Hygro-elasto-plastic behavior of planar orthotropic material

The mechanical and hygroscopic properties of paper and board are factors affecting the whole lifecycle of a product, including paper/board quality, production, converting, and material and energy savings. The progress of shrinkage profiles, loose edges of web, baggy web causing wrinkling and misregistration in printing are examples of factors affecting runnability and end product quality in the drying section and converting processes, where paper or board is treated as a moving web. The structural properties and internal stresses or plastic strain differences built up during production also cause the end-product defects related to distortion of the shape of the product such as sheet or box. The objective of this work was to construct a model capable of capturing the characteristic behavior of hygroscopic orthotropic material under moisture change, during different external in-plane stretch or stress conditions. Two independent experimental models were constructed: the elasto-plastic material model and the hygroexpansivity-shrinkage model. Both describe the structural properties of the sheet with a fiber orientation probability distribution, and both are functions of the dry solids content and fiber orientation anisotropy index. The anisotropy index, introduced in this work, simplifies the procedure of determining the constitutive parameters of the material model and the hygroexpansion coefficients in different in-plane directions of the orthotropic sheet. The mathematically consistent elasto-plastic material model and the dry solids content dependent hygroexpansivity have been constructed over the entire range from wet to dry. The presented elastoplastic and hygroexpansivity-shrinkage models can be used in an analytical approach to estimate the plastic strain and shrinkage in simple one-dimensional cases. For studies of the combined and more complicated effects of hygro-elasto-plastic behavior, both models were implemented in a finite element program for a numerical solution. The finite element approach also offered possibilities for studying different structural variations of orthotropic planar material, as well as local buckling behavior and internal stress situations of the sheet or web generated by local strain differences. A comparison of the simulation examples presented in this work to results published earlier confirms that the hygro-elasto-plastic model provides at least qualitatively reasonable estimates. The application potential of the hygro-elasto-plastic model is versatile, including several phenomena and defects appearing in the drying, converting and end-use conditions of the paper or board webs and products, or in other corresponding complex planar materials.

Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

Chaos and Unpredictability in the Vibration of an Elasto-Plastic Beam

This contribution discusses the nonlinear dynamics of a pin-ended elasto-plastic beam with both kinematic and isotropic hardening. An iterative numerical procedure based on the operator split technique is developed in order to deal with the nonlinearities in the equations of motion. Free and forced responses for harmonic sinusoidal and square wave excitations are investigated. Numerical simulations present many interesting behaviors such as jump phenomena, sensitivity to initial conditions, chaos and transient chaos. These results indicate that there are practical problems in predicting the response of the beam even when periodic steady state response is expected.

Elasto-plastic structural stability of arches

The elastic-plastic structural stability behaviour of arches is analysed in the present work.The application of the developed mathematical model, allows to determine the elastic-plastic equilibrium paths, looking for critical points, bifurcation or limit, along those paths, associated to the critical load, in case it comes to happen.The equilibrium paths in the elastic-plastic behaviour when compared with the paths in the linear elastic behaviour, may show that, due to influence of the material plasticity, modifications paths appear and consequently alterations in the values of its critical loads.

B.I.E.M.in 3-D elasto-plastic problems

In this paper we present the application of BIEM to elastoplastic axysimetric problems. After a brief presentation of the basic integral formulation we introduce the discretizing and iterative process for its resolution. Simple problems are compared in order to test the possibilities of the method and we finish commenting on future research needs.

Basic research in crashworthiness II - pre-collapse dynamic analysis of plane, ideal elasto-plastic frame structures including the case of collision into a narrow rigid pole obstacle. Interim technical report.

National Highway Traffic Safety Administration, Washington, D.C.

Basic research in crashworthiness II - large deflection computerized analysis of rate sensitive elasto-plastic frame structures. Interim technical report.

National Highway Traffic Safety Administration, Washington, D.C.

