Stress and Riemannian Metrics in Nonlinear Elasticity

@inproceedings{Marsden1984StressAR,
  title={Stress and Riemannian Metrics in Nonlinear Elasticity},
  author={J. Marsden},
  year={1984}
}
  • J. Marsden
  • Published 1984
  • Mathematics
  • In Doyle and Ericksen [1956, p. 77] it is observed that the Cauchy stress tensor σ can be derived by varying the internal energy e with respect to the Riemannian metric on space: σab = 2pбe/σgab Their formula has gone virtually unnoticed in the elasticity literature. In this lecture we shall explain some of the reasons why this formula is, in fact, of fundamental significance. Some additional reasons for its importance follow. First of all, it allows for a rational derivation of the Duhamel… CONTINUE READING
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