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Titlebook: Lectures on Viscoelasticity Theory; Allen C. Pipkin Book 19721st edition Springer-Verlag New York Inc. 1972 Mathematica.applied mathematic

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书目名称Lectures on Viscoelasticity Theory
编辑Allen C. Pipkin
视频video
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Lectures on Viscoelasticity Theory;  Allen C. Pipkin Book 19721st edition Springer-Verlag New York Inc. 1972 Mathematica.applied mathematic
描述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
出版日期Book 19721st edition
关键词Mathematica; applied mathematics; elasticity; mathematics; polymer; proof; rheology; theorem
版次1
doihttps://doi.org/10.1007/978-1-4615-9970-8
isbn_ebook978-1-4615-9970-8Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer-Verlag New York Inc. 1972
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发表于 2025-3-21 22:51:16 | 显示全部楼层
Relations Between Modulus and Compliance,ing that, given one response function in graphical or numerical form, graphs of all others can be sketched immediately with fair quantitative accuracy. More refined numerical techniques which can give arbitrarily accurate results are not discussed because they do not lead to any qualitative understanding of the situation.
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Thermal Effects,mean relaxation time of a material depends very strongly on the temperature. Generally, the higher the temperature is, the quicker the material relaxes or complies. This kind of temperature-dependence is, of course, absent from the theories that involve no relaxation time.
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Some One-Dimensional Dynamical Problems,e wish to illustrate that viscoelasticity problems can be analyzed to significant depth even if the basic response functions are given only graphically or numerically, in the form of data. Third, the mathematical techniques used in these problems are of interest in themselves because they find applications in many areas.
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Slow Viscoelastic Flow, nothing changes much in one relaxation time, but may be arbitrarily fast if by “fast” one means something to do with the Reynolds number. We discuss the nature of approximations based on this notion of slowness and show how to solve flow problems within this approximation scheme.
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Stress Analysis,We now consider some problems involving small, gradually changing deformations. The stresses and their changes over long periods are the matters of main interest. Deformations can also be of interest in themselves if the structure creeps, i.e., the deformation continues to change for a long time.
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