Preliminary reference earth model

A unified treatment of the mechanics of deformation and acoustic propagation in porous media is presented, and some new results and generalizations are derived. The writer's earlier theory of deformation of porous media derived from general principles of nonequilibrium thermodynamics is applied. The fluid‐solid medium is treated as a complex physical‐chemical system with resultant relaxation and viscoelastic properties of a very general nature. Specific relaxation models are discussed, and the general applicability of a correspondence principle is further emphasized. The theory of acoustic propagation is extended to include anisotropic media, solid dissipation, and other relaxation effects. Some typical examples of sources of dissipation other than fluid viscosity are considered.

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Mechanics of deformation and acoustic propagation in porous media

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 theory of the yielding and plastic flow of anisotropic metals

Micro-structure in linear elasticity

The Classical Field Theories

The present treatise is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity. He has unfortunately found himself unable to proceed with it, and I have therefore been obliged to take upon myself the whole of the work and the whole of the responsibility. I wish to acknowledge at the outset the debt that I owe to him as a teacher of the subject, as well as my obligation for many valuable suggestions chiefly with reference to the scope and plan of the work, and to express my regret that other engagements have prevented him from sharing more actively in its production.

The division of the subject adopted is that originally made by Clebsch in his classical treatise, where a clear distinction is ill-awn between exact solutions for bodies all whose dimensions are finite and approximate solutions for bodies some of whose dimensions can be regarded as infinitesimal. The present volume contains the general mathematical theory of the elastic properties of the first class of bodies, and I propose to treat the second class in another volume. At Mr Webb's suggestion, the exposition of the theory is preceded by an historical sketch of its origin and development. Anything like an exhaustive history has been rendered unnecessary by the work of the late Dr Todhunter as edited by Prof Karl Pearson, but it is hoped that the brief account given will at once facilitate the comprehension of the theory and add to its interest.

Readers of the historical work referred to will appreciate the difficulty of giving within a reasonable compass a complete account of all the valuable researches that have been made; and the aim of this book is rather to present a connected account of the theory in its present state, and an indication of the way in which that state has been attained, avoiding on the one hand merely analytical developments, and on the other purely technical details.

https://hal.archives-ouvertes.fr/hal-01307751/document

A treatise on the mathematical theory of elasticity

The Mathematical Theory of Elasticity.

Some Problems of Geodynamics

The first three Chapters deal with the problem of determining the Stress produced in the Interior of the Earth by the Weight of Continents and Mountains. Chapter I contains a brief discussion of the distribution of land and water on the surface of the globe. This discussion is designed to evaluate roughly the amplitudes of those spherical harmonic inequalities which are most prominent in the shape of the lithosphere. By the lithosphere is here meant the surface of the land in places where there is land, and the surface at the bottom of the sea in places where there is sea. The most important deviation of this surface from a spherical form is the inequality specified by the ellipticity of the meridians; but this inequality is without influence upon the distribution of land and water, for the lithosphere and the surface of the sea both have elliptic meridians, and the difference of their ellipticities is trifling. After the ellipticity of the meridians the most prominent inequalities are those which are manifested in the existence of a single continental block, embracing all the continents, and surrounding two great areas of depression, the basin of the Pacific Ocean and the basin of the Atlantic and Indian Oceans, the portions of the Southern Ocean which lie to the south of these oceans respectively being counted as parts of them. The inequalities manifested in mountain ranges and deeps have not nearly so much importance in regard to the figure of the Earth as a whole. In Chapter I it is explained how the shape of the lithosphere could, if the elevation or depression of every point above or below a mean level were known accurately, be expressed by equating the radius vector, which joins the centre of gravity and a point of assigned latitude and longitude, to a sum of spherical surface harmonics, which are definite functions of the latitude and longitude, each provided with a suitable coefficient. Further it is shown, on the basis of previous work by the writer, that the inequalities manifested in the continental block and ocean basins may be represented roughly by restricting the sum in question to harmonics of the first, second, and third degrees. It appears that the elevations and depressions answering to the first and third harmonics are nearly equal, the third slightly the greater, and greater than those answering to the second harmonic ; and that

Some Problems of Geodynamics; Being an Essay to Which the Adams Prize in the University of Cambridge Was Adjudged in 1911

Mots-clefs: Elasticite ; Statique Reference Notice creee le 2004-09-07, modifiee le 2016-08-08

Augustus Edward Hough Love

Papers

A treatise on the mathematical theory of elasticity

The Mathematical Theory of Elasticity.

Some Problems of Geodynamics

Some Problems of Geodynamics; Being an Essay to Which the Adams Prize in the University of Cambridge Was Adjudged in 1911

A treatise on the mathematical theory