Rodney Hill

Bio: Rodney Hill is an academic researcher from University of Cambridge. The author has contributed to research in topics: Uniqueness & Isotropy. The author has an hindex of 46, co-authored 83 publications receiving 41976 citations. Previous affiliations of Rodney Hill include University of Nottingham & University of Bristol.

The Elastic Behaviour of a Crystalline Aggregate

Abstract: The connection between the elastic behaviour of an aggregate and a single crystal is considered, with special reference to the theories of Voigt, Reuss, and Huber and Schmid. The elastic limit under various stress systems is also considered, in particular, it is shown that the tensile elastic limit of a face-centred aggregate cannot exceed two-thirds of the stress at which pronounced plastic distortion occurs.

The mathematical theory of plasticity

Abstract: 1. Introduction 2. Foundations of the thoery 3. General theorems 4. The solution of plastic-elastic problems I 5. The solution of plastic-elastic problems II 6. Plane plastic strain and the theory of the slip-line field 7. Two-dimensional problems of steady motion 8. Non-steady motion problems of steady motion 9. Non-steady motion problems in two dimensions II 10. Axial symmetry 11. Miscellaneous topics 12. Platic anisotropy

Elastic properties of reinforced solids: some theoretical principles

Abstract: The title problem concerns two isotropic phases firmly bonded together to form a mixture with any concentrations. An elementary account of several theoretical methods of attack is given, among them the derivation of inequalities between various moduli. The approach is completely general and exact. Additionally, the problem is fully solved when the phases have equal rigidities but different compressibilities, the geometry being entirely arbitrary.

A theory of the yielding and plastic flow of anisotropic metals

Abstract: A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises' concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Korber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thin-walled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.

A self-consistent mechanics of composite materials

Abstract: T he macroscopic elastic moduli of two-phase composites are estimated by a method that takes account of the inhomogeneity of stress and strain in a way similar to the Hershey-Kroner theory of crystalline aggregates. The phases may be arbitrarily aeolotropic and in any concentrations, but are required to have the character of a matrix and effectively ellipsoidal inclusions. Detailed results arc given for an isotropic dispersion of spheres.

The Elastic Behaviour of a Crystalline Aggregate

Abstract: The connection between the elastic behaviour of an aggregate and a single crystal is considered, with special reference to the theories of Voigt, Reuss, and Huber and Schmid. The elastic limit under various stress systems is also considered, in particular, it is shown that the tensile elastic limit of a face-centred aggregate cannot exceed two-thirds of the stress at which pronounced plastic distortion occurs.

A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks

Abstract: : An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recourse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.

On the ductile enlargement of voids in triaxial stress fields

Abstract: The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. First, a variational principle is established to characterize the flow field in an elastically rigid and incompressible plastic material containing an internal void or voids, and subjected to a remotely uniform stress and strain rate field. Then an approximate Rayleigh-Ritz procedure is developed and applied to the enlargement of an isolated spherical void in a nonhardening material. Growth is studied in some detail for the case of a remote tensile extension field with superposed hydrostatic stresses. The volume changing contribution to void growth is found to overwhelm the shape changing part when the mean remote normal stress is large, so that growth is essentially spherical. Further, it is found that for any remote strain rate field, the void enlargement rate is amplified over the remote strain rate by a factor rising exponentially with the ratio of mean normal stress to yield stress. Some related results are discussed, including the long cylindrical void considered by F.A. McClintock (1968, J. appl. Mech . 35 , 363), and an approximate relation is given to describe growth of a spherical void in a general remote field. The results suggest a rapidly decreasing fracture ductility with increasing hydrostatic tension.

Cenozoic Tectonics of Asia: Effects of a Continental Collision: Features of recent continental tectonics in Asia can be interpreted as results of the India-Eurasia collision.

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