Mechanics of Elastic and Inelastic Solids – Serie

This book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and re­ searchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materi­ als: plasticity, fracture and fatigue, constitutive equations, composite materi­ als, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method. ' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.

"During the last two decades, research on structural optimization became increasingly concerned with two aspects: the application of general numeri- cal methods of optimization to structural design of complex real structures, and the analytical derivation of necessary and sufficient conditions for the optimality of broad classes of comparatively simple and more or less ideal- ized structures. Both kinds of research are important: the first for obvious reasons; the second, because it furnishes information that is useful in testing the validity, accuracy and convergence of numerical methods and in assess- ing the efficiency of practical designs. " (Prager and Rozvany, 1977a) The unexpected death of William Prager in March 1980 marked, in a sense, the end of an era in structural mechanics, but his legacy of ideas will re- main a source of inspiration for generations of researchers to come. Since his nominal retirement in the early seventies, Professor and Mrs. Prager lived in Savognin, an isolated alpine village and ski resort surrounded by some of Switzerland's highest mountains.It was there that the author's close as- sociation with Prager developed through annual pilgrimages from Australia and lengthy discussions which pivoted on Prager's favourite topic of struc- tural optimization. These exchanges took place in the picturesque setting of Graubunden, on the terrace of an alpine restaurant overlooking snow-capped peaks, on ski-lifts or mountain walks, or during evening meals in the cosy hotels of Savognin, Parsonz and Riom.

The present book is the result of work carried out over a period of about ten years by the author and his co-workers in order to describe more accurately the slow irreversible deformation in time of the rocks surrounding underground openings. To begin with, our efforts were directed toward a better under­ standing of the mechanical behaviour of rocks and to the formulation of more precise mathematical models for their dominant mechanical properties, mainly irreversible dilatancy and/or compressibility during creep. Subsequent efforts were focused on finding improved solutions to important mining and oil engineering problems, such as, for instance, the creep of rocks around wells and tunnels, short-term failure which may occur around an underground opening, damage and failure which take place after long-time intervals, the tunnel support analysis incorporating rock creep, etc. The book is the result of a great number of questions posed either by mining engineers or by the author himself, and of the corresponding answers (unfor­ tunately often only partial answers). This dialogue must certainly be continued in order to improve the models and to formulate models for other kinds of rocks, or, ultimately to obtain solutions for other important engineering problems. It is hoped that the book will also contribute to a better description, by means of mathematical models, of the mechanical behaviour of rocks.

This book contains the proceedings of a workshop on the Theoretical Founda­ tion for Large-Scale Computations of Nonlinear Material Behavior, held under the auspices of the National Science Foundation (NSF) and the Defense Advance Re­ search Projects Agency (DARPA), at Northwestern University, October 24-26, 1983. The main objective of this workshop was to provide a forum for the exchange of information and views on major issues relating to the fundamentals of character­ izing the inelastic constitutive material behavior. Comments on the Aims of the Workshop, by Drs. William Snowden and Thomas Bache, pp. 1-5, outline reasons for holding this workshop, and provide further background. The format of the workshop was designed to optimize the interaction between researchers whose primary interest is material characterization and numerical analysts whose primary interest is the development and practical use of large computer codes. The program of the workshop and a list of the workshop partic­ ipants are found at the end of these proceedings.

In this monograph I record those parts of the theory of transverse isotropic elastic wave propagation which lend themselves to an exact treatment, within the framework of linear theory. Emphasis is placed on transient wave motion problems in two- and three-dimensional unbounded and semibounded solids for which explicit results can be obtained, without resort to approximate methods of integration. The mathematical techniques used, many of which appear here in book form for the first time, will be of interest to applied mathematicians, engeneers and scientists whose specialty includes crystal acoustics, crystal optics, magnetogasdynamics, dislocation theory, seismology and fibre wound composites. My interest in the subject of anisotropic wave motion had its origin in the study of small deformations superposed on large deformations of elastic solids. By varying the initial stretch in a homogeneously deformed solid, it is possible to synthesize aniso­ tropic materials whose elastic parameters vary continuously. The range of the parameter variation is limited by stability considerations in the case of small deformations super­ posed on large deformation problems and (what is essentially the same thing) by the of hyperbolicity (solids whose parameters allow wave motion) for anisotropic notion solids. The full implication of hyperbolicity for anisotropic elastic solids has never been previously examined, and even now the constraints which it imposes on the elasticity constants have only been examined for the class of transversely isotropic (hexagonal crystals) materials.

Hydraulic fracturing has been and continues to be a major techno­ logical tool in oil and gas recovery, nuclear and other waste disposal, mining and particularly in-situ coal gasification, and, more recently, in geothermal heat recovery, particularly extracting heat from hot dry rock masses. The understanding of the fracture process under the ac­ tion of pressurized fluid at various temperatures is of fundamental scientific importance, which requires an adequate description of thermomechanical properties of subsurface rock, fluid-solid interaction effects, as well as degradation of the host rock due to temperature gradients introduced by heat extraction. Considerable progress has been made over the past several years in laboratory experiments, analytical and numerical modeling, and in-situ field studies in various aspects of hydraulic fracturing and geothermal energy extraction, by researchers in the United States and Japan and also elsewhere. However, the results have been scattered throughout the literature. Therefore, the time seemed ripe for bringing together selected researchers from the two countries, as well as observers from other countries, in order to survey the state of the art, exchange scientific information, and establish closer collaboration for further, better coordinated scientific effort in this important area of research and exploration.

"During the last two decades, research on structural optimization became increasingly concerned with two aspects: the application of general numeri- cal methods of optimization to structural design of complex real structures, and the analytical derivation of necessary and sufficient conditions for the optimality of broad classes of comparatively simple and more or less ideal- ized structures. Both kinds of research are important: the first for obvious reasons; the second, because it furnishes information that is useful in testing the validity, accuracy and convergence of numerical methods and in assess- ing the efficiency of practical designs. " (Prager and Rozvany, 1977a) The unexpected death of William Prager in March 1980 marked, in a sense, the end of an era in structural mechanics, but his legacy of ideas will re- main a source of inspiration for generations of researchers to come. Since his nominal retirement in the early seventies, Professor and Mrs. Prager lived in Savognin, an isolated alpine village and ski resort surrounded by some of Switzerland's highest mountains.It was there that the author's close as- sociation with Prager developed through annual pilgrimages from Australia and lengthy discussions which pivoted on Prager's favourite topic of struc- tural optimization. These exchanges took place in the picturesque setting of Graubunden, on the terrace of an alpine restaurant overlooking snow-capped peaks, on ski-lifts or mountain walks, or during evening meals in the cosy hotels of Savognin, Parsonz and Riom.