroscopic inelastic behaviour is characterised through the periodic homogenisation technique, especially the softening observed in compression for the hexagonal pattern. Finally, an extension of the HELs identified in small deformations is proposed to model the behaviour observed in large deformations.

The strain amplitude dependency , i.e. the Fletcher-Gent effect and Payne effect, and the strain rate dependency of rubber with reinforcing fillers is modelled using a modified boundary surface model and implemented uniaxially. In this thesis, a split of strain instead of stress is utilized, and the storage and loss modulus are captured over two decades of both strain amplitudes and frequencies. In addition, experimental results from bimodal excitation are replicated well, even though material parameters were obtained solely from harmonic excitation. These results are encouraging since the superposition principle is not valid for filled rubber, and real-life operational conditions in general contain several harmonics. This means that formulating constitutive equations in the frequency domain is a cumbersome task, and therefore the derived model is implemented in the time domain. Filled rubber is used irreplaceable in several engineering solutions, such as tires, bushings, vibrations isolators, seals and tread belts, to name just a few. In certain applications, it is sufficient to model the elastic properties of a component during finite strains. However, Hooke’s law is inadequate for this task. Instead, hyperelastic material models are used. Finally, the thesis presents a methodology for obtaining the required material parameters utilizing experiments in pure shear, uniaxial tension and the inflation of a rubber membrane. It is argued that the unloading curve rather than the loading curve is more suitable for obtaining these parameters, even at very low strain rates. / <p>QC 20140917</p>