In this dissertation, the finite deformations of a certain class of compressible, isotropic elastic materials are investigated. The class is characterized by a two-parameter family of strain energy functions which includes the well-known Blatz-Ko material model for foam rubbers. The Blatz-Ko material, which has been arrived at by experiment and whose deformations have been studied previously, is obtained from the considered class of materials by specifying one of the two parameters involved in the definition of the class. On employing the semi-inverse method, according to which the form of the solution is given at the outset in terms of functions which are then determined from the equilibrium equations and boundary conditions, closed-form solutions to the equilibrium equations are obtained for the non-homogeneous deformations describing the straightening of a sector of a circular tube, the bending of a rectangular block into a sector of a circular tube, the eversion of cylindrical and spherical shells, and the cylindrical and spherical expansions, and a number of associated boundary value problems are investigated using both analytical and numerical methods. Certain situations in which solutions of the pre-assigned form cannot exist are identified and cases of non-uniqueness are dealt with by discriminating between the different solutions on physical grounds. The homogeneous deformations of the materials in this class are also examined and, throughout, comparison is being made with the behaviour of the Blatz-Ko material. For the whole range of deformations examined, it is found that the materials for which one of the parameters is greater than, or equal to, two (the case when this parameter equals to two corresponds to the Blatz-Ko material) become harder as this parameter increases, but that otherwise they all behave in a similar manner. Consequently, it is concluded that the materials in this particular subclass will also represent foam rubbers of the type described by the Blatz-Ko material. In order to describe the situations in which the solutions become unstable, the conditions for the strong ellipticity of the equilibrium equations for non-linearly elastic materials are reformulated so as to be expressible in terms of the derivatives of the strain-energy function regarded as a function of the principal stretches. Use of these conditions reveals that the solutions to the considered boundary value problems become unstable at certain critical values of the applied loads.

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Fourier transformed amplitudes of the compressional waves recorded between 9° and 91° (about 1000 to 10,000 km) epicentral distance from Gnome, Shoal, Haymaker,and Bilby underground nuclear explosions have been compared with Fourier transformed amplitudes of P waves measured at distances between 9.0 and 1 3. 0 km from the explosions. Using a formula of the type A= ε AoF(ξ)e - πfr/QV apparent Qs have been computed for frequency ranges of 0.5 to 1.0 cps and 0.7 to 1.0 cps at the various epicentral distances. The geometrical spreading factor F(ξ) and interface loss parameter ε drop out of the computations when assumed to be frequency independent in the narrow frequency pass-bands considered. The computed apparent Q values indicate that the mantle is inhomogeneous with respect to the absorption of seismic energy. Relatively low Q (high absorption) regions are centered around 25°, 42° and 74° and high Q (low absorption) regions are centered around 20°, 31°, 71°, and 78° epicentral distances. These are superimposed on a gradually increasing Q with epicentral distance trend. The average apparent Q value for the upper mantle is found to be 286 ± 38. The highest Q value of this study occurs between 78° and 80° epicentral distance where it is greater than 3000. The high and low Q values obtained in this investigation are of the same order of magnitude as those reported by other investigators from body wave studies and the general variation of the absorption properties with depth agrees reasonably well with those obtained from surface wave studies. The depth of great increase in electrical conductivity and the observed maximum depth of earthquake foci both agree roughly with a region of large increase in Q in the upper mantle. A relatively high absorption zone is found to occur below this depth. / Graduation date: 1967

Typescript (photocopy) / vi, 225 leaves : ill. ; 30 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 Applied Mathematics, 1981

ix, 99 leaves : ill., tables ; 30 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 Applied Mathematics, 1978

Typescript (photocopy) / vi, 225 leaves : ill. ; 30 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 Applied Mathematics, 1981