The main emphasis of this thesis is to study a posteriori error analysis of discontinuous Galerkin (DG) methods for the elliptic variational inequalities. The DG methods have become very pop-ular in the last two decades due to its nature of handling complex geometries, allowing irregular meshes with hanging nodes and different degrees of polynomial approximation on different ele-ments. Moreover they are high order accurate and stable methods. Adaptive algorithms refine the mesh locally in the region where the solution exhibits irregular behaviour and a posteriori error estimates are the main ingredients to steer the adaptive mesh refinement. The solution of linear elliptic problem exhibits singularities due to change in boundary con-ditions, irregularity of coefficients and reentrant corners in the domain. Apart from this, the solu-tion of variational inequality exhibits additional irregular behaviour due to occurrence of the free boundary (the part of the domain which is a priori unknown and must be found as a component of the solution). In the lack of full elliptic regularity of the solution, uniform refinement is inefficient and it does not yield optimal convergence rate. But adaptive refinement, which is based on the residuals ( or a posteriori error estimator) of the problem, enhance the efficiency by refining the mesh locally and provides the optimal convergence. In this thesis, we derive a posteriori error estimates of the DG methods for the elliptic variational inequalities of the first kind and the second kind. This thesis contains seven chapters including an introductory chapter and a concluding chap-ter. In the introductory chapter, we review some fundamental preliminary results which will be used in the subsequent analysis. In Chapter 2, a posteriori error estimates for a class of DG meth-ods have been derived for the second order elliptic obstacle problem, which is a prototype for elliptic variational inequalities of the first kind. The analysis of Chapter 2 is carried out for the general obstacle function therefore the error estimator obtained therein involves the min/max func-tion and hence the computation of the error estimator becomes a bit complicated. With a mild assumption on the trace of the obstacle, we have derived a significantly simple and easily com-putable error estimator in Chapter 3. Numerical experiments illustrates that this error estimator indeed behaves better than the error estimator derived in Chapter 2. In Chapter 4, we have carried out a posteriori analysis of DG methods for the Signorini problem which arises from the study of the frictionless contact problems. A nonlinear smoothing map from the DG finite element space to conforming finite element space has been constructed and used extensively, in the analysis of Chapter 2, Chapter 3 and Chapter 4. Also, a common property shared by all DG methods allows us to carry out the analysis in unified setting. In Chapter 5, we study the C0 interior penalty method for the plate frictional contact problem, which is a fourth order variational inequality of the second kind. In this chapter, we have also established the medius analysis along with a posteriori analy-sis. Numerical results have been presented at the end of every chapter to illustrate the theoretical results derived in respective chapters. We discuss the possible extension and future proposal of the work presented in the Chapter 6. In the last chapter, we have documented the FEM codes used in the numerical experiments.

Engineering assemblies are very frequently subject to fretting fatigue, which is a damage process that results when very small slip displacements arise at nominally stationary frictional interfaces. Fretting accelerates the initiation and early propagation of fatigue cracks, thereby causing significant reductions in the fatigue performance of many critical engineering components. A majority of the previous research on fretting fatigue has focused on incomplete (i.e. smooth-edged) contacts, while complete (i.e. sharp-edged) contacts have received less attention. The aim of this thesis is to contribute to the theoretical understanding of complete contacts, especially when they are subject to fatigue conditions. This problem is addressed in two separate ways. First, because fretting failures almost invariably initiate from the edge of contact, a detailed understanding of the conditions in this region should enable more accurate assessments of fatigue performance to be made. Thus, an asymptotic analysis is presented, which provides an accurate description of the contact edge under many conditions. This is done by using the elasticity solution for a semi-infinite notch to represent the state of stress near the contact edge in an asymptotic sense. Attention is then placed on the fact that cyclically loaded frictional contacts tend toward a steady-state response in which less frictional slip (and energy dissipation) occurs than in the first few load cycles. To investigate this effect, a numerical sub-structuring procedure is described, which significantly reduces the number of degrees of freedom in finite element models of frictional contact. This reduced model is then used to calculate the shakedown limit, i.e. the amplitude of cyclic load above which frictional slip is guaranteed to persist in the steady state. The sensitivity of the steady-state solution to the initial residual displacement state is then investigated, and it is shown that initial conditions can have a large influence on the steady-state behaviour of complete contacts.

