This paper deals with two-dimensional Finite Element Analysis of the End Notched Flexure (ENF) specimen. The specimen is known to be unstable if the crack length is shorter than some critical crack length acr. A geometric linear two-dimensional Finite Element (FE) analysis of the ENF specimen is performed to evaluate acr for isotropic and orthotropic elastic materials, respectively. Moreover, the Mode II Energy Release Rate (ERR) JII and the compliance of the specimen are calculated. The influence of anisotropy is studied. Comparisons are made with the results from beam theory. This work is an extension of previous work.

In this study, it is aimed to investigate the mixed-mode fracture behavior of orthotropic functionally graded material (FGM) coatings bonded to a homogeneous substrate through a homogeneous bond-coat. Analytical and computational methods are used to solve the embedded cracking problems under mechanical or thermal loading conditions. It is assumed that the material property gradation of the FGM coating is in the thickness direction and cracks are parallel to the boundaries. The principal axes of orthotropy are parallel and perpendicular to the boundaries. A single embedded crack in the orthotropic FGM coating is investigated analytically assuming that crack surfaces are subjected to either uniform normal or uniform shear stresses. Using Fourier transformations, the problem is reduced to a couple of singular integral equations that are solved numerically to obtain the mixed-mode stress intensity factors, energy release rate and crack opening displacements. To investigate the analytically untractable problems without restrictive assumptions, a computational approach is employed. The adopted computational approach is based on finite element method and displacement correlation technique. Using the computational approach, fracture parameters are obtained considering single and periodic embedded cracking conditions in the orthotropic FGM coatings under mechanical or thermal loads. The results obtained in this study show the effects of material nonhomogeneity, material orthotropy and geometric variables on the fracture behavior of the structure.

The main objective of this study is to examine the three-dimensional surface crack problems in orthotropic materials subjected to mechanical or thermal loading. The cracks are modeled and embedded in the orthotropic material by considering semielliptical crack front geometry. In the model special elements are embedded in the crack front region, in this way it is possible to include crack tip singular fields along the crack front. Three-dimensional finite element analyses are conducted to obtain mode I stress intensity factors. The stress intensity factor is calculated by using the displacement correlation technique. In the analysis, collapsed 20-node iso-parametric elements are utilized to simulate strain singularity around the semi-elliptical crack front. The surface crack problem is analyzed under both mechanical and thermal stresses. In the case of mechanical loading, uniform tension and fixed grip tension loading cases are applied on the model. In thermal analysis, thermal boundary conditions are defined. Comparisons of the results generated to those available in the literature verify the developed techniques.

Functionally graded materials processed by the thermal spray techniques such as electron beam physical vapor deposition and plasma spray forming are known to have an orthotropic structure with reduced mechanical properties. Debonding related failures in these types of material systems occur due to embedded cracks that are perpendicular to the direction of the material property gradation. These cracks are inherently under mixed-mode loading and fracture analysis requires the extraction of the modes I and II stress intensity factors. The present study aims at developing semi-analytical techniques to study embedded crack problems in graded orthotropic media under various boundary conditions. The cracks are assumed to be aligned parallel to one of the principal axes of orthotropy. The problems are formulated using the averaged constants of plane orthotropic elasticity and reduced to two coupled integral equations with Cauchy type dominant singularities. The equations are solved numerically by adopting an expansion - collocation technique. The main results of the analyses are the mixed mode stress intensity factors and the energy release rate as functions of the material nonhomogeneity and orthotropy parameters. The effects of the boundary conditions on the mentioned fracture parameters are also duly discussed.

