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Dynamics of chains with non-monotone stress-strain relations. II: Nonlinear waves and waves of phase transition. (English) Zbl 1005.74047
Summary: We investigate the dynamics of a one-dimensional mass-spring chain with non-monotone dependence of spring force vs. spring elongation. For this strongly nonlinear system, we find a family of exact solutions that represent nonlinear waves. We establish numerically that this system displays a dynamical phase transition from stationary phase (when all masses are at rest) to twinkling phase (when the masses oscillate in a wave motion). This transition has two fronts which propagate with different speeds. We study this phase transition analytically, and derive relations between its quantitative characteristics.

74N20 Dynamics of phase boundaries in solids
74J30 Nonlinear waves in solid mechanics
Full Text: DOI
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