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Synopsis
Three decades of research on viscoelastic boundary problems, mainly with moving boundary regions, are drawn together here into a systematic and unified text including many new results and techniques. The book is oriented towards applied mathematics, though with the ultimate aim of addressing a wide readership of engineers and scientists using or studying polymers and other viscoelastic materials. Physical phenomena are carefully described and the book may serve as a reference work on such topics as hysteretic friction and impact problems. Isothermal, non-inerital problems are treated in a systematic, unified manner relying ultimately on a fundamental decomposition of hereditary integrals. Relevant background topics like viscoelastic functions, constitutive and dynamical equations and the correspondence principle and its extensions are discussed. General techniques, based on these extensions, are then developed for solving non-inertial isothermal problems, a method for handling non-isothermal problems. Plane contact problems and crack problems are considered, including extension criteria, and also the behaviour of cracks in a field of bending. The viscoelastic Hertz problem and its application to impact problems are treated. There is discussion of the steady-state normal contact problem under a periodic load, and of the phenomenon of hysteretic friction.
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- PublisherSpringer
- Publication date2013
- ISBN 10 3662061589
- ISBN 13 9783662061589
- BindingPaperback
- LanguageEnglish
- Number of pages280
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Boundary Value Problems in Linear Viscoelasticity
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ISBN 10: 3662061589
ISBN 13: 9783662061589
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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). 284 pp. Englisch. Seller Inventory # 9783662061589
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Boundary Value Problems in Linear Viscoelasticity
Published by
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ISBN 10: 3662061589
ISBN 13: 9783662061589
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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). Seller Inventory # 9783662061589
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Boundary Value Problems in Linear Viscoelasticity
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