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Author: Nicholas W. Tschoegl
Publisher: Springer Science & Business Media
ISBN: 3642736025
Category : Science
Languages : en
Pages : 791
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Book Description
One of the principal objects of theoretical research in any department of knowledge is to find the point of view from which the subject appears in its greatest simplicity. J. Willard Gibbs This book is an outgrowth of lectures I have given, on and off over some sixteen years, in graduate courses at the California Institute of Technology, and, in abbreviated form, elsewhere. It is, nevertheless, not meant to be a textbook. I have aimed at a full exposition of the phenomenological theory of linear viscoelastic behavior for the use of the practicing scientist or engineer as well as the academic teacher or student. The book is thus primarily a reference work. In accord with the motto above, I have chosen to describe the theory of linear viscoelastic behavior through the use of the Laplace transformation. The treatment oflinear time-dependent systems in terms of the Laplace transforms of the relations between the excitation add response variables has by now become commonplace in other fields. With some notable exceptions, it has not been widely used in viscoelasticity. I hope that the reader will find this approach useful.
Author: Nicholas W. Tschoegl
Publisher: Springer Science & Business Media
ISBN: 3642736025
Category : Science
Languages : en
Pages : 791
Get Book Here
Book Description
One of the principal objects of theoretical research in any department of knowledge is to find the point of view from which the subject appears in its greatest simplicity. J. Willard Gibbs This book is an outgrowth of lectures I have given, on and off over some sixteen years, in graduate courses at the California Institute of Technology, and, in abbreviated form, elsewhere. It is, nevertheless, not meant to be a textbook. I have aimed at a full exposition of the phenomenological theory of linear viscoelastic behavior for the use of the practicing scientist or engineer as well as the academic teacher or student. The book is thus primarily a reference work. In accord with the motto above, I have chosen to describe the theory of linear viscoelastic behavior through the use of the Laplace transformation. The treatment oflinear time-dependent systems in terms of the Laplace transforms of the relations between the excitation add response variables has by now become commonplace in other fields. With some notable exceptions, it has not been widely used in viscoelasticity. I hope that the reader will find this approach useful.
Author: D. R. Bland
Publisher: Courier Dover Publications
ISBN: 0486816389
Category : Technology & Engineering
Languages : en
Pages : 145
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Book Description
This concise introduction to the concepts of viscoelasticity focuses on stress analysis. Three detailed sections present examples of stress-related problems, including sinusoidal oscillation problems, quasi-static problems, and dynamic problems. 1960 edition.
Author: Mauro Fabrizio
Publisher: SIAM
ISBN: 0898712661
Category : Science
Languages : en
Pages : 210
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Book Description
Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.
Author: John M. Golden
Publisher: Springer Science & Business Media
ISBN: 3662061562
Category : Science
Languages : en
Pages : 276
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Book Description
The classical theories of Linear Elasticity and Newtonian Fluids, though trium phantly elegant as mathematical structures, do not adequately describe the defor mation and flow of most real materials. Attempts to characterize the behaviour of real materials under the action of external forces gave rise to the science of Rheology. Early rheological studies isolated the phenomena now labelled as viscoelastic. Weber (1835, 1841), researching the behaviour of silk threats under load, noted an instantaneous extension, followed by a further extension over a long period of time. On removal of the load, the original length was eventually recovered. He also deduced that the phenomena of stress relaxation and damping of vibrations should occur. Later investigators showed that similar effects may be observed in other materials. The German school referred to these as "Elastische Nachwirkung" or "the elastic aftereffect" while the British school, including Lord Kelvin, spoke ofthe "viscosityofsolids". The universal adoption of the term "Viscoelasticity", intended to convey behaviour combining proper ties both of a viscous liquid and an elastic solid, is of recent origin, not being used for example by Love (1934), though Alfrey (1948) uses it in the context of polymers. The earliest attempts at mathematically modelling viscoelastic behaviour were those of Maxwell (1867) (actually in the context of his work on gases; he used this model for calculating the viscosity of a gas) and Meyer (1874).
Author: R. M. Christensen
Publisher: Courier Corporation
ISBN: 0486318966
Category : Technology & Engineering
Languages : en
Pages : 386
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Book Description
Integration of theoretical developments offers complete description of linear theory of viscoelastic behavior of materials, with theoretical formulations derived from continuum mechanics viewpoint and discussions of problem solving. 1982 edition.
