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Journal Articles Wave Motion Year : 2017

Analytical solution to the 1D nonlinear elastodynamics with general constitutive laws

Abstract

Under the hypothesis of small deformations, the equations of 1D elastodynamics write as a 2 × 2 hyperbolic system of conservation laws. Here, we study the Riemann problem for convex and nonconvex constitutive laws. In the convex case, the solution can include shock waves or rarefaction waves. In the nonconvex case, compound waves must also be considered. In both convex and nonconvex cases, a new existence criterion for the initial velocity jump is obtained. Also, admissibility regions are determined. Lastly, analytical solutions are completely detailed for various constitutive laws (hyperbola, tanh and polynomial), and reference test cases are proposed.
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Dates and versions

hal-01350116 , version 1 (07-08-2016)

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H Berjamin, Bruno Lombard, Guillaume Chiavassa, N Favrie. Analytical solution to the 1D nonlinear elastodynamics with general constitutive laws. Wave Motion, 2017, 74, pp.35-55. ⟨10.1016/j.wavemoti.2017.06.006⟩. ⟨hal-01350116⟩
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