In endoprosthesis surgery there are typically a high percentage of implant defects, these can lead to failure of the whole prosthesis. One type of total hip replacement function loss is acetabular cup loosening from the pelvic bone. This disertation examines manufacture perturbations as one of the possible reasons for this kind of failure. Both dimension and geometry manufacturing perturbations of ceramic head and polyethylen cup were analyzed. We find that perturbations in the variables analysed here affect considered values of contact pressure and frictional moment. Furthermore, contact pressure and frictional moment are quantities affecting replacement success and durability. From obtained results it can be recommended to fit head and cup with a clearance of between 0 mm and 0.05 mm. It can not be recommend using interference type of fit because of strong deterioration of the contact conditions. Roundness perturbation of ceramic head should not exceed 0.025 mm.

In this study, dynamic crack propagation in brittle materials has been studied using a regularized phase field approach.The phase field model used has been validated using specific experimental results of a dynamic in-plane fracture. The crack branching phenomena and existence of a limiting crack tip velocity has been validated using a mode I simulation set-up. A parametric study has also been performed so as to normalize the various numerical parameters that affect the velocity at the crack tip. Following the validation of the phase field model a stochastic analysis of a PBX microstructure has been performed. The microstructure has a high HMX volume fraction of 79\%. The energetic material is HMX and the binder used is Sylgard. Artificial defects are introduced in the system using phase field cracks. The analysis uses a finite element framework that accounts for various thermal-mechanical processes like deformation, heat generation, conduction, fracture and frictional heating at the crack surfaces. The effect on the temperature and damage field due to varying parameters like loading velocities and critical energy release rates is studied. Critical hotspot formation due to localized frictional heating is also studied. A concept of dirty binder is introduced to increase the grain volume fraction of the energetic in the composite. This amounts to a homogenized binder that accounts for the influence of the subsume particles that do not contribute to fracture but affect material properties of the binder.