Elasto-plastic impact of fine particles and fragmentation of small agglomerates

Surface deposition of dense aerosol particles is of major concern in the nuclear industry for safety assessment. This study presents theoretical investigations and computer simulations of single gas-born U3O8 particles impacting with the in-reactor surface and the fragmentation of small agglomerates. A theoretical model for elasto-plastic spheres has been developed and used to analyse the force-displacement and force-time relationships. The impulse equations, based on Newton's second law, are applied to govern the tangential bouncing behaviour. The theoretical model is then incorporated into the Distinct Element Method code TRUBAL in order to perform computer simulated tests of particle collisions. A comparison of simulated results with both theoretical predictions and experimental measurements is provided. For oblique impacts, the results in terms of the force-displacement relationship, coefficients of restitution, trajectory of the impacting particle, and distribution of kinetic energy and work done during the process of impact are presented. The effects of Poisson's ratio, friction, plastic deformation and initial particle rotation on the bouncing behaviour are also discussed. In the presence of adhesion an elasto-plastic collision model, which is an extension to the JKR theory, is developed. Based on an energy balance equation the critical sticking velocity is obtained. For oblique collisions computer simulated results are used to establish a set of criteria determining whether or not the particle bounces off the target plate. For impact velocities above the critical sticking value, computer simulated results for the coefficients of restitution and rebound angles of the particle are presented. Computer simulations of fracture/fragmentation resulting from agglomerate-wall impact have also been performed, where two randomly generated agglomerates (one monodisperse, the other polydisperse), each consisting of 50 primary particles are used. The effects of impact angle, local structural arrangements close to the impact point, and plastic deformation at the contacts on agglomerate damage are examined. The simulated results show a significant difference in agglomerate strength between the two assemblies. The computer data also shows that agglomerate damage resulting from an oblique impact is determined by the normal velocity component rather than the impact speed.

Aspects of Mechanical Behavior and Modeling of a Tropical Unsaturated Soil

The research studies the applicability of two elastoplastic models for the collapse prediction of the lateritic soil profile from Southeastern Brazil. These tropical soils have peculiar geotechnical behavior, due to their mineralogical composition and porous structure coming from intense process of formation. Two elastoplastic models were analyzed: the Barcelona Basic Model (BBM) and another one based on BBM, however developed for tropical soils. Oedometric tests with suction control were performed at three distinct depths of the soil profile. The BBM was not suitable for the upper layer of the soil profile, because BBM considers the compressible behavior of the soil in function of the reduction of the elastoplastic compressibility index with the increase of the matric suction. The model developed for tropical soils showed better suited to the compressible behavior of the soil profile, resulting in good prediction of the collapse potential, mainly by accepting increasing values of the elastoplastic compressibility index of the soil profile with the matric suction rise. © 2013 Springer Science+Business Media Dordrecht.

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelas- ticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We para- metrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complemen- tarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.

TECTONICS OF THE HELVETIC NAPPE SYSTEM (W SWITZERLAND): CONTROL OF STRAIN LOCALIZATION AND BASEMENT-COVER DEFORMATION. Insights from models based on continuum mechanics

