Boundary Value Problems in Linear Viscoelasticity - Golden, John M.

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Résumé :
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.

Sommaire:
1. Fundamental Relationships.- 2. General Theorems and Methods of Solution of Boundary Value Problems.- 3. Plane Non-inertial Contact Problems.- 4. Plane Non-inertial Crack Problems.- 5. Three-dimensional Contact Problems.- 6. Thermoviscoelastic Boundary Value Problems.- 7. Plane Inertial Problems.- Appendix I Tables of Relevant Integrals and Other Formulae.- Table A1.1 Hilbert Transforms on [-1, 1].- Table A1.3 Miscellaneous Integrals Associated with Hilbert Transforms.- Table A1.4 Other Miscellaneous Integrals and Relationships.- Appendix II Boundary Value Problems for Analytic Functions.- A2.1 Some Properties of Analytic Functions.- A2.1.1 The Principle Value of a Singular Integral.- A2.1.2 Analytic Continuation.- A2.1.3 Liouville's Theorem.- A2.1.4 Singularities.- A2.1.5 Branch Points.- A2.2 Cauchy Integrals.- A2.3 The Hilbert Problem with Constant Coefficient.- A2.4 The Hilbert Transform.- Appendix III Fourier Transforms.- A3.1 Definition and Basic Properties.- A3.2 Analytic Properties of Fourier Integrals.- Appendix IV Non-singular Integral Equations.- A4.1 Fredholm Equations.- A4.2 Volterra Equations.- References.