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Thesis (Ph.D.)--University of Nebraska-Lincoln, 2006. / Title from title screen (site viewed on Mar. 13, 2007). PDF text: xxi, 171, p. : col. ill. UMI publication number: AAT 3225793. Includes bibliographical references. Also available in microfilm and microfiche format.

In this dissertation, we present the Slattery-Oh-Fu theory extending continuum mechanics to the nanoscale and its applications. We begin with an analysis of supercritical adsorption of argon, krypton, and methane on Graphon before we fully develop the theory. We compare our results both with existing experimental data and with prior molecular-based theories. Then, we present the general theory, which is based upon a long history of important developments beginning with Hamaker (1937). In the context of continuum mechanics, nanoscale problems always involve the immediate neighborhood of a phase interface or the immediate neighborhood of a three-phase line of contact or common line. We test this theory by using it to predict both the surface tensions of the n-alkanes and the static contact angles for the n-alkanes on PTFE and for several liquids on PDMS. For the contact angle predictions, the results are compatible with previously published experimental data. The results for the contact angle analysis also provide a successful test of a previously derived form of Young??s equation for the true, rather than apparent, common line. We also studied Mode I fracture at nanoscale. While we don??t have experimental data to compare, we get reasonable crack configuration and avoid stress singularity at the crack tip. Coalescence problems are revisited to explore the retardation effects in the computation of intermolecular forces. We get good agreement with experimental results. We conclude with a confidence that this theory can be used as a bridge between continuum mechanics and other molecular-based methods.

Thesis (Ph.D.) in Physics--University of Maine, 2007. / Includes vita. Includes bibliographical references (leaves 118-129).

Thesis (M.S.)--Tennessee Technological University, 2009. / Title from title page screen (viewed on Mar. 18, 2010). Bibliography: leaves 69-72.

Thesis (M.Phil.) - University of Queensland, 2004. / Includes bibliographical references.

The thesis divides naturally into two parts. Part I raises, and in some cases answers, questions concerning symmetry in classical mechanics. The main result (Theorem 6.4) shows that the assumption of the existence of a realization puts an upper limit on the rank of the algebra. The heart of the thesis (covering three-quarters of the volume) is section II on the quantization of classical systems. §1 lists axioms desirable in any quantization rule for the 'functions of the q's'. The momentum observables are introduced in §2 prior to their quantization in §4. §5 essentially shows how conventional quantum mechanics fits into this scheme of things. By progressive specialization from a general manifold to a vector space, from a general quantization scheme to one which is linear on the linear momentum functions, and finally to an entirely well-behaved (admissible) quantization rule, into which conventional quantum mechanics fits nicely, we obtain in §7-§9 results which become progressively more and more powerful. The final theorem (Theorem 9.2) is perhaps the most significant of all. This result states that there exists a class of functions, which contains all functions of the q's and functions of the p's and all momentum observables and which is closed with respect to any linear canonical transformation L; a rule A assigning a unique self-adjoint operator to each such function f; a unitary operator WL corresponding to L and an equation ̧›Ơ(̧‘“ ́˜˜ ̧¿) = ̧‘Š[sub]̧¿́» ̧›Ơ ̧‘“ ̧‘Š[sub]̧¿.

The propagation of stress waves in long polymer rods forms the basis of two major experimental techniques. The first is a modified Split-Hopkinson pressure bar (SHPB) arrangement that employs polymer Hopkinson bars (as opposed to metallic bars) in order to determine the high strain-rate mechanical properties of soft materials. The second experimental technique consists of a group of methods for determining the viscoelastic properties of polymer rods within a frequency range of 20 Hz to 30 kHz. An experimental, analytical and finite element study of stress waves propagating in viscoelastic rods is reported. A propagation coefficient is used to account for the attenuation and dispersion of stress waves propagating in polymer rods. Through experimental investigations, an optimal experimental arrangement is used to determine the propagation coefficient of a PMMA rod with an improved level of accuracy in comparison with results available in the open literature. Analytical investigations show difficulties associated with experimental arrangements as well as the numerical procedure adopted which tend to reduce the accurate frequency range of the determined propagation coefficient. The FE analysis of stress waves propagating in polymer rods suggests end effects are important; these end effects are not accounted for in any analytical bar wave theory. The high strain-rate mechanical properties of Hydroxyl-terminated polybutadiene (HTPB) are measured via a viscoelastic SHPB set-up. A scheme for processing the strain signals from the tests that allows for large strain measurement (approximately 60%) is presented. The use of viscoelastic SHPB set-up is able to produce a more sensitive measurement when compared with test results in the literature which are obtained using conventional metallic bars. A Finite element model of a viscoelastic Hopkinson bar set-up is developed. The applicability of the model in viscoelastic SHPB testing is validated.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2002. / Includes bibliographical references (p. 113-119).

The energy convergence of mixed methods of approximate analysis for problems involving linear self-adjoint operators is investigated. A new energy product and the associated energy norm are defined for such indefinite systems and then used in establishing the strain energy convergence and estimation of error for problems in continuum mechanics. In the process, the completeness requirements are laid out for approximate solutions. Also established is the mean convergence of the basic variable e.g. displacements and stresses. After accomplishing a new mathematical framework for the mixed methods in continuum, the theory is then extended to the finite element method. The completeness requirements, convergence criteria and the effect of continuity requirements on convergence are established. The flexibility offered by the mixed methods in incorporating the boundary con ditions is also demonstrated. For stress singular problems, the strain energy convergence is established and an energy release method for determining the crack intensity factor K. is presented. A detailed eigenvalue-eigenvector analysis of the mixed finite element matrix is carried out for various combinations of interpolations for the plane stress linear elasticity and the linear part of the Navier-Stokes equations. Also discussed is its relation to the completeness requirements. Finally, numerical results are obtained from applying the mixed finite element method to several examples. These include beam bending, a plane stress square plate with parabolically varying end loads, a plane stress cantilever and plane strain stress concentration around a circular hole. A plane stress example of a square plate with symmetric edge cracks is also solved to study the strain energy convergence. Lastly, two rectangular plates, one with symmetric edge cracks and the other with a central crack are considered to determine the crack intensity factor K. In most of the examples, the strain energy convergence rates are predicted and compared with the numerical results, and excellent agreement is observed. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate