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General and Exact Theory of Waves in Finite Elastic Strain

Conference paper

Abstract

After the classical researches of Christoffel, Hugoniot, Hadamard, and Duhem on waves in elastic materials, it might seem that little remains to be learned. Such is not the case. As for most parts of mechanics, it has been necessary in the last decade to go over the matter again, not only so as to free the conceptual structure from lingering linearizing and to fix it more solidly in the common foundation of modern mechanics, but also so as to derive from it specific predictions satisfying modern needs for contact between theory and rationally conceived experiment. After reading the recent papers by Toupin & Bernstein [1961, 1] and by Hayes & Rivlin [1961, 2], I have seen that more can be learned than is there proved. In the present paper I follow Toupin & Bernstein’s approach to the general theory yet try to achieve the elegant and explicit directness of Ericksen’s earlier treatment of isotropic incompressible materials [1953]. At the same time, all the results of Hayes & Rivlin are obtained in shorter but more general form as immediate corollaries.

Keywords

Elastic Material Wave Speed Isotropic Material Hyperelastic Material Singular Surface 
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1965

Authors and Affiliations

  1. 1.The Johns Hopkins UniversityBaltimoreUSA

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