Objetivos: O objetivo desta pesquisa foi comparar a resistência ao deslocamento de fios de níquel e titânio superelásticos termoativados sobrepostos, em braquetes ortodônticos metálicos autoligáveis passivos. Material e Métodos: Foram utilizadas três espessuras de fios de níquel e titânio superelásticos termoativados (NiTi-TA): 0,014 sobreposto ao 0,016 e 0,020 (FlexyNiTi Thermal - Orthometric, Marília, SP, BR), associados a dois tipos de braquetes metálicos autoligáveis passivos: SmartClip SL3® (3M Unitek, Monrovia, CA, EUA) e OrthoClip SLB® (Orthometric, Marília, SP, BR). Um dispositivo que continha 5 braquetes de cada tipo (do incisivo central superior direito ao 2º pré-molar superior direito) foi desenvolvido para realização dos testes. O braquete do canino foi colado em uma barra de aço inoxidável móvel que permitia alterar sua posição vertical, enquanto os demais braquetes foram colados a uma barra fixa de acrílico. As forças obtidas por meio do deslocamento vertical do braquete do canino de 0mm para 1,5mm, 3,0 mm, 4,5mm e 6,0 mm foram registradas. O ambiente de teste foi seco com temperatura controlada de 36,5º C ± 1º C. Um total de 160 testes foi realizado na máquina de ensaios universal Instron. Os testes estatísticos de Shapiro-Wilk, teste t de Student não pareado e ANOVA com testes post-hoc de Tukey foram aplicados aos dados (p<0,05). Resultados: A distribuição normal da amostra foi confirmada, e os testes paramétricos demonstraram que houve diferenças estatisticamente significativas no braquete SmartClip SL3® quando associados aos fios de NiTi-TA 0,020 e 0,014 sobreposto ao 0,016 nas alturas de 1,5mm (p=0,003) e 6mm (p0,0001). Porém, não foram encontradas diferenças estatísticas nas alturas de 3mm (p=0,76) e 4,5mm (p=0,09). No braquete OrthoClip SLB® houve diferenças estatisticamente significativas entre os fios de NiTi-TA 0,020 e 0,014 sobreposto ao 0,016 em todas as alturas avaliadas (p0,0001). Na comparação entre os braquetes, quando associados ao fio 0,020 de NiTi-TA houve diferenças estatisticamente significativas na altura de 1,5mm; 3mm e 6mm (p0,0001). No entanto, na altura de 4,5mm as diferenças não foram significativas estatisticamente (p=0,32). Quando associados aos fios de NiTi-TA 0,014 e 0,016 sobrepostos, as diferenças em todas as alturas avaliadas foram significativas estatisticamente (1,5mm - p=0,0006; nas demais alturas p0,0001). Conclusão: Nos braquetes SmartClip SL3®, em desnivelamentos de 1,5mm, os fios de NiTi-TA 0,014 e 0,016 sobrepostos apresentaram menor resistência ao deslocamento, enquanto que na altura de 6mm a menor resistência foi obtida com o fio de NiTi-TA 0,020. Nas demais alturas não houve diferenças estatísticas entre os fios. Para os braquetes OrthoClip SLB®, os fios de NiTi-TA 0,014 e 0,016 sobrepostos apresentaram menor resistência ao deslocamento em todas as alturas avaliadas. Na comparação entre os dois tipos de braquetes, associados ao fio de NiTi-TA 0,020 na altura de 1,5mm, o braquete OrthoClip SLB® apresentou menor resistência ao deslocamento, ao passo que nas alturas de 3mm e 6mm foi o braquete SmartClip SL3®. Na altura de 4,5mm não foram encontradas diferenças estatisticamente significativas entre os dois braquetes avaliados. / Objective: The objective of this research was to compare the displacement resistance of overlapped heat-activated superelastic nickel titanium wires, in passive self-ligating metallic brackets. Material and Methods: Three thicknesses of heat-activated superelastic nickel titanium wires (NiTi-TA) were used: 0.014 overlapped with 0.016 and 0.020 (FlexyNiTi Thermal - Orthometric, Marília, SP, BR), associated with two types of passive self-ligating metallic brackets: SmartClip SL3® (3M Unitek, Monrovia, CA, EUA) and OrthoClip SLB® (Orthometric, Marília, SP, BR). A device with 5 brackets of each type (from right central incisor to the second maxillary premolar) was developed for this research. The canine bracket was attached to a sliding stainless steel bar which allowed the alteration of its vertical position, while the remaining brackets were attached to a fixed acrylic bar. The forces generated by means of the canine bracket vertical displacement from 0mm to 1.5mm; 3.0mm; 4.5mm and 6.0mm were recorded. The test environment was dry with a controlled temperature of 36.5º C ± 1º C. A total of 160 tests were carried out in the Instron Testing Machine. The Shapiro-Wilk test, non-paired Student t-test and ANOVA with Tukey post hoc test were applied to the data (p<0.05). Results: The normal distribution was confirmed, and the parametric tests showed that there were statistically significant differences in the SmartClip SL3® when associated with the NiTi-TA 0.020 and 0.014 wires overlapped to the 0.016 wire in the height of 1.5mm (p=0.003) and 6mm (p<0.0001). However, statistically significant differences were not found in the heights of 3mm (p=0.76) and 4.5mm (p=0.09). For the OrthoClip SLB® brackets, there were statistically significant differences between the NiTi-TA 0.020 and 0.014 wires overlapped with the 0.016 wire in all the heights assessed (p<0.0001). In the comparison between the brackets when associated with the NiTi-TA 0.020 wire, there were statistically significant differences in the heights of 1.5mm, 3mm and 6mm (p<0.0001). However, in the height of 4.5mm the differences were not statistically significant (p=0.32). When associated with the overlapped NiTi-TA 0.014 and 0.016 wires, the differences in all assessed heights were statistically significant (1.5mm - p=0.0006; other height - p0.0001). Conclusion: For the SmartClip SL3® brackets, with 1.5mm of displacement, the overlapped NiTi-TA 0.014 and 0.016 wires showed less displacement resistance, while in the height of 6mm the least displacement resistance was found with the NiTi-TA 0.020. In the remaining heights, there were no statistically significant differences between the wires. For the OrthoClip SLB® brackets, the overlapped NiTi-TA 0.014 and 0.016 wires showed the least displacement resistance in all the assessed heights. In the comparison between the two types of brackets, associated with the NiTi-TA 0.020 wire, for the height of 1.5mm, the OrthoClip SLB® bracket showed less displacement resistance, while for the heights of 3mm and 6mm the SmartClip SL3® brackets showed less displacement resistance. For the height of 4.5mm there were no statistically significant differences found between the assessed brackets.

