Stress analysis in visco-elastic bodies
Author:
E. H. Lee
Journal:
Quart. Appl. Math. 13 (1955), 183-190
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/69741
MathSciNet review:
69741
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Abstract: The analysis of stress and strain in linear visco-elastic bodies is considered when the loading is quasi-static so that inertia forces due to the deformation are negligible. It is shown that removal of the time variable by applying the Laplace transform enables the solution to be obtained in terms of an associated elastic problem. Thus the extensive literature in the theory of elasticity can be utilized in visco-elastic analysis. The operation of the transform on the prescribed boundary tractions and displacements and body forces may completely modify the spatial distribution in the associated problem. For proportional loading, in which the space and time variations of the prescribed quantities separate, the spatial distribution is maintained in the associated problem. A convenient method of treating a common case of non-proportional loading, moving surface tractions, is demonstrated. This work is compared with related approaches to this problem in the literature of visco-elastic stress analysis.
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T. Alfrey, Mechanical behavior of high polymers, Interscience, New York, 1948.
W. T. Read, Stress analysis for compressible visco-elastic materials, J. Appl. Phys. 21, 671-674 (1950).
H. S. Tsien, A generalization of Alfrey’s theorem for visco-elastic media, Quart. Appl. Math. 8, 104-106 (1950).
E. Volterra, On elastic continua with hereditary characteristics, J. Appl. Mechanics 18, 273-279 (1951).
H. S. Carslaw and J. C. Jaeger, Operational methods in applied mathematics, 1st ed. Oxford University Press, 1941.
S. Timoshenko, Theory of elasticity, 1st ed., McGraw-Hill, New York, 1934.
T. Alfrey, Non-homogeneous stresses in visco-elastic media, Quart, Appl. Math. 2, 113-119 (1944).
H. Jeffreys, On plasticity and creep in solids, Proc. Roy. Soc. 138A, 283-297 (1932).
R. D. Mindlin, A mathematical theory of photo-visco-elasticity, J. Appl. Phys. 20, 206-216 (1949).
D. Graffi, Su alcune questioni di elasticità ereditaria, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Nat. (8) 10, 25-30 (1951).
D. Graffi, Sulla teoria dei materiali elastico-viscosi, Atti Accad. Ligure 9 (1952); 77–83 (1953).
Oestreicher, Field and impedance of an oscillating sphere in a visco-elastic medium with an application to biophysics, J. Acous. Soc. Amer. 23, 707-714, 1951.
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Article copyright:
© Copyright 1955
American Mathematical Society