The Helvetic nappe system in Western Switzerland is a stack of fold nappes and thrust sheets em-placed at low grade metamorphism. Fold nappes and thrust sheets are also some of the most common features in orogens. Fold nappes are kilometer scaled recumbent folds which feature a weakly deformed normal limb and an intensely deformed overturned limb. Thrust sheets on the other hand are characterized by the absence of overturned limb and can be defined as almost rigid blocks of crust that are displaced sub-horizontally over up to several tens of kilometers. The Morcles and Doldenhom nappe are classic examples of fold nappes and constitute the so-called infra-Helvetic complex in Western and Central Switzerland, respectively. This complex is overridden by thrust sheets such as the Diablerets and Wildhörn nappes in Western Switzerland. One of the most famous example of thrust sheets worldwide is the Glariis thrust sheet in Central Switzerland which features over 35 kilometers of thrusting which are accommodated by a ~1 m thick shear zone. Since the works of the early Alpine geologist such as Heim and Lugeon, the knowledge of these nappes has been steadily refined and today the geometry and kinematics of the Helvetic nappe system is generally agreed upon. However, despite the extensive knowledge we have today of the kinematics of fold nappes and thrust sheets, the mechanical process leading to the emplacement of these nappe is still poorly understood. For a long time geologist were facing the so-called 'mechanical paradox' which arises from the fact that a block of rock several kilometers high and tens of kilometers long (i.e. nappe) would break internally rather than start moving on a low angle plane. Several solutions were proposed to solve this apparent paradox. Certainly the most successful is the theory of critical wedges (e.g. Chappie 1978; Dahlen, 1984). In this theory the orogen is considered as a whole and this change of scale allows thrust sheet like structures to form while being consistent with mechanics. However this theoiy is intricately linked to brittle rheology and fold nappes, which are inherently ductile structures, cannot be created in these models. When considering the problem of nappe emplacement from the perspective of ductile rheology the problem of strain localization arises. The aim of this thesis was to develop and apply models based on continuum mechanics and integrating heat transfer to understand the emplacement of nappes. Models were solved either analytically or numerically. In the first two papers of this thesis we derived a simple model which describes channel flow in a homogeneous material with temperature dependent viscosity. We applied this model to the Morcles fold nappe and to several kilometer-scale shear zones worldwide. In the last paper we zoomed out and studied the tectonics of (i) ductile and (ii) visco-elasto-plastic and temperature dependent wedges. In this last paper we focused on the relationship between basement and cover deformation. We demonstrated that during the compression of a ductile passive margin both fold nappes and thrust sheets can develop and that these apparently different structures constitute two end-members of a single structure (i.e. nappe). The transition from fold nappe to thrust sheet is to first order controlled by the deformation of the basement. -- Le système des nappes helvétiques en Suisse occidentale est un empilement de nappes de plis et de nappes de charriage qui se sont mis en place à faible grade métamorphique. Les nappes de plis et les nappes de charriage sont parmi les objets géologiques les plus communs dans les orogènes. Les nappes de plis sont des plis couchés d'échelle kilométrique caractérisés par un flanc normal faiblement défor-mé, au contraire de leur flanc inverse, intensément déformé. Les nappes de charriage, à l'inverse se caractérisent par l'absence d'un flanc inverse bien défini. Elles peuvent être définies comme des blocs de croûte terrestre qui se déplacent de manière presque rigide qui sont déplacés sub-horizontalement jusqu'à plusieurs dizaines de kilomètres. La nappe de Mordes et la nappe du Doldenhorn sont des exemples classiques de nappes de plis et constitue le complexe infra-helvétique en Suisse occidentale et centrale, respectivement. Ce complexe repose sous des nappes de charriages telles les nappes des Diablerets et du Widlhörn en Suisse occidentale. La nappe du Glariis en Suisse centrale se distingue par un déplacement de plus de 35 kilomètres qui s'est effectué à la faveur d'une zone de cisaillement basale épaisse de seulement 1 mètre. Aujourd'hui la géométrie et la cinématique des nappes alpines fait l'objet d'un consensus général. Malgré cela, les processus mécaniques par lesquels ces nappes se sont mises en place restent mal compris. Pendant toute la première moitié du vingtième siècle les géologues