This thesis presents research into the micromechanical modelling of composite materials using numerical techniques. Composite materials are generally examined from two points of view: macromechanics and micromechanics, owing to their inherent heterogeneous nature. In this research, the material behaviour is examined on a microscopic scale, as the properties of interest, i.e. strength and toughness, are dependent on local phenomena. In general, the strength and toughness of composite materials are not as well understood as the simpler elastic properties, because in many cases the modes of failure under a given system of external load are not predictable in advance. Previous research in this field has typically involved specially designed experiments, theoretical/statistical studies, or the use of numerical models. In this study, advanced implementations of numerical methods in continuum mechanics, i.e. the boundary element and the finite element methods are employed to gain a greater understanding of composite behaviour. The advantage of using numerical methods, as opposed to experimental studies, is that the geometric and material characteristics can be investigated parametrically, in addition to the reduced time and expense involved. However, to model the complete behaviour of real composites is still not possible, due to the degree of complexity and uncertainty involved in modelling the various mechanisms of damage and failure, etc. and also due to the immense computational cost. Therefore, simplified models must be employed which are limited by their assumptions. For the preliminary studies within this thesis, geometrically simplified models are presented to provide an understanding of the influence of embedding second phase inclusions on the local stress fields, and also to validate the numerical techniques with readily available analytical solutions. These models are then extended to accommodate additional phenomena, such as inclusion interaction, spatial inclusion arrangement, material formulation, i.e. consisting of two- and three-phases of various material properties. The influence of such factors on the local stress concentrations, which play an important role in determining the strength of the composite, is analysed through a series of parametric studies. The localised toughening of composites is also considered through novel investigations into the interaction between a propagating crack with inclusions and microcracks. Through the development of the numerical models a more realistic representation of composite behaviour is achieved, which in tum, provides an improved knowledge of the factors that control strength and toughness. Such information is invaluable to composite material designers, who presently rely heavily on experimental studies to develop composite materials.

This thesis investigates the integrability of the sine-Gordon system of nonlinear partial differential equations when the dependent variables are subject to some very particular boundary conditions. In chapter 1 the sine-Gordon system is introduced and, with N ϵ Z, P, Q ϵ R, the sets of initial-boundary value problems A(_N) and B(_P,Q) are defined. In the set A(_N) at the spatial variable x is unbounded and the boundary conditions are fixed by initially choosing the topological charge N. This set of problems is the one usually associated with the sine-Gordon system. In the set B(_P,Q) the spatial coordinate is constrained to the semi-line (-oo,0) and there exists two boundary parameters P,Q ϵ R to be chosen a priori. It is the study of this second set of initial-boundary value problems for arbitrary P, Q which forms all the original work of this dissertation. The study presented here is primarily concerned with the development of three separate inverse scattering methods for solving these sets of initial-boundary value problems. The first of these is developed in chapter 3 and is applicable to a subset of the problems in A(_N). The method is the one usually associated with the sine-Gordon system and studies the asymptotics of the initial data as x → ±oo. It is included in this thesis for completeness and as background for the original material which follows. Next, in chapters 4 and 5, the inverse scattering methods appropriate to initial-boundary value problems in subsets of B(_P,O) and B(_P,Q#O) are constructed. In these cases it is important to realise that it is only possible to study the asymptotics of the initial data as x → -oo. Once these three methods have been formulated they are used to find soliton solutions and infinite sets of integrals of motion for these boundary value problems. When a boundary is present at x = 0 the interaction of the solitons with this boundary is studied. These topics are addressed in chapter 6. Finally in chapter 7 the question of the integrability of both sets of problems is addressed. By interpreting the various inverse scattering methods in terms of canonical coordinate transformations of phase space it is seen that the existence of such methods can be viewed as a constructive proof of the integrability of these boundary value problems.

No description available.

Graduation date:1978

Graduation date: 1981

Bibliography: leaves 201-207. / xxvi, 207 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis presents studies of the non-linear mass-transfer kinetics and a linear analysis of the hydrodynamic stability of systems under conditions of intense interfacial mass transfer. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2001

iv, 124 leaves ; 31 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1977

x, 97 leaves : ill., reprint / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematics, 1972

Thesis (M.S.)--Virginia Polytechnic Institute, 1966. / Vita. Abstract. Includes bibliographical references (leaves 23-24). Also available via the Internet.

Thesis (Ph. D.)--Oregon State University, 1989. / Typescript (photocopy). Includes bibliographical references. Also available on the World Wide Web.