Abstract
The behavior of viscoelastic materials in uni-axial stress closely resembles that of models built from discrete elastic and viscous elements. We shall see how such models can be used to describe viscoelastic materials and to establish their differential equations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.H. Lee: Viscoelastic Stress Analysis, in J.N. Goodier and N.J. Hoff (eds.) Structural Mechanics, Proceedings of the 1st Symposium on Naval Structural Mechanics, Stanford, 1958 ( London, Pergamon, 1960 ), pp. 456–482.
D.R. Bland: The Theory of Linear Viscoelasticity (London, Pergamon, 1960 ). ( Monograph on the subject contains many cases of stress analysis problems. )
R.M. Christensen: Theory of Viscoelasticity, an Introduction (New York, Academic Press, 1971 ). ( Another monograph, mathematically more demanding than the present book. )
J.M. Burgers: Mechanical Considerations, Model Systems, Phenomenological Theories, in Akademie van Wetenschappen, First Report on Viscosity and Plasticity (Amsterdam: 1935 ), pp. 21–33.
R.V. Churchill: Operational Mathematics (3rd ed.) ( New York, McGraw-Hill, 1972 ).
W.T. Thomson: Laplace Transformation (2nd ed.))(Englewood Cliffs, N.J., Prentice-Hall, 1960 ).
H.S. Carslaw and J.C. Jaeger: Operational Methods in Applied Mathematics (2nd ed.) (Oxford, Oxford University Press, 1947; also New York, Dover Publications, 1963 ).
E.J. Scott: Transform Calculus with an Introduction to Complex Variables ( New York, Harper and Row, 1955 ).
C.R. Wylie: Advanced Engineering Mathematics (2nd ed.))(New York, McGraw-Hill, 1960), Chap. 8.
E.J. Scott: Laplace Transformation, in W. Flügge (ed.), Handbook of Engineering Mechanics (New York, McGraw-Hill, 1962 ), Chap. 19.
G. Doetsch: Guide to the Application of the Laplace and Z-Transforms (2nd ed.))(New York, Van Nostrand, 1971 ).
A. Erdélyi, W. Magnus, F. Oberhettinger and F. Tricomi: Tables of Integral Transforms (New York, McGraw-Hill, 1954), Vol. 1, Chaps. 4 and 5.
G.A. Campbell and R.M. Foster: Fourier Integrals for Practical Applications (Princeton, N.J., D. Van Nostrand, 1948 ). ( With proper precautions, this table may be used for Laplace transforms. It is easy to use and contains much material. )
W. Magnus and F. Oberhettinger: Formeln und Sätze für die speziellen Funktionen der mathematischen Physik (Berlin, Springer-Verlag, 1943) pp. 122–136. (Part of a book containing much additional information about some of the exotic functions occurring as inverses of simple Laplace transforms.)
G. Doetsch: Tabellen zur Laplace-Transformation ( Berlin, Springer-Verlag, 1947 ).
H. Ramsey: Problems of Related Elastic and Viscoelastic Buckling in one and two Dimensions. Ph. D. Diss., Stanford, 1962.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1975 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Flügge, W. (1975). Viscoelastic Models. In: Viscoelasticity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02276-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-02276-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02278-8
Online ISBN: 978-3-662-02276-4
eBook Packages: Springer Book Archive