Author: Wilhelm Flügge
Publisher: Springer Science & Business Media
ISBN: 3662022761
Category : Technology & Engineering
Languages : en
Pages : 204
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Book Description
No mathematical theory can completely describe the complex world around us. Every theory is aimed at a certain class of phenomena, formulates their essential features, and disregards what is of minor importance. The theory meets its limits of applicability where a dis regarded influence becomes important. Thus, rigid-body dynamics describes in many cases the motion of actual bodies with high accu racy, but it fails to produce more than a few general statements in the case of impact, because elastic or anelastic deformation, no matter how local or how small, attains a dominating influence. For a long time mechanics of deformable bodies has been based upon Hooke's law - that is, upon thE" assumption of linear elasticity. It was well known that most engineering materials like metals, con crde, wood, soil, are not linearly elastic or, are so within limits too narrow to cover tne range of pl'actical intcrest. Nevertheless, almost all routine stress analysis is still based on Hooke T s law be cause of its simplicity. In the course of time engineers have become increasingly con scious of the importance of the anelastic behavior of many materials, and mathematical formulations have been attempted and applied to practical problems. Outstanding among them are the theories of ide ally plastic and of viscoelastic materials. While plastic behavior is essentially nonlinear (piecewise linear at best), viscoelasticity, like elasticity, permits a linear theory. This theory of linear visco elasticity is the subject of tbe present book.
Author: Francesco Mainardi
Publisher: World Scientific
ISBN: 1908978570
Category : Mathematics
Languages : en
Pages : 368
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Book Description
This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types.It is intended to serve as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature given in the huge general bibliography.This book is likely to be of interest to applied scientists and engineers./a
Author: William N. Findley
Publisher: Courier Corporation
ISBN: 0486145174
Category : Technology & Engineering
Languages : en
Pages : 402
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Book Description
This pioneering book presents the basic theory, experimental methods, experimental results and solution of boundary value problems in a readable, useful way to designers as well as research workers and students. The mathematical background required has been kept to a minimum and supplemented by explanations where it has been necessary to introduce specialized mathematics. Also, appendices have been included to provide sufficient background in Laplace transforms and in step functions. Chapters 1 and 2 contain an introduction and historic review of creep. As an aid to the reader a background on stress, strain, and stress analysis is provided in Chapters 3 and 4, an introduction to linear viscoelasticity is found in Chapter 5 and linear viscoelastic stress analysis in Chapter 6. In the next six chapters the multiple integral representation of nonlinear creep and relaxation, and simplifications to single integral forms and incompressibility, are examined at length. After a consideration of other representations, general relations are derived, then expanded to components of stress or strain for special cases. Both constant stress (or strain) and variable states are described, together with methods of determining material constants. Conversion from creep to relaxation, effects of temperature and stress analysis problems in nonlinear materials are also treated here. Finally, Chapter 13 discusses experimental methods for creep and stress relaxation under combined stress. This chapter considers especially those experimental problems which must be solved properly when reliable experimental results of high precision are required. Six appendices present the necessary mathematical background, conversion tables, and more rigorous derivations than employed in the text. An extensive updated bibliography completes the book.
Author: Eduard Starovoitov
Publisher: CRC Press
ISBN: 1926895118
Category : Science
Languages : en
Pages : 366
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Book Description
Foundations of the Theory of Elasticity, Plasticity, and Viscoelasticity details fundamental and practical skills and approaches for carrying out research in the field of modern problems in the mechanics of deformed solids, which involves the theories of elasticity, plasticity, and viscoelasticity. The book includes all modern methods of research as well as the results of the authors’ recent work and is presented with sufficient mathematical strictness and proof. The first six chapters are devoted to the foundations of the theory of elasticity. Theory of stress-strain state, physical relations and problem statements, variation principles, contact and 2D problems, and the theory of plates are presented, and the theories are accompanied by examples of solving typical problems. The last six chapters will be useful to postgraduates and scientists engaged in nonlinear mechanics of deformed inhomogeneous bodies. The foundations of the modern theory of plasticity (general, small elastoplastic deformations and the theory of flow), linear, and nonlinear viscoelasticity are set forth. Corresponding research of three-layered circular plates of various materials is included to illustrate methods of problem solving. Analytical solutions and numerical results for elastic, elastoplastic, lineaer viscoelastic and viscoelastoplastic plates are also given. Thermoviscoelastoplastic characteristics of certain materials needed for numerical account are presented in the eleventh chapter. The informative book is intended for scientists, postgraduates and higher-level students of engineering spheres and will provide important practical skills and approaches.
Author: Allen C. Pipkin
Publisher: Springer Science & Business Media
ISBN: 1461599709
Category : Mathematics
Languages : en
Pages : 190
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Book Description
This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely de tailed explanation. Furthermore, much of the content of the course is in the prob lems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not given, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA~, 291(1962)) remains the best reference for proofs of theorems.
