✦ LIBER ✦

The existence of riemann invariants in the one-dimensional equations of the non-linear theory of elasticity

✍ Scribed by A.P. Chugainova

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 354 KB
Volume: 63
Category: Article
ISSN: 0021-8928
DOI: 10.1016/s0021-8928(99)00077-5

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✦ Synopsis

The conditions for the existence of Riemann invariants of a one-dimensional system of equations of the non-linear theory of elasticity are investigated. Haantjes' diagonalization criterion is used to determine the form of the elastic potential for which the system has six Riemann invariants or three Riemann invariants (for waves which propagate in one direction). In particular, it is shown that the Haantjes criterion is satisfied and there are three Riemann invariants in the case of the elastic potential for slightly-non-linear wealdy-anisotropic elastic media . A procedure for computing Riemann invariants is described. The Riemann invariants are computed approximately for a form of elastic potential which satisfies the Haantjes criterion.

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