Avant la généralisation des toiles vers le XVI-XVII ème siècle, le bois a servi de support à d’innombrables peintures qui constituent aujourd’hui une part importante, dans les musées et les églises notamment, de notre patrimoine culturel. Après plusieurs siècles d’existence, les planches servant de support aux panneaux peints sont très souvent courbées : cette courbure est généralement imputée à la présence unilatérale de la couche picturale,imposant des échanges asymétriques d’humidité entre le bois, matériau hygroscopique, et son environnement de conservation. Par ailleurs il existe dans ces déformations une forte contribution de l’orthotropie cylindrique du bois qui est une conséquence de la croissance des arbres. Enfin, l’historique des variations hygrométriques à proximité d’un panneau peint renvoie à l’étude plus générale du comportement thermo-hygro-mécanique différé du bois.Une compréhension d’ensemble de ces phénomènes doit permettre d’orienter des décisions difficiles de conservation, notamment celles relatives au déplacement des œuvres ou à la maîtrise des environnements dans les musées. Nous proposons dans ce travail une approche générale de mécanique du matériau et des structures bois appliquée aux panneaux peints. La méthode utilisée intègre des moyens expérimentaux en laboratoire et sur des œuvres in-situ, des méthodes numériques, et l’accent est mis sur le lien fort existant entre les aspects « comportement » propres au bois (anisotropie, couplages hygromécaniques, etc.) et les aspects de structure relatifs aux panneaux peints (débit des planches, efforts extérieurs dus à leur assemblage, etc.). Un outil de calcul basé sur la modélisation mécanique des plaques orthotropes est développé. Il prend appui sur un code préexistant de transfert de masse et de chaleur décrivant les mouvements d’eau dans le support. Ce code de calcul complet est utilisé notamment sur un cas d’étude : un panneau peint de 500 ans environ, en situation d’exposition dans une église. / Until canvas became the most popular support medium in the 16th century, wood was used in numerous paintings which represent today a significant part of our cultural heritage,particularly in museums and churches. A few centuries later, wooden panel paintings exhibit cupping deformations: this cupping is generally interpreted as the consequence of asymmetrical moisture exchanges through panel thickness due to the painted layer. It is also known that wood growth rings and orthotropic orientation are possible causes ofdeformations due to drying. History of the climatic variations near the panel raises thecomplex question of time-dependant (thermo-hygro-mechanical) behavior of wood. Betterunderstanding of such behavior could help wood scientists and curators in taking decisions relating to panel transport or museum climate regulations. We suggest a general mechanical approach of this problem, dealing with both material (wood) and structure (panel) point ofview. The method includes experimental, theoretical and numerical aspects. Particular attention is put on interaction between wood material (anisotropy, hygromechanicalcouplings) and the structural level (sawing pattern of panel, joints between planks). Anumerical calculation tool is developed, based on orthotropic plate theory and existing heatand mass transfer formulation: numerical simulations are performed to discuss theconservation of a 500 years old wooden panel located in a French church.

Original analytical theories are developed for partitioning mixed-mode fractures on rigid interfaces in laminated orthotropic double cantilever beams (DCBs) based on 2D elasticity by using some novel methods. Note that although the DCB represents a simplified case, it provides a deep understanding and predictive capability for real applications and does not restrict the analysis to a simple class of fracture problems. The developed theories are generally applicable to so-called 1D fracture consisting of opening (mode I) and shearing (mode II) action only with no tearing (mode III) action, for example, straight edge cracks, circular blisters in plates and shells, etc. A salient point of the methods is to first derive one loading condition that causes one pure fracture mode. It is conveniently called the first pure mode. Then, all other pure fracture modes can be determined by using this pure mode and the property of orthogonality between pure mode I modes and pure mode II modes. Finally, these 2D-elasticity-based pure modes are used to partition mixed-mode fractures into contributions from the mode I and mode II fracture modes by considering a mixed-mode fracture as the superposition of pure mode I and mode II fractures. The partition is made in terms of the energy release rate (ERR) or the stress intensity factor (SIF). An analytical partition theory is developed first for a DCB composed of two identical linear elastic layers. The first pure mode is obtained by introducing correction factors into the beam-theory-based mechanical conditions. The property of orthogonality is then used to determine all other pure modes in the absence of through-thickness-shear forces. To accommodate through-thickness shear forces, first two pure through-thickness-shear-force pure modes (one pure mode I and one pure mode II) are discovered by extending a Timoshenko beam partition theory. Partition of mixed-mode fractures under pure through-thickness shear forces is then achieved by using these two pure modes in conjunction with two thickness-ratio-dependent correction factors: (1) a shear correction factor, and (2) a pure-mode-II ERR correction factor. Both correction factors closely follow a normal distribution around a symmetric DCB geometry. The property of orthogonality between all pure mode I and all pure mode II fracture modes is then used to complete the mixed-mode fracture partition theory for a DCB with bending moments, axial forces and through-thickness shear forces. Fracture on bimaterial interfaces is an important consideration in the design and application of composite materials and structures. It has, however, proved an extremely challenging problem for many decades to obtain an analytical solution for the complex SIFs and the crack extension size-dependent ERRs, based on 2D elasticity. Such an analytical solution for a brittle interfacial crack between two dissimilar elastic layers is obtained in two stages. In the first stage the bimaterial DCB is under tip bending moments and axial forces and has a mismatch in Young s modulus; however, the Poisson s ratios of the top and bottom layers are the same. The solution is achieved by developing two types of pure fracture modes and two powerful mathematical techniques. The two types of pure fracture modes are a SIF-type and a load-type. The two mathematical techniques are a shifting technique and an orthogonal pure mode technique. In the second stage, the theory is extended to accommodate a Poisson s ratio mismatch. Equivalent material properties are derived for each layer, namely, an equivalent elastic modulus and an equivalent Poisson s ratio, such that both the total ERR and the bimaterial mismatch coefficient are maintained in an alternative equivalent case. Cases for which no analytical solution for the SIFs and ERRs currently exist can therefore be transformed into cases for which the analytical solution does exist. It is now possible to use a completely analytical 2D-elasticity-based theory to calculate the complex SIFs and crack extension size-dependent ERRs. The original partition theories presented have been validated by comparison with numerical simulations. Excellent agreement has been observed. Moreover, one partition theory is further extended to consider the blister test and the adhesion energy of mono- and multi-layered graphene membranes on a silicon oxide substrate. Use of the partition theory presented in this work allows the correct critical mode I and mode II adhesion energy to be obtained and all the experimentally observed behaviour is explained.