Friction and wear have been observed m mechanical systems when there is a relative motion between two solid bodies Friction mainly results in loss of energy and wear results in matenal loss The proper understanding of friction and wear mechanisms provides practical solutions to tribological related problems Various models are available m tribology literature to calculate function coefficient and wear rate of matenals However, expenments suggest that these models are incomplete and fortuitous as the tnbological response is system dependent The objective of present investigation is to understand the tribological lesponse of commercially puie titanium and OFHC copper pins sliding on polyciystallme alumina discs Di\ shdm% tests were conducted in air, and vacuum (1 5 x 10~2Pa) at room tempeiatuie under different experimental conditions The normal load was vaned from 15 3 N to 76 0 N, sliding speed was vaned from 0 01 ms"1 to 1 4 ms"1, and tempeiatuie was varied from 293 K to 793 K It is found that the haidness of metals do not have any effect on their tribological response The experimental obseivations indicate that tribological response of metals mainly depends up on miciostructural evolution, oxygen activity and relative shear strength of metals and ceramics Chapter 1 starts with the background and concepts of tribology A brief literature survey is given with published work in relation with the present work In Chapter 2, the experimental proceduies of the dry sliding test and compression test are given Chapter 3 explains the tribological response of titanium during shdmg against alumina Different wear mechanisms such as oxidation, deformation and adhesion were identified Deformation wear mechanism is explained using strain rate response approach Chapter 4 explains the tribological response of copper during sliding against alumina The influence of environment and microstructural evolution on its tribological behavior are studied Chaptei 5 explains the dependence of tribological response of metals on micro structural evolution, oxygen activity and relative shear strength of metals and ceramics This thesis ends with the conclusions of the present investigation

By examining continuous data from the Poker Flat Incoherent Scatter Radar (PFISR) in Poker Flat, Alaska, short-lived enhancements in the F-region ion temperature, or "Tᵢ spikes", were discovered in the evening while the radar was on the equatorward edge of the high latitude convection region. These enhancements were several hundred Kelvin above the background temperature, would last less than 15 minutes and were preceded by sharp depletions in plasma density (of roughly one half). Though they were mostly detected in the summer, 25 events throughout a whole year of data were identi ed in which the spike occurred within 1.5 hours of the density drop. By examining the location of PFISR at the time of the enhancements, as well as the conditions under which these spikes occurred, it was concluded that these enhancements were the result of electric elds increasing the frictional heating between ions and neutrals. By then examining geophysical data, it was found that these events were temporal and related to changes in magnetic indices. One possible explanation for the observations is that the electric eld is at its strongest near the plasmapause during substorms. Another more likely possibility is that during substorms the region of sunward ion convection expands into a region in the evening side where the neutral gas moves in a direction opposite to the ions, thereby enhancing the frictional heating rate.

Heat transfer and pressure drop during condensation of propane flowing through minichannels is investigated in this study. Studies of condensation of hydrocarbons are important for applications in the petrochemical industry. Insights into the mechanisms of propane condensation are required for accurate design of heat transfer equipment for use in hydrocarbon processing. At present, there is very little research on vertical condensation, especially of hydrocarbons, for the tube sizes and flow conditions of interest to the present study. An experimental facility was designed and fabricated to measure the frictional pressure drop and heat transfer coefficients during condensation of propane in plain tubes with an inner diameter of 1.93 mm. Measurements were taken across the vapor-liquid dome in nominal quality increments of 0.25 for two saturation temperatures (47°C and 74°C) and four mass flux conditions (75 – 150 kg m‾² s‾¹). The data were compared to the predictions of relevant correlations in the literature. The data from this study were also used to develop models for the frictional pressure drop and heat transfer coefficient based on the measurements and the underlying condensation mechanisms. These results and the corresponding correlations contribute to the understanding of condensation of hydrocarbons in vertical minichannels.

Thesis (Ph.D.)--University of Melbourne, School of Physics, 2007. / Typescript. Includes bibliographical references (leaves 275-308).

To ensure that manufactured cartridges is safe to use, a tensile test is performed. The frictional force between the bullet and the case is required according to Normas standard to be between 15 – 75 Kg. Variations of the frictional force, with values outside of the standard had been noted by Norma Precision without understanding the cause. The aim of this report was to investigate and evaluate possible causes of the variations measured by tensile tests, difference between extreme values and to find a solution to what can be done to prevent the variations. Two different cases and three different bullets were used by request from Norma in the scope of this report. Different combinations of the bullets and cases was tested by alternating process parameter, surfaces and loading procedures. The loaded cartridges went through tensile tests to investigate differences. Bullets and cases with extreme values from the measured frictional force were chosen for further investigation in SEM and profilometer. To be able to draw further conclusions four different simulation models was created in Abaqus and different parameters was calculated. The dimensions and shape of the bullet resulted as the cause of changes of the tensile test curves. The smallest frictional force was found to differ from the largest by a change in wear mechanism from mainly abrasive ploughing to cutting and adhesion that caused transfer of material from the bullet to the case. The change in wear mechanism was found to be caused by an increased bullet diameter. The loading procedure was found to cause variations in plastic deformation on the neck of the case and damage the bottom of the bullet. The loading procedure was assumed to have the largest impact on the variations in frictional force. To minimize the variations the central axis of the case was suggested to be in line with the central axis of the bullet.