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The topic of this thesis is a mathematically rigorous derivation of formulae for the magnetic force which is exerted on a part of a bounded magnetized body by its surrounding. Firstly, the magnetic force is considered within a continuous system based on macroscopic magnetostatics. The force formula in this setting is called Brown''s force formula referring to W. F. Brown, who gave a mainly physically motivated discussion of it. This formula contains a surface integral which shows a nonlinear dependence on the normal. Brown assumes the existence of an additional term in the surface force which cancels the nonlinearity to allow an application of Cauchy''s theorem in continuum mechanics to a magnetoelastic material. The proof of Brown''s formula which is given in this work involves a suitable regularization of a hypersingular kernel and uses singular integral methods. Secondly, we consider a discrete, periodic setting of magnetic dipoles and formulate the force between a part of a bounded set and its surrounding. In order to pass to the continuum limit we start from the usual force formula for interacting magnetic dipoles. It turns out that the limit of the discrete force is different from Brown''s force formula. One obtains an additional nonlinear surface term which allows one to regard Brown''s assumption on the surface force as a consequence of the atomistic approach. Due to short range effects one obtains moreover an additional linear surface term in the continuum limit of the discrete force. This term contains a certain lattice sum which depends on a hypersingular kernel and the underlying lattice structure. / Das Thema dieser Arbeit ist eine mathematisch strenge Herleitung von Formeln für die magnetische Kraft, die auf einen Teil eines beschränkten, magnetischen Körpers durch seine Umgebung ausgeübt wird. Zunächst wird die magnetische Kraft in einem kontinuierlichen System auf Grundlage der makroskopischen Magnetostatik betrachtet. Mit Bezug auf W. F. Brown, der eine vor allem physikalisch motivierte Herleitung der Kraftformel gegeben hat, wird diese auch Brownsche Kraftformel genannt. Das Oberflächenintegral in dieser Formel zeigt eine nichtlineare Abhängigkeit von der Normalen. Um Cauchys Theorem aus der Kontinuumsmechanik in einem magnetoelastischen Material anwenden zu können, nimmt Brown an, dass die Oberflächenkraft einen zusäatzlichen Term enthält, der den nichtlinearen Ausdruck aufhebt. Der Beweis der Brownschen Kraftformel in dieser Arbeit beruht auf einer geeigneten Regularisierung eines hypersingulären Kerns und benutzt Methoden für singuläre Integrale. Danach gehen wir von einem diskreten, periodischen System von magnetischen Dipolen aus und betrachten die Kraft zwischen einem Teil einer beschränkten Menge und der Umgebung. Um zum Kontinuumslimes überzugehen, starten wir von der üblichen Kraftformel für wechselwirkende magnetische Dipole. Es zeigt sich, dass sich der Limes der diskreten Kraft von der Brownschen Kraftformel unterscheidet. Man erhält einen zusätzlichen nichtlinearen Oberflächenterm, der es ermöglicht, Browns Annahme als Konsequenz des atomistischen Zugangs zu sehen. Kurzreichweitige Effekte führen zudem zu einem linearen Oberflächenterm im Kontinuumlimes der diskreten Kraft. Dieser Zusatzterm enthält eine gewisse Gittersumme, die von einem hypersingulären Kern und der Struktur des zugrundeliegenden Gitters abhängt.

This study focuses on molecular dynamics (MD) simulations, coupled with a discrete mathematical framework, and crystal plasticity (CP) simulations to investigate micro void nucleation and the plastic spin. The origin and historical use of the plastic spin are discussed with particular attention to quantifying the plastic spin at the atomistic scale. Two types of MD simulations are employed: (a) aluminum single crystals undergoing simple shear and (b) aluminum triple junctions (TJ) with varying grain orientations and textures undergoing uniaxial tension. The high-angle grain boundary simulations nucleate micro voids at or around the TJ and the determinant of the deformation gradient shows the ability to predict such events. Crystal plasticity simulations are used to explore the stress-state of the aluminum TJ from uniaxial tension at a higher length scale with results indicating a direct correlation between CP stress-states and the location of micro void nucleation in the MD simulations.

