Download or read book Mathematical Problems in Viscoelasticity written by Michael Renardy and published by Longman Scientific and Technical. This book was released on 1987 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Problems in Linear Viscoelasticity written by Mauro Fabrizio and published by SIAM. This book was released on 1992-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Boundary Value Problems in Linear Viscoelasticity written by John M. Golden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity written by Weimin Han and published by American Mathematical Soc.. This book was released on 2002 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Índice: Function spaces and their properties; Introduction to finite difference and finite element approximations; Variational inequalities; Constitutive relations in solid mechanics; Background on variational and numerical analysis in contact mechanics; Contact problems in elasticity; Bilateral contact with slip dependent friction; Frictional contact with normal compliance; Frictional contact with normal damped response; Other viscoelastic contact problems; Frictionless contact with dissipative potential; Frictionless contact between two viscoplastic bodies; Bilateral contact with Tresca's friction law; Other viscoelastic contact problems; Bibliography; Index.
Download or read book Stability in Viscoelasticity written by A.D. Drozdov and published by Elsevier. This book was released on 2013-10-22 with total page 623 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of stability problems for viscoelastic solids and elements of structures, with which this book is concerned, has been the focus of attention in the past three decades. This has been due to the wide inculcation of viscoelastic materials, especially polymers and plastics, in industry. Up-to-date studies in viscoelasticity are published partially in purely mathematical journals, partially in merely applied ones, and as a consequence, they remain unknown to many interested specialists. Stability in Viscoelasticity fills the gap between engineers and mathematicians and converges theoretical and applied directions of investigations. All chapters contain extensive bibliographies of both purely mathematical and engineering works on stability problems. The bibliography includes a number of works in Russian which are practically inaccessible to the Western reader.
Download or read book Mathematical Analysis of Viscoelastic Flows written by Michael Renardy and published by SIAM. This book was released on 2000-01-01 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.
Download or read book Viscoelasticity and Rheology written by Arthur S. Lodge and published by Academic Press. This book was released on 2014-06-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Viscoelasticity and Rheology covers the proceedings of a symposium by the same title, conducted by the Mathematics Research Center held at the University of Wisconsin-Madison on October 16-18, 1984. The contributions to the symposium are divided into four broad categories, namely, experimental results, constitutive theories, mathematical analysis, and computation. This 16-chapter work begins with experimental topics, including the motion of bubbles in viscoelastic fluids, wave propagation in viscoelastic solids, flows through contractions, and cold-drawing of polymers. The next chapters covering constitutive theories explore the molecular theories for polymer solutions and melts based on statistical mechanics, the use and limitations of approximate constitutive theories, a comparison of constitutive laws based on various molecular theories, network theories and some of their advantages in relation to experiments, and models for viscoplasticity. These topics are followed by discussions of the existence, regularity, and development of singularities, change of type, interface problems in viscoelasticity, existence for initial value problems and steady flows, and propagation and development of singularities. The remaining chapters deal with the numerical simulation of flow between eccentric cylinders, flow around spheres and bubbles, the hole pressure problem, and a review of computational problems related to various constitutive laws. This book will prove useful to chemical engineers, researchers, and students.
Download or read book Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models written by Francesco Mainardi and published by World Scientific. This book was released on 2010-05-18 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Viscoelasticity written by Wilhelm Flügge and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on Viscoelasticity Theory written by Allen C. Pipkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on Viscoelasticity Theory written by A.C. Pipkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 detailed explanation. Furthermore, much of the content of the course is in the problems 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 give, 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 II, 291 (I962» remains the best reference for proofs of theorems.
Download or read book Creep and Relaxation of Nonlinear Viscoelastic Materials written by William N. Findley and published by Courier Corporation. This book was released on 2013-01-15 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Understanding Viscoelasticity written by Nhan Phan-Thien and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the necessary background for understanding viscoelasticity is covered; both the continuum and microstructure approaches to modelling viscoelastic materials are discussed, since neither approach alone is sufficient.
Download or read book Numerical Analysis of Viscoelastic Problems written by Patrick Le Tallec and published by . This book was released on 1990-01-01 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of computing the deformations of viscoelastic, viscoplastic or elastoplastic bodies is of great relevance to practical problems e.g. in the numerical modelling of viscoelastic structures of hot metal forming or of polymer melt flows. This book shows how such practical engineering problems may be written as standard problems of functional analysis and how this mathematical framework is used for their analysis and numerical solution. The author looks at the mechanical and the mathematical problem in a unified context, especially for the case of nonlinear Maxwell problems, and gives a mixed discrete formulation for viscoelastic flow problems. Some classical numerical strategies are described as extensions of the mathematical theory. The treatment is restricted to small strain situations (with an introduction to the large strain problem at the end) and to constitute laws of differential type, and will be of interest to researchers and graduate students in mechanical engineering, computer science and applied mathematics.
Download or read book Viscoelastic Materials written by Roderic S. Lakes and published by Cambridge University Press. This book was released on 2009-04-27 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate text on viscoelastic materials addresses design applications as diverse as earplugs, computer disks and medical diagnostics.
Download or read book Polymer Engineering Science and Viscoelasticity written by Hal F. Brinson and published by Springer. This book was released on 2015-01-24 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified mechanics and materials perspective on polymers: both the mathematics of viscoelasticity theory as well as the physical mechanisms behind polymer deformation processes. Introductory material on fundamental mechanics is included to provide a continuous baseline for readers from all disciplines. Introductory material on the chemical and molecular basis of polymers is also included, which is essential to the understanding of the thermomechanical response. This self-contained text covers the viscoelastic characterization of polymers including constitutive modeling, experimental methods, thermal response, and stress and failure analysis. Example problems are provided within the text as well as at the end of each chapter. New to this edition: · One new chapter on the use of nano-material inclusions for structural polymer applications and applications such as fiber-reinforced polymers and adhesively bonded structures · Brings up-to-date polymer production and sales data and equipment and procedures for evaluating polymer characterization and classification · The work serves as a comprehensive reference for advanced seniors seeking graduate level courses, first and second year graduate students, and practicing engineers
Download or read book Viscoelastic Solids 1998 written by Roderic S. Lakes and published by CRC Press. This book was released on 2017-11-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Viscoelastic Solids covers the mathematical theory of viscoelasticity and physical insights, causal mechanisms, and practical applications. The book: presents a development of the theory, addressing both transient and dynamic aspects as well as emphasizing linear viscoelasticity synthesizes the structure of the theory with the aim of developing physical insight illustrates the methods for the solution of stress analysis problems in viscoelastic objects explores experimental methods for the characterization of viscoelastic materials describes the phenomenology of viscoelasticity in a variety of materials, including polymers, metals, high damping alloys, rock, piezoelectric materials, cellular solids, dense composite materials, and biological materials analyzes high damping and extremely low damping provides the theory of viscoelastic composite materials, including examples of various types of structure and the relationships between structure and mechanical properties contains examples on the use of viscoelastic materials in preventing and alleviating human suffering Viscoelastic Solids also demonstrates the use of viscoelasticity for diverse applications, such as earplugs, gaskets, computer disks, satellite stability, medical diagnosis, injury prevention, vibration abatement, tire performance, sports, spacecraft explosions, and music.