les géologues ont été confrontés au «paradoxe mécanique». Celui-ci survient du fait qu'un bloc de roche haut de plusieurs kilomètres et long de plusieurs dizaines de kilomètres (i.e., une nappe) se fracturera de l'intérieur plutôt que de se déplacer sur une surface frictionnelle. Plusieurs solutions ont été proposées pour contourner cet apparent paradoxe. La solution la plus populaire est la théorie des prismes d'accrétion critiques (par exemple Chappie, 1978 ; Dahlen, 1984). Dans le cadre de cette théorie l'orogène est considéré dans son ensemble et ce simple changement d'échelle solutionne le paradoxe mécanique (la fracturation interne de l'orogène correspond aux nappes). Cette théorie est étroitement lié à la rhéologie cassante et par conséquent des nappes de plis ne peuvent pas créer au sein d'un prisme critique. Le but de cette thèse était de développer et d'appliquer des modèles basés sur la théorie de la méca-nique des milieux continus et sur les transferts de chaleur pour comprendre l'emplacement des nappes. Ces modèles ont été solutionnés de manière analytique ou numérique. Dans les deux premiers articles présentés dans ce mémoire nous avons dérivé un modèle d'écoulement dans un chenal d'un matériel homogène dont la viscosité dépend de la température. Nous avons appliqué ce modèle à la nappe de Mordes et à plusieurs zone de cisaillement d'échelle kilométrique provenant de différents orogènes a travers le monde. Dans le dernier article nous avons considéré le problème à l'échelle de l'orogène et avons étudié la tectonique de prismes (i) ductiles, et (ii) visco-élasto-plastiques en considérant les transferts de chaleur. Nous avons démontré que durant la compression d'une marge passive ductile, a la fois des nappes de plis et des nappes de charriages peuvent se développer. Nous avons aussi démontré que nappes de plis et de charriages sont deux cas extrêmes d'une même structure (i.e. nappe) La transition entre le développement d'une nappe de pli ou d'une nappe de charriage est contrôlé au premier ordre par la déformation du socle. -- Le système des nappes helvétiques en Suisse occidentale est un emblement de nappes de plis et de nappes de chaînage qui se sont mis en place à faible grade métamoiphique. Les nappes de plis et les nappes de charriage sont parmi les objets géologiques les plus communs dans les orogènes. Les nappes de plis sont des plis couchés d'échelle kilométrique caractérisés par un flanc normal faiblement déformé, au contraire de leur flanc inverse, intensément déformé. Les nappes de charriage, à l'inverse se caractérisent par l'absence d'un flanc inverse bien défini. Elles peuvent être définies comme des blocs de croûte terrestre qui se déplacent de manière presque rigide qui sont déplacés sub-horizontalement jusqu'à plusieurs dizaines de kilomètres. La nappe de Morcles and la nappe du Doldenhorn sont des exemples classiques de nappes de plis et constitue le complexe infra-helvétique en Suisse occidentale et centrale, respectivement. Ce complexe repose sous des nappes de charriages telles les nappes des Diablerets et du Widlhörn en Suisse occidentale. La nappe du Glarüs en Suisse centrale est certainement l'exemple de nappe de charriage le plus célèbre au monde. Elle se distingue par un déplacement de plus de 35 kilomètres qui s'est effectué à la faveur d'une zone de cisaillement basale épaisse de seulement 1 mètre. La géométrie et la cinématique des nappes alpines fait l'objet d'un consensus général parmi les géologues. Au contraire les processus physiques par lesquels ces nappes sont mises en place reste mal compris. Les sédiments qui forment les nappes alpines se sont déposés à l'ère secondaire et à l'ère tertiaire sur le socle de la marge européenne qui a été étiré durant l'ouverture de l'océan Téthys. Lors de la fermeture de la Téthys, qui donnera naissance aux Alpes, le socle et les sédiments de la marge européenne ont été déformés pour former les nappes alpines. Le but de cette thèse était de développer et d'appliquer des modèles basés sur la théorie de la mécanique des milieux continus et sur les transferts de chaleur pour comprendre l'emplacement des nappes. Ces modèles ont été solutionnés de manière analytique ou numérique. Dans les deux premiers articles présentés dans ce mémoire nous nous sommes intéressés à la localisation de la déformation à l'échelle d'une nappe. Nous avons appliqué le modèle développé à la nappe de Morcles et à plusieurs zones de cisaillement provenant de différents orogènes à travers le monde. Dans le dernier article nous avons étudié la relation entre la déformation du socle et la défonnation des sédiments. Nous avons démontré que nappe de plis et nappes de charriages constituent les cas extrêmes d'un continuum. La transition entre nappe de pli et nappe de charriage est intrinsèquement lié à la déformation du socle sur lequel les sédiments reposent.