<p>This thesis studies the effect of-floor slabs on the static and dynamic behaviour of the shear wall structure. A single component has been analysed using the 'Matrix Transfer' technique along with Vlaspv's thin walled elastic beam theory. Experimental verification was done on a small scale plexiglas eight storey model in the form of a channel section for both static and dynamic loading. The thesis also deals with the ·analysis of the nonplanar shear walls coupled through floor beams subjected to static loading. The continuum approach along with Vlasov's theory h&s been used in the analysis. Experimental verification was done on a small scale plexiglas model in the form of two equal angles connected by eight floor beams at equal spacing.</p> / Thesis / Master of Engineering (ME)

The structured winds of single massive stars can be classified into two broad groups: stochastic structure and organized structure. While the former is typically identified with clumping, the latter is typically associated with rotational modulations, particularly the paradigm of corotating interaction regions (CIRs). While CIRs have been explored extensively in the ultraviolet band, and moderately in the X-ray and optical, here we evaluate radio variability from CIR structures assuming free-free opacity in a dense wind. Our goal is to conduct a broad parameter study to assess the observational feasibility, and to this end, we adopt a phenomenological model for a CIR that threads an otherwise spherical wind. We find that under reasonable assumptions, it is possible to obtain radio variability at the 10 per cent level. The detailed structure of the folded light curve depends not only on the curvature of the CIR, the density contrast of the CIR relative to the wind, and viewing inclination, but also on wavelength. Comparing light curves at different wavelengths, we find that the amplitude can change, that there can be phase shifts in the waveform, and the entire waveform itself can change. These characterstics could be exploited to detect the presence of CIRs in dense, hot winds.

<p>Rolling contact fatigue (RCF) is a common cause of failure in tribological machine components such as rolling-element bearings (REBs). Steels selected for RCF applications are subject to various material processes in order to produce martensitic microstructures. An effect of such material processing is the retention of the austenitic phase within the steel microstructure. Retained austenite (RA) transformation in martensitic steels subjected to RCF is a well-established phenomenon. In this investigation, a novel approach is developed to predict martensitic transformations of RA in steels subjected to RCF. A criteria for phase transformations is developed by comparing the required thermodynamic driving force for transformations to the energy dissipation in the microstructure. The method combines principles from phase transformations in solids with a damage mechanics framework to calculate energy availability for transformations. The modeling is then extended to incorporate material alterations as a result of RA transforming within the material. A continuum damage mechanics (CDM) FEM simulation is used to capture material deterioration, phase transformations, and the formation of internal stresses as a result of RCF. Crystal lattice orientation is included to modify energy requirements for RA transformation. Damage laws are modified to consider residual stresses and different components of the stress state as the drivers of energy dissipation. The resulting model is capable of capturing microstructural evolution during RCF.</p> <p>The development and stability of internal stresses caused by RA transformation in bearing steel material was experimentally investigated. Specimens of 8620 case carburized steel were subjected to torsional fatigue at specific stress levels for a prescribed number of cycles. X-ray diffraction techniques were used to measure residual stress and RA volume fraction as a function of depth in the material. A model is set forth to predict compressive residual stress in the material as a function of RA transformation and material relaxation. Modeling results are corroborated with experimental data. In addition, varying levels of retained austenite (RA) were achieved through varying undercooling severity in uniformly treated case carburized 8620 steel. Specimens were characterized via XRD and EBSD techniques to determine RA volume fraction and material characteristics prior to rolling contact fatigue (RCF). Higher RA volume fractions did not lead to improvement in RCF lives. XRD measurements after RCF testing indicated that little RA decomposition had occurred during RCF. The previously established RCF simulations were modified to investigate the effects of RA stability on RCF. The results obtained from the CDM FEM captured similar behavior observed in the experimental results. Utilizing the developed model, a parametric study was undertaken to examine the effects of RA quantity, RA stability, and applied pressure on RCF performance. The study demonstrates that the energy requirements to transform the RA phase is critical to RCF performance.</p>

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