As a musical instrument construction material, wood is both musically and aesthetically pleasing. Easy to work and abundant, it has traditionally been the material of choice. Unfortunately, wood is also a very inconsistent material. Due to great environmental and climatic variations, wooden specimens present large variations in their mechanical properties, even within species of a similar region. Surprisingly, an industry based entirely on acoustics has done very little to account for these variations. For this reason, manufactured wooden guitars are acoustically inconsistent. Previous work has shown that varying the dimensions of a guitar soundboard brace is a good method for taking into account variations in the mechanical properties of the wooden soundboard plate. In this thesis, the effects of a scalloped-shaped brace on the natural frequencies of a brace-plate system have been studied and tools have been developed in order to calculate the dimensions of the brace required to account for variations in the mechanical properties of the plate. It has been shown that scalloped braces can be used to modify two natural frequencies of a brace-plate system simultaneously. Furthermore, the most important criteria in modifying any given frequency of a brace-plate system is the mass and stiffness properties of the brace at the antinode of the given frequency’s associated modeshape. Subsequently, designing a brace for desired system natural frequencies, by taking into account the mechanical properties of the wooden plate, is an inverse eigenvalue problem. Since few methods exist for solving the inverse eigenvalue problem of general matrices, a new method based on the generalized Cayley-Hamilton theorem was proposed in the thesis. A further method, based on the determinant of the generalized eigenvalue problem was also presented. Both methods work well, although the determinant method is shown to be more efficient for partially described systems. Finally, experimental results were obtained for the natural frequencies of simply supported wooden plates, with and without a brace, as well as the inverse eigenvalue determinant method. Good correlation was found between theoretical and experimental results.

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This thesis deals with the reconstruction of a road bridge with two simple fields over the river Olše in Třinec. The reconstruction of the bridge structure is designed in two versions, for which there is an executed design and assessment of a supporting structure according to applicable standards. The calculation of internal strenght is carried out by using the Scia Engineer 2016 program. This work contains a static calculation, a drawing documentation , an economical comparison of variants and visualization.

Many studies have previously been done on moisture-induced strains in wood. An in- finitesimal/engineering strain model has been used for most of these studies, which is often an accurate approximation for small rotations. However, if large deformations oc- cur, then fictive strains are obtained resulting from the simplified engineering strain.  This work aims to develop a finite element formulation for problems of moisture- induced strains in orthotropic materials based on the total Lagrangian approach, where large displacements and rotations are considered. This model is then used to examine static drying deformations and their effect on dynamic vibrations. A dynamic vibration test was also done to estimate the modulus of elasticity in the fibre direction. The pur- pose is to increase the understanding of moisture-induced strains in wood and also to emphasize the advantages of using a large deformation model.  To facilitate the understanding of large deformation theory, the implementation is first done for a 2D isotropic beam where static and dynamic simulations are made. Re- sults will be compared with a standard model based on engineering strains. For the static part, two types of wooden species are studied, radiata pine and Norway spruce, and com- pared with a previous research study [32] where engineering strain theory is used. The dynamical considerations are divided into a theoretical and an experimental part. The theoretical part analyzes the vibration of radiata pine and Norway spruce samples from a study by Cown and Ormarsson 2005 [32]. In the experimental part, three Norway spruce boards were analyzed.  The results from the numerical implementation showed, among other things, that by taking moisture-induced strains into account two additional properties, the matrix Gm and the vector Emf appear in the finite element formulation. It was concluded that by using a large deformation model the accuracy will increase without causing any extra computational costs.  The transient numerical mass flow analysis showed reasonable results although the sorption exchange rate has to be slightly higher than indicated by comparable measure- ments. For the dynamic part, the performed experiment showed a difference in response between the three Norway spruce species. It was shown that the frequency increases with distance from the pith and also with lower moisture content. The difference in vibration response between Norway spruce and radiata pine was analyzed based on boards from a study by Cown and Ormarsson 2005 [32]. The response for Norway spruce tends to show a higher frequency compared to radiata pine for the test performed in this investigation. This is mainly due to a higher modulus of elasticity and lower density for Norway spruce compared to radiata pine.