Desenvolvimento de modelos numéricos e análise experimental de subestruturas soldadas de transformadores de potência, sujeitas a forças de curto-circuito em regime transitório

Dissertação de mestrado integrado em Engenharia Mecânica

Ein Beitrag zur realitätsnahen Modellierung und Analyse von stahlfaserverstärkten Stahlbeton- und Stahlbetonflächentragwerken

Das Werkstoffverhalten von stahlfaserfreiem bzw. stahlfaserverstärktem Stahlbeton unter biaxialle Druck- Zugbeanspruchung wurde experimentell und theoretisch untersucht. Die Basis der experimentellen Untersuchungen waren zahlreiche Versuche, die in der Vergangenheit an faserfreiem Stahlbetonscheiben zur Bestimmung des Werkstoffverhaltens von gerissenem Stahlbeton im ebenen Spannungszustand durchgeführt wurden. Bei diesen Untersuchungen wurde festgestellt, dass infolge einer Querzugbeanspruchung eine Abminderung der biaxialen Druckfestigkeit entsteht. Unter Berücksichtigung dieser Erkenntnisse sind zur Verbesserung der Werkstoffeigenschaften des Betons, Stahlbetonscheiben aus stahlfaserverstärktem Beton hergestellt worden. Die aus der Literatur bekannten Werkstoffmodelle für Beton sowie Stahlbeton, im ungerissenen und gerissenen Zustand wurden hinsichtlich der in der Vergangenheit ermittelten Materialeigenschaften des Betons bzw. Stahlbetons unter proportionalen sowie nichtproportionalen äußeren Belastungen erklärt und kritisch untersucht. In den frischen Beton wurden Stahlfasern hinzugegeben. Dadurch konnte die Festigkeits- und die Materialsteifigkeitsabminderung infolge Rissbildung, die zur Schädigung des Verbundwerkstoffs Beton führt, reduziert werden. Man konnte sehen, dass der Druckfestigkeitsabminderungsfaktor und insbesondere die zur maximal aufnehmbaren Zylinderdruckfestigkeit gehörende Stauchung, durch Zugabe von Stahlfasern besser begrenzt wird. Die experimentelle Untersuchungen wurden an sechs faserfreien und sieben stahlfaserverstärkten Stahlbetonscheiben unter Druck-Zugbelastung zur Bestimmung des Verhaltens des gerissenen faserfreien und stahlfaserverstärkten Stahlbetons durchgeführt. Die aus eigenen Versuchen ermittelten Materialeigenschaften des Betons, des stahlfaserverstärkten Betons und Stahlbetons im gerissenen Zustand wurden dargelegt und diskutiert. Bei der Rissbildung des quasi- spröden Werkstoffs Beton und dem stahlfaserverstärkten Beton wurde neben dem plastischen Fließen, auch die Abnahme des Elastizitätsmoduls festgestellt. Die Abminderung der aufnehmbaren Festigkeit und der zugehörigen Verzerrung lässt sich nicht mit der klassischen Fließtheorie der Plastizität ohne Modifizierung des Verfestigungsgesetzes erfassen. Es wurden auf elasto-plastischen Werkstoffmodellen basierende konstitutive Beziehungen für den faserfreien sowie den stahlfaserverstärkten Beton vorgeschlagen. Darüber hinaus wurde in der vorliegenden Arbeit eine auf dem elasto-plastischen Werkstoffmodell basierende konstitutive Beziehung für Beton und den stahlfaser-verstärkten Beton im gerissenen Zustand formuliert. Die formulierten Werkstoffmodelle wurden mittels dem in einer modularen Form aufgebauten nichtlinearen Finite Elemente Programm DIANA zu numerischen Untersuchungen an ausgewählten experimentell untersuchten Flächentragwerken, wie scheibenartigen-, plattenartigen- und Schalentragwerken aus faserfreiem sowie stahlfaserverstärktem Beton verwendet. Das entwickelte elasto-plastische Modell ermöglichte durch eine modifizierte effektive Spannungs-Verzerrungs-Beziehung für das Verfestigungsmodell, nicht nur die Erfassung des plastischen Fließens sondern auch die Berücksichtigung der Schädigung der Elastizitätsmodule infolge Mikrorissen sowie Makrorissen im Hauptzugspannungs-Hauptdruckspannungs-Bereich. Es wurde bei den numerischen Untersuchungen zur Ermittlung des Last-Verformungsverhaltens von scheibenartigen, plattenartigen- und Schalentragwerken aus faserfreiem und stahlfaserverstärktem Stahlbeton, im Vergleich mit den aus Versuchen ermittelten Ergebnissen, eine gute Übereinstimmung festgestellt.

Non-linear analysis of reinforced concrete plates by the boundary element method and continuum damage mechanics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Blade design and forming for fans using finite elements

The necessity of adapting the standardized fan models to conditions of higher temperature has emerged due to the growth of concerning referring to the consequences of the gas expelling after the Mont Blanc tunnel accident in Italy and France, where even though, with 100 fans in operation, 41 people died. However, since then, the defied solutions have pointed to aerodynamic disadvantages or have seemed nonappropriate in these conditions. The objective of this work is to present an alternative to the market standard fans considering a new technology in constructing blades. This new technology introduces the use of the stainless steel AISI 409 due to its good adaptation to temperatures higher than 400°C, particularly exposed to temperatures of gas exhaust from tunnels in fire situation. Furthermore, it presents a very good resistance to corrosion and posterior welding and pressing, due to its alloyed elements. The innovation is centered in the process of a deep drawing of metallic shells and posterior welding, in order to keep the ideal aerodynamic superficies for the fan ideal performance. On the other hand, the finite element method, through the elasto-plastic software COSMOS permitted the verification of the thickness and structural stability of the blade in relation to the aerodynamic efforts established in the project. In addition, it is not advisable the fabrication of blades with variable localized thickness not even, non-uniform ones, due to the verified concentration of tensions and the difficulties observed in the forming. In this way, this study recommends the construction of blades with uniform variations of thickness. © 2007 Springer.