Dynamics of chains with non-monotone stress-strain relations. I. Model and numerical experiments

We discuss dynamic processes in materials with non-monotonic constitutive relations. We introduce a model of a chain of masses joined by springs with a non-monotone strain-stress relation. Numerical experiments are conducted to find the dynamics of that chain under slow external excitation. We find that the dynamics leads either to a vibrating steady state (twinkling phase) with radiation of energy, or (if dissipation is introduced) to a hysteresis, rather than to an unique stress-strain dependence that would correspond to the